不确定参数机构动力分析与动力可靠性优化
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摘要
本学位论文以随机或区间参数机构为研究对象,探索性地研究了当构件参数和外载荷为区间变量或随机变量时弹性机构的动力特性分析方法,动力响应分析和动力可靠性方法。主要内容如下：
1、随机参数齿轮-转子系统扭转振动的动力特性分析和区间参数平面弹性连杆的动力特性分析
应用拓广的随机因子法分析了物理参数和几何参数均为随机变量的齿轮-转子系统的时变固有频率。将系统的刚度矩阵和质量矩阵分解为具有相同随机因子的矩阵之和的形式,再由求解系统固有频率的瑞利商公式出发,将系统频率展成部分频率分量之和的形式,利用求解随机函数数字特征的代数综合法求解系统固有频率的数字特征。通过算例分析了随机参数对系统固有频率的影响,并验证了方法的可行、有效和正确性。应用区间因子法分析了具有区间参数弹性连杆机构的固有频率。将系统的刚度矩阵和质量矩阵分解为具有相同区间因子的矩阵之和的形式,然后利用区间因子法将区间变量表示为其区间因子和确定性量的乘积,再由求解系统固有频率的瑞利商公式出发,应用区间算法,推导出了系统固有频率上、下限与均值的计算表达式。通过算例,分析了机构物理参数和几何尺寸的不确定性对机构固有频率的影响。
2、随机参数时变齿轮副的动力响应分析和随机参数齿轮-转子系统的扭转振动分析
研究基于概率的齿轮副动力响应问题。考虑齿轮副的物理参数、几何参数和作用荷载幅值同时具有随机性和齿轮时变刚度时,从Duhamel积分关系式出发利用随机因子法导出齿轮副动力响应的数字特征计算表达式。通过算例考察齿轮副的物理参数、几何参数和作用荷载幅值的随机性对其动力响应的影响,研究结果表明：几何参数的随机性对系统位移响应的随机性影响较大,系统的时变刚度对系统响应有冲击作用。建立了考虑物理参数和几何参数均为随机变量的齿轮-转子扭转振动系统在随机荷载激励下的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的动力学方程转换为拟静力学控制方程。利用求解随机变量函数数字特征的矩法,导出了系统动态位移反应的均值和方差计算公式。通过算例得出了：系统的时变刚度对系统响应有冲击作用,系统的物理参数、几何参数和外荷载幅值的随机性对系统动力响应的影响不可忽略,其中几何参数的随机性对系统位移响应的随机性影响较大。
3、随机参数齿轮系统的非线性动力响应分析和基于可靠性的随机参数齿轮-转子系统的动态优化
建立了物理参数和几何参数均为随机变量,并考虑具有齿轮侧隙、轴承间隙、时变刚度、齿间摩擦力和静态传递误差的齿轮-转子系统非线性振动的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的非线性动力学方程转换为随机参数的拟静力学控制方程,然后利用求解随机变量函数数字特征的代数综合法和矩法,导出了系统动态位移响应的均值和均方差计算公式。分析了系统中的诸随机参数、间隙和摩擦系数对系统非线性动力响应的影响,并获得了一些有意义的结论。在考虑系统物理参数、几何参数和作用载荷同时具有随机性时,建立了以齿轮-转子系统的各参数为设计变量,以振动加速度的均方根值最小为目标函数,同时具有齿间振动应力、轴扭矩可靠性约束和齿轮静态约束的优化设计模型,并将其中的可靠性概率约束等价转换为对应的数字特征约束,利用遗传算法进行优化。算例表明：系统中参数的随机性对优化的结果影响不可忽视。
4、随机参数刚弹耦合平面连杆的动力分析和区间参数平面连杆机构的动力分析
建立了考虑物理参数、几何参数及荷载均为不确定变量的平面连杆机构的动力学方程,在建模中计入了刚弹耦合项和运动副的粘性摩擦。利用Newmark-β逐步积分法将此不确定参数机构系统的动力学方程转换为随机参数的拟静力控制方程。利用求解随机变量函数数字特征的矩法和代数综合法或区间算法,导出了机构动态弹性位移的均值和方差计算公式或区间上下限。通过算例考察了机构的杆长、截面半径、质量密度、弹性模量的不确定性,以及刚弹耦合项和运动副摩擦对机构动力响应的影响。
5、随机参数机构的动力可靠性分析
将一对啮合齿轮等效为单自由度随机振动系统,研究随机参数齿轮副在平稳随机激励下的动力可靠度的求解方法。从其平稳随机响应的表达式出发,同时考虑齿轮物理参数、几何尺寸的随机性,利用求解随机变量数字特征的矩法和代数综合法,导出随机参数齿轮副在平稳随机激励下位移及其导数响应的数字特征,再由动力可靠度的公式导出随机参数齿轮副动力可靠度的均值和方差的计算公式。通过与Monte Carlo方法结果的比较,验证文中方法的可行性和有效性。研究了随机参数弹性连杆机构在平稳随机激励下的动力响应分析。首先利用拓广的随机因子法,从求解系统固有频率的瑞利商公式出发,得出了物理参数和几何参数均为随机变量的弹性连杆的时变固有频率的均值和方差。然后再从动力平稳随机响应在频域上的表达式出发,利用求解随机变量函数的矩法和数字特征的代数综合法,计算出了随机参数弹性连杆机构在平稳随机激励下弹性位移和速度的均方值的均值、方差的表达式。再由动力可靠度的公式导出了其动力可靠度的均值和方差的计算公式。通过算例,分析了机构物理参数和几何尺寸的随机性对机构动力可靠度随机性的影响。
Mechanisms with random parameters or interval parameters is considered in this paper. The system dynamic characteristic, dynamic response and dynamic reliability are investigated in the scenario that physical parameters of system, geometric dimensions of components and applied loads are all random or interval variables. The main research works can be described as follows:
1. Dynamic characteristic analysis for torsional vibration of a gear-rotor system with random parameters and dynamic characteristics analysis of elastic linkage mechanism with interval parameters.
Firstly, based on the generalized random factor method, the time-variable natural frequencies were analyzed for the torsional vibration of a gear-rotor system with random physical and geometrical parameters. The stiffness and mass. matrices of the system were discomposed into a sum of matrices with same random factors, respectively. Based on the Rayleigh quotient formula, the natural frequencies of this system were represented as a sum of partial ones. And then the mathematic characteristics expressions of the natural frequencies were obtained by utilizing the algebra synthesis method for solving a random function. Finally, numerical examples showed that the influence of the randomness of the physical and geometrical parameters on the natural frequencies, and verified the feasibility of the proposed method. Secondly, based on the interval factor method, the analysis of system dynamic characteristic for interval elastic linkage mechanism is presented. The stiff and mass matrices of the system are discomposed into a sum of matrices with same interval factors, respectively. By using interval factor method, all of the interval parameters can be expressed as the products of two parts corresponding to the interval factors and deterministic value. Based on the Rayleigh's quotient formula, the computational expressions for the lower, upper bonds and mean value of system dynamic characteristic are developed using the interval operations. The effects of the uncertainty of the bar length and radius, mass density, and elastic modulus on mechanism dynamic characteristic are studied through an example.
2. Dynamic response of gear with random parameters and torsional vibration of Gear-Rotor with random parameters
Firstly, the dynamic response of gear based on probability is investigated. Considering the randomness of the system physical parameters, and the geometric dimensions parameters, as well as the randomness of the amplitude peak of applied load and the time-varying stiffness of gear pairs, the numerical characteristics of the system dynamic response are formulated from the dynamic expression of Duhamel integral by the random factor method. The influences of the randomness of physical parameters and geometric dimensions parameters on the randomness of the mean square value of system displacement are inspected and some significant conclusions are obtained as follows:the randomness of geometric parameters have greater effected on displacement response of system and the time-varying stiffness of system have impacted on the response of system through the example. Secondly, the vibration equations of torsional vibration of Gear-Rotor with random physical parameters and geometrical parameters under random excitation were established. Dynamic equations with random parameters and time-varying stiffness were reformulated as static governing equations by using the Newmark-βstep-by-step integration method. Considering system parameters and force as inhomogeneous random parameters, the mean value and the variance of dynamic displacement response were calculated by moment method for solving the characteristic of a function with random variable. It can be shown from the numerical examples that the time-varying stiffness of system have impacted on the response of system, the influences of the randomness of physical parameters, geometrical parameters and the amplitude of loads on system dynamic response can not be ignored, and the randomness of geometric parameters have greater effected on displacement response of system.
3. Nonlinear dynamic analysis of response of gear-rotor with random parameters and dynamic response optimization for gear-rotor with random parameters based on reliability.
Firstly, the nonlinear dynamical model of gear-rotor is established, where the random physical and geometrical parameters, the backlash, the time-varying stiffness, and the friction between teeth and the static transmission error are all included. Nonlinear dynamic equations are transformed into static governing equations by exploiting the Newmark-βstep-by-step integration method. The mean value and the variance of dynamic displacement response are calculated by algebra synthesis method and moment method for obtaining the numerical characteristics of a function with random variables. The influences of the randomness of physical parameters, geometrical parameters, the backlash and the friction coefficient on system dynamic response are studied through an example and some useful conclusions are obtained. Secondly, the randomness of the physical parameters, geometrical parameters and the stochastic loads applied Gear-Rotor with random parameters is considered. In this case, the various parameters of the system are regarded as the design variables, the root of stochastic vibration acceleration minimum is considered as the objective function with the reliability constraints of dynamic stress between teeth of gear and bearing torque and gear static constraint. Genetic algorithm is applied, where constraints based on reliability probability are converted to equivalent constraints based on corresponding numerical characteristics. Example shows that the randomness of the parameters of system can not be neglected.
4. Dynamic response of rigid-elastic coupling linkage mechanism with uncertain parameters.
The vibration equations of rigid-elastic coupling linkage mechanism with random or interval physical and geometrical parameters are established by incorporating random or interval excitation into the equations. Dynamic equations with random or interval parameters are transformed into static governing equations by the Newmark-βstep-by-step integration method. The mean value and variance or the upper and lower limit of dynamic displacement response are calculated by algebra synthesis method.and moment method or interval algorithm. The influences of the uncertainty of the bar length and radius, mass density, and elastic modulus on mechanism dynamic response are studied through an example and some useful conclusions are obtained.
5. Dynamic reliability analysis of gear with stochastic parameters under stationary random excitation and dynamic reliability analysis of elastic linkage mechanism with stochastic parameters under stationary random excitation.
Firstly, a method for calculating dynamic reliability of gear with stochastic parameters stationary random excitation is proposed under the condition of single degree random vibration. Considering the randomness of the structural physical parameters and the geometric dimensions parameters, the mean value and the variance of the mean square value of the structural displacement and stationary random excitation are computed firstly from the expressions of system stationary response in frequency domain by utilizing the random variable's functional moment method and the algebra synthesis method. And then the expressions of the mean value and the variance of stochastic gear dynamic reliability are deduced from the Poisson formula for calculating dynamic reliability. Finally, the influence of the randomness of system physical and geometric dimensions parameters on the system dynamic reliability is analyzed through comparing with the Monte Carlo method, validating the feasibility of this method. Secondly, the stationary random vibration analysis of elastic linkage mechanism with random with random parameters was investigated. Firstly, based on the Rayleigh quotient formula, the expressions of the mean value and the variance of the time-variable natural frequencies of elastic linkage mechanism with random physical and geometrical parameters were formulated by using the generalized random factor method. From the expression of dynamic stationary random response of the frequency domain, the computational expressions of the mean value, variance and variation coefficient of the mean square value of elastic displacement and velocity responses under the stationary random excitation were developed by means of the random variable's functional moment method and the algebra synthesis method. And then the expressions of the mean value and the variance of system dynamic reliability are deduced from the Poisson formula of calculating dynamic reliability. Finally, the influence of the random of mechanism physical and geometric dimensions parameters on the system dynamic reliability is analyzed through the examples, validating the feasibility of this method.
1、随机参数齿轮-转子系统扭转振动的动力特性分析和区间参数平面弹性连杆的动力特性分析
应用拓广的随机因子法分析了物理参数和几何参数均为随机变量的齿轮-转子系统的时变固有频率。将系统的刚度矩阵和质量矩阵分解为具有相同随机因子的矩阵之和的形式,再由求解系统固有频率的瑞利商公式出发,将系统频率展成部分频率分量之和的形式,利用求解随机函数数字特征的代数综合法求解系统固有频率的数字特征。通过算例分析了随机参数对系统固有频率的影响,并验证了方法的可行、有效和正确性。应用区间因子法分析了具有区间参数弹性连杆机构的固有频率。将系统的刚度矩阵和质量矩阵分解为具有相同区间因子的矩阵之和的形式,然后利用区间因子法将区间变量表示为其区间因子和确定性量的乘积,再由求解系统固有频率的瑞利商公式出发,应用区间算法,推导出了系统固有频率上、下限与均值的计算表达式。通过算例,分析了机构物理参数和几何尺寸的不确定性对机构固有频率的影响。
2、随机参数时变齿轮副的动力响应分析和随机参数齿轮-转子系统的扭转振动分析
研究基于概率的齿轮副动力响应问题。考虑齿轮副的物理参数、几何参数和作用荷载幅值同时具有随机性和齿轮时变刚度时,从Duhamel积分关系式出发利用随机因子法导出齿轮副动力响应的数字特征计算表达式。通过算例考察齿轮副的物理参数、几何参数和作用荷载幅值的随机性对其动力响应的影响,研究结果表明：几何参数的随机性对系统位移响应的随机性影响较大,系统的时变刚度对系统响应有冲击作用。建立了考虑物理参数和几何参数均为随机变量的齿轮-转子扭转振动系统在随机荷载激励下的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的动力学方程转换为拟静力学控制方程。利用求解随机变量函数数字特征的矩法,导出了系统动态位移反应的均值和方差计算公式。通过算例得出了：系统的时变刚度对系统响应有冲击作用,系统的物理参数、几何参数和外荷载幅值的随机性对系统动力响应的影响不可忽略,其中几何参数的随机性对系统位移响应的随机性影响较大。
3、随机参数齿轮系统的非线性动力响应分析和基于可靠性的随机参数齿轮-转子系统的动态优化
建立了物理参数和几何参数均为随机变量,并考虑具有齿轮侧隙、轴承间隙、时变刚度、齿间摩擦力和静态传递误差的齿轮-转子系统非线性振动的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的非线性动力学方程转换为随机参数的拟静力学控制方程,然后利用求解随机变量函数数字特征的代数综合法和矩法,导出了系统动态位移响应的均值和均方差计算公式。分析了系统中的诸随机参数、间隙和摩擦系数对系统非线性动力响应的影响,并获得了一些有意义的结论。在考虑系统物理参数、几何参数和作用载荷同时具有随机性时,建立了以齿轮-转子系统的各参数为设计变量,以振动加速度的均方根值最小为目标函数,同时具有齿间振动应力、轴扭矩可靠性约束和齿轮静态约束的优化设计模型,并将其中的可靠性概率约束等价转换为对应的数字特征约束,利用遗传算法进行优化。算例表明：系统中参数的随机性对优化的结果影响不可忽视。
4、随机参数刚弹耦合平面连杆的动力分析和区间参数平面连杆机构的动力分析
建立了考虑物理参数、几何参数及荷载均为不确定变量的平面连杆机构的动力学方程,在建模中计入了刚弹耦合项和运动副的粘性摩擦。利用Newmark-β逐步积分法将此不确定参数机构系统的动力学方程转换为随机参数的拟静力控制方程。利用求解随机变量函数数字特征的矩法和代数综合法或区间算法,导出了机构动态弹性位移的均值和方差计算公式或区间上下限。通过算例考察了机构的杆长、截面半径、质量密度、弹性模量的不确定性,以及刚弹耦合项和运动副摩擦对机构动力响应的影响。
5、随机参数机构的动力可靠性分析
将一对啮合齿轮等效为单自由度随机振动系统,研究随机参数齿轮副在平稳随机激励下的动力可靠度的求解方法。从其平稳随机响应的表达式出发,同时考虑齿轮物理参数、几何尺寸的随机性,利用求解随机变量数字特征的矩法和代数综合法,导出随机参数齿轮副在平稳随机激励下位移及其导数响应的数字特征,再由动力可靠度的公式导出随机参数齿轮副动力可靠度的均值和方差的计算公式。通过与Monte Carlo方法结果的比较,验证文中方法的可行性和有效性。研究了随机参数弹性连杆机构在平稳随机激励下的动力响应分析。首先利用拓广的随机因子法,从求解系统固有频率的瑞利商公式出发,得出了物理参数和几何参数均为随机变量的弹性连杆的时变固有频率的均值和方差。然后再从动力平稳随机响应在频域上的表达式出发,利用求解随机变量函数的矩法和数字特征的代数综合法,计算出了随机参数弹性连杆机构在平稳随机激励下弹性位移和速度的均方值的均值、方差的表达式。再由动力可靠度的公式导出了其动力可靠度的均值和方差的计算公式。通过算例,分析了机构物理参数和几何尺寸的随机性对机构动力可靠度随机性的影响。
Mechanisms with random parameters or interval parameters is considered in this paper. The system dynamic characteristic, dynamic response and dynamic reliability are investigated in the scenario that physical parameters of system, geometric dimensions of components and applied loads are all random or interval variables. The main research works can be described as follows:
1. Dynamic characteristic analysis for torsional vibration of a gear-rotor system with random parameters and dynamic characteristics analysis of elastic linkage mechanism with interval parameters.
Firstly, based on the generalized random factor method, the time-variable natural frequencies were analyzed for the torsional vibration of a gear-rotor system with random physical and geometrical parameters. The stiffness and mass. matrices of the system were discomposed into a sum of matrices with same random factors, respectively. Based on the Rayleigh quotient formula, the natural frequencies of this system were represented as a sum of partial ones. And then the mathematic characteristics expressions of the natural frequencies were obtained by utilizing the algebra synthesis method for solving a random function. Finally, numerical examples showed that the influence of the randomness of the physical and geometrical parameters on the natural frequencies, and verified the feasibility of the proposed method. Secondly, based on the interval factor method, the analysis of system dynamic characteristic for interval elastic linkage mechanism is presented. The stiff and mass matrices of the system are discomposed into a sum of matrices with same interval factors, respectively. By using interval factor method, all of the interval parameters can be expressed as the products of two parts corresponding to the interval factors and deterministic value. Based on the Rayleigh's quotient formula, the computational expressions for the lower, upper bonds and mean value of system dynamic characteristic are developed using the interval operations. The effects of the uncertainty of the bar length and radius, mass density, and elastic modulus on mechanism dynamic characteristic are studied through an example.
2. Dynamic response of gear with random parameters and torsional vibration of Gear-Rotor with random parameters
Firstly, the dynamic response of gear based on probability is investigated. Considering the randomness of the system physical parameters, and the geometric dimensions parameters, as well as the randomness of the amplitude peak of applied load and the time-varying stiffness of gear pairs, the numerical characteristics of the system dynamic response are formulated from the dynamic expression of Duhamel integral by the random factor method. The influences of the randomness of physical parameters and geometric dimensions parameters on the randomness of the mean square value of system displacement are inspected and some significant conclusions are obtained as follows:the randomness of geometric parameters have greater effected on displacement response of system and the time-varying stiffness of system have impacted on the response of system through the example. Secondly, the vibration equations of torsional vibration of Gear-Rotor with random physical parameters and geometrical parameters under random excitation were established. Dynamic equations with random parameters and time-varying stiffness were reformulated as static governing equations by using the Newmark-βstep-by-step integration method. Considering system parameters and force as inhomogeneous random parameters, the mean value and the variance of dynamic displacement response were calculated by moment method for solving the characteristic of a function with random variable. It can be shown from the numerical examples that the time-varying stiffness of system have impacted on the response of system, the influences of the randomness of physical parameters, geometrical parameters and the amplitude of loads on system dynamic response can not be ignored, and the randomness of geometric parameters have greater effected on displacement response of system.
3. Nonlinear dynamic analysis of response of gear-rotor with random parameters and dynamic response optimization for gear-rotor with random parameters based on reliability.
Firstly, the nonlinear dynamical model of gear-rotor is established, where the random physical and geometrical parameters, the backlash, the time-varying stiffness, and the friction between teeth and the static transmission error are all included. Nonlinear dynamic equations are transformed into static governing equations by exploiting the Newmark-βstep-by-step integration method. The mean value and the variance of dynamic displacement response are calculated by algebra synthesis method and moment method for obtaining the numerical characteristics of a function with random variables. The influences of the randomness of physical parameters, geometrical parameters, the backlash and the friction coefficient on system dynamic response are studied through an example and some useful conclusions are obtained. Secondly, the randomness of the physical parameters, geometrical parameters and the stochastic loads applied Gear-Rotor with random parameters is considered. In this case, the various parameters of the system are regarded as the design variables, the root of stochastic vibration acceleration minimum is considered as the objective function with the reliability constraints of dynamic stress between teeth of gear and bearing torque and gear static constraint. Genetic algorithm is applied, where constraints based on reliability probability are converted to equivalent constraints based on corresponding numerical characteristics. Example shows that the randomness of the parameters of system can not be neglected.
4. Dynamic response of rigid-elastic coupling linkage mechanism with uncertain parameters.
The vibration equations of rigid-elastic coupling linkage mechanism with random or interval physical and geometrical parameters are established by incorporating random or interval excitation into the equations. Dynamic equations with random or interval parameters are transformed into static governing equations by the Newmark-βstep-by-step integration method. The mean value and variance or the upper and lower limit of dynamic displacement response are calculated by algebra synthesis method.and moment method or interval algorithm. The influences of the uncertainty of the bar length and radius, mass density, and elastic modulus on mechanism dynamic response are studied through an example and some useful conclusions are obtained.
5. Dynamic reliability analysis of gear with stochastic parameters under stationary random excitation and dynamic reliability analysis of elastic linkage mechanism with stochastic parameters under stationary random excitation.
Firstly, a method for calculating dynamic reliability of gear with stochastic parameters stationary random excitation is proposed under the condition of single degree random vibration. Considering the randomness of the structural physical parameters and the geometric dimensions parameters, the mean value and the variance of the mean square value of the structural displacement and stationary random excitation are computed firstly from the expressions of system stationary response in frequency domain by utilizing the random variable's functional moment method and the algebra synthesis method. And then the expressions of the mean value and the variance of stochastic gear dynamic reliability are deduced from the Poisson formula for calculating dynamic reliability. Finally, the influence of the randomness of system physical and geometric dimensions parameters on the system dynamic reliability is analyzed through comparing with the Monte Carlo method, validating the feasibility of this method. Secondly, the stationary random vibration analysis of elastic linkage mechanism with random with random parameters was investigated. Firstly, based on the Rayleigh quotient formula, the expressions of the mean value and the variance of the time-variable natural frequencies of elastic linkage mechanism with random physical and geometrical parameters were formulated by using the generalized random factor method. From the expression of dynamic stationary random response of the frequency domain, the computational expressions of the mean value, variance and variation coefficient of the mean square value of elastic displacement and velocity responses under the stationary random excitation were developed by means of the random variable's functional moment method and the algebra synthesis method. And then the expressions of the mean value and the variance of system dynamic reliability are deduced from the Poisson formula of calculating dynamic reliability. Finally, the influence of the random of mechanism physical and geometric dimensions parameters on the system dynamic reliability is analyzed through the examples, validating the feasibility of this method.
引文
[1]Schweppe F C. Uncertain dynamics systems[C]. Prentice-Hall, Englewood Cliffs, N. J., 1973.
[2]Ibrahim R.A. Structural dynamics with parameter uncertainties [J]. Applied Mechanics, Reviews,1987,40(3):309-328.
[3]张圣坤.不确定问题的有限元方法及应用[J].固体力学学报,1987,3：277-281.
[4]李杰.结构动力分析的若干发展趋势[J].世界地震工程,1993,(2)：1-8.
[5]李杰.随机结构系统分析与建模[M].第一版.北京：科学出版社,1996.
[6]王光远.论不确定性结构力学的进展[J].力学进展,2002,32(2)：205-211.
[7]邱志平.不确定参数结构静力响应和特征值问题的区间分析方法[D].吉林工业大学博士论文,1994.
[8]郭书祥,吕震宙.区间运算和静力区间有限元[J].应用数学和力学,2001,22(12)：1249-1254.
[9]Chen J J, Che J W, Sun H A, et al. Probabilistic dynamic analysis of truss structures[J]. Structural-Engineering & Mechanics,2002,13(2):231-239.
[10]Dai J, Chen J J, Li Y G. Dynamic response optimization design for engineering structures based on reliability [J]. Applied Mathematics and Mechanics,2003,24(1):43-52.
[11]胡太彬,陈建军,徐亚兰.随机参数平面刚架结构频率特性分析的随机因子法[J].机械强度,2006,28(2)：196-200.
[12]胡太斌.随机结构动力分析与动力可靠性优化设计[D].西安电子科技大学博士学位论文,2005.
[13]Gao W, Chen J J, Ma H B. Dynamic response analysis of closed loop control system for intelligent truss structures based on probability[J]. Structural Engineering & Mechanics,2003, 15(2):239-248.
[14]高伟,陈建军等.随机钢架结构在平稳随机激励下的动力响应分析[J].振动与冲击,2004,23(2)：88-91.
[15]张策.机械动力学[M].第二版.北京：高等教育出版社,2008.
[16]Erdman A G, Sandor G N. Kineto-elstodynamnic:a review of the state-of-the art and trends[J]. Mechanism and Machine Theory,1972,7(1):19-33.
[17]Hrones J A. Analysis of dynamic force in a cam-driven system[J]. Trans. ASME,1948,70(5): 473-482.
[18]Mitchell D B. Test on dynamic response of cam follower systems. Mechanical. Engineering, 1950,72(6):467-471.
[19]Sunada W, Dubowsky S. On the dynamic analysis and behavior of industrial robotic manipulators with elastic members [J]. AMSE Journal of Mechanisms, Transmissions, and Automation Design,1983,105(1):42-51.
[20]张策,王玉新,杨玉虎,陆锡年.机构动力学最新发展动态综述[J].唐山工程技术学院学报,1993,15(2)：34-43.
[21]李润方,王建军.齿轮系统动力学—振动、冲击、噪声[M].第1版.北京：科学出版社,1997.
[22]张义民,闻邦椿.齿轮的可靠性设计[J].传动技术.1997(2)：34-40.
[23]徐宏伟,成刚虎,黄玉美等.一种圆柱齿轮强度可靠性的现代设计方法[J].西安理工大学学报.2005,21(3)：268-271.
[24]魏任之,张永忠,史兴虹.关于直齿圆柱齿轮轮齿受载变形量的计算[J].机械传动,1980,4：1-8.
[25]张永忠,王洪.齿根动态应力分析[J].机械工程学报,1986,22(3)：58-65.
[26]Kahraman A, Singh R. Non-linear dynamic of a spur gear pair[J]. J Sound Vib,1990,142(1): 49-75.
[27]Nakamura K. Tooth separations and abnormal noise on power transmission gears[J]. Bull JSME,1967,10:846-854.
[28]Blankenship G W, Singh R. A new gear mesh interface dynamic model to predict multi-dimensional force coupling and excitation[J]. Mech Mach Theory,1995,30(1):43-57.
[29]Vaishya M, Houser R. Modeling and analysis of sliding friction in gear dynamics[C]. Proceedings of the 2000ASME Design Engineering Technical Conferences, Baltimore, USA: DETC2000/TG-14430,2000,601-610.
[30]孙月海,张策等.直齿圆柱齿轮传动系统振动的动力学模型[J].机械工程学报,2000,36(8)：47-50.
[31]Kahraman A. Dynamic analysis of a multi-mesh helical gear train[J]. ASME Mech Des,1994, 116:706-712.
[32]Rook T E, Singh R. Dynamic analysis of a rever-idler gear pair with concurrent clearances[J]. J Sound Vib,1995,182(2):303-322.
[33]Vinayak H, Singh R, Padmanabhan C. Linear dynamic analysis of multi-mesh transmissions containing external rigid gears[J]. J Sound Vib,1995,185(1):1-32.
[34]Benton M, Seireg A. Simulation of resonances and instability conditions in pinion-geared system[J]. ASME Mech Des,1978,100:26-32.
[35]Benton M, Seireg A. Factors influencing instability and resonance in geared systems[J]. ASME Mech Des,1981,103:372-378.
[36]Wang K L, Cheng H S. A numerical solution to the dynamiv load, film thickness, and surface temperatures inspur gears, part I analysis[J]. ASME Mech Des,1981,103:177-187.
[37]Kahraman A, Singh R. Interactions between time-varying mesh stiffness and clearance non-linearties in a geared system[J]. J Sound Vib,1991,146(1):135-156.
[38]Cai Y. Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (a new stiffness function of helical involute tooth pair) [J]. ASME Mech Des,1995,117:460-469.
[39]Kahraman A, Blankenship G W. Interactions between commensurate parametric and forcing excitations in a system with clearance[J]. J Sound Vib,1996,194 (3):317-336.
[40]Theodossiades S, Natsiavas S. Non-linear dynamics of gear-pair systems with periodic stiffness and backlash[J]. J Sound Vib,2000,229(2):287-310.
[41]Lee A S Ha J W, Choi D H. Coupled lateral and torsional vibration characteristics of a speed increasing geared rotor-bearing system[J]. Journal of Sound and Vibration,2003,263: 725-742.
[42]欧卫林,王三民,袁茹.齿轮耦合复杂转子系统弯扭耦合振动分析的轴单元法[J].航空动力学报,2005,20(3)：537-538.
[43]庞辉,方宗德,欧卫林.多平行齿轮耦合转子系统的振动特性分析[J].振动与冲击,2007,26(6)：21-25.
[44]方宗德,蒋孝煜,宋镜瀛.用状态空间方法的齿轮传动系统动态分析[J].清华大学学报,1987,5(27)：1-11.
[45]姚文席.渐开线直齿轮单级齿轮传动系统的振动[J].西安交通大学学报,1990,4(24)：39-49.
[46]唐增宝,钟毅芳.直齿圆柱齿轮传动系统的振动分析[J].机械工程学报,1992,28(4)：86-93.
[47]Cai Y. Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (A new stiffness function of helical involute tooth pair)[J]. ASME, Journal of Mechanical Design,1995,117(9):460-468.
[48]LIN Jian, Robert G. Parker. Mesh stiffness variation instabilities in two-stage gear systems[J]. Journal of Vibration and Acoustics,2002,124(1):68-76.
[49]张锁怀,沈允文,董海军等.齿轮时变系统对扭矩激励的响应[J].航空动力学报,2003,18(6)：737-743.
[50]A. Parey, Badaoui M El, Guillet F, Tandon N. Dynamic modelling of spur gear pair and application of empirical mode decomposition-based statistical analysis for early detection of localized tooth defect[J]. Journal of Sound and Vibration,2006,294(3):547-561.
[51]Vaishya M, Houser R. Modeling and analysis of sliding friction in gear dynamics[C]. Proceedings of the 2000ASME Design Engineering Technical Conferences, Baltimore, USA: DETC2000/TG-14430,2000,601-610.
[52]Grzegorz Litak, Michael I. Friswell. Dynamics of a gear system with faults in meshing stiffness[J]. Nonlinear Dynamic,2005,41(4):415-421.
[53]王三民,沈允文,董海军.多间隙耦合非线性动力系统的分叉与混沌[J].西北工业大学学报,2003,21(2)：191-194.
[54]Gang Liu, Robert G Parker. Nonlinear dynamics of idler gear systems[J]. Nonlinear dynamics, 2008,53(4):345-367.
[55]唐进元,陈思雨,钟掘.一种改进的齿轮非线性动力学模型[J].工程力学,2008,25(1)：217-223.
[56]Tobe, T., Sato, K., Takasu, N. Statistical analysis of dynamic loads on spur gear teeth[J]. Bull. of the JSME,1976,19(133):800-813.
[57]Tobe, T., Sato, K., Takasu, N. Statistical analysis of dynamic loads on spur gear teeth[J]. Bull. of the JSME,1977,20(148):1315-1328.
[58]Neriya, S., V., Bhat, R. B., Sankar, T. S. On the dynamic response of a helical geared system subjected to a static transmission error in the form of deterministic and filtered white noise inputs[J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design, Transactions of the ASME,1988,110(4):501-506.
[59]Y. Wang, W. J. Zhang. Modelling of gear stochastic vibration considering non-white noise errors[J]. Chinese science bulletin,1999,44(4):375-378.
[60]刘梦军,沈允文,董海军.随机外激励下齿轮非线性系统的全局分析[J].中国机械工程,2004,15(13)：1182-1185.
[61]孙宜强,温建明,冯奇.随机阻尼拍击振动的二级传动模型[J].力学季刊,2010,31(2)：243-249.
[62]卢剑伟,曾凡灵,杨汉生,刘梦军.随机装配侧隙对齿轮系统动力学特性的影响分析[J].机械工程学报,2010,46(21)：82-86.
[63]袁哲,孙志礼,李国权,牟峰.齿轮随机参数结构固有频率灵敏度分析[J].机械与电子,2009,12：16-17.
[64]张明辉,黄田.Diamond机构的弹性动力分析与实验研究[J].机械设计,2004,21(11)：6-8.
[65]Erdman A G, Imam I, Sandor G N. Applied koneto-elastodynamics:Proceedings of 2ed OSU applied mechanism conference. Oklahoma:Oklahoma State University,1971.
[66]Alexander, R. M., Lawrance, K. L.. Experimentally determined dynamic strains in an elastic mechanism[J]. ASME Journal of Engineering for Industry 102,1975,791-794.
[67]Stamps, F. R., Bagci, C.. Dynamics of planar, elastic, high speed mechanisms considering three dimensional offset geometry:Analytical and experimental investigations[J]. ASME Journal of Mechanisms Transmissions and Automation in Design 105,1983,498-510.
[68]张策,陈树勋等.弹性连杆机构的分析与设计[M].第2版.北京：机械工业出版社,1997.
[69]Imam I, Sandor G N, Kramer S N. Deflection and stress analysis of high-peed mechanisms with elastic links[J]. ASME Journal of Engineering for Industry,1973,95(2):541-548.
[70]Bahgat B M, Willmert K D. Finite element vibration analysis of planar mechanism[J]. Mechanism and Machine Theory,1976,11(1):47-71.
[71]Midha A, Erdman A G., Finite element approach to mathematical modeling of high-speed elastic linkages[J]. Mechanism and Machine Theory,1978,13(6):603-618.
[72]Wang Yuxin. Dynamics of an Elastic Four Bar Linkage Mechanism with Geometric Nonlinearities[J]. Nonlinear Dynamics,1997,14(4):357-375.
[73]Nath P K, Ghosh A. Steady state response of mechanism with elastic links by finite element method[J]. Mechanism and Machine Theory,1980,15(3):199-211.
[74]Turcic D A, Midha A. Generalized equations of motion for the dynamic analysis of elastic mechanism systems[J]. ASME Journal of Dynamic Systems Measurement and Control,1984, 106(4):243-248.
[75]Turcic D A, Midha A. Dynamic analysis of elastic mechanism system[J]. Part 1:Applications ASME Journal of Dynamic Systems Measurement and Control,1984,106(4):249-254.
[76]Cleghom W L, Fenton R G, Tabarrok B. Steady-state vibration response of high-speed mechanisms[J]. Mechanism and Machine Theory,1984,19(4-5):417-423.
[77]Lieh J. Dynamic modeling of a slider-crank mechanism with coupler and joint flexibility[J]. Mechanism and Machine Theory,1994,29(1):139-147.
[78]Fallahi B, Lai S, Venkat C. A finite element formulation of a flexible slider-crank mechanism using local coordinate[J]. ASME J of Dynamic Systems, Measurement & Control,1995, 117(3):329-338.
[79]Makwana K C, Cupta K N. On mathematical modeling for the elastic coupler response of a planar four-bar linkage with possible speed perturbation at crank[J]. Mechanism and Machine Theory,1998,33(8):1105-1115.
[80]Chen J S, Chian C H. Effects of crank length on the dynamic of a flexible connecting rods [J].ASME Journal of Vibration and Acoustics,2001,123(3):318-323.
[81]刘建琴,张策等.变长度曲柄-连杆机构的动力学分析[J].机械工程学报,2000,36(4)：41-44.
[82]陆念力,兰朋,金奕山.弹性连杆机构动力分析的一种新方法[J].中国机械工程学报,2003,1(1)：6-10.
[83]张利,黄文振,周志革.灵敏度方法在连杆机构动态响应重分析中的应用[J].上海交通大学学报,2000,34(3)：378-380.
[84]阎绍泽,季林红等.柔性机械系统动力学的变形耦合方法[J].机械工程学报,2001,37(8)：1-4.
[85]Ren Jiazhi, Yu Chongwen. Influence of Dropping scales of E7/6 Comber on Process Performance[J]. Journal of Donghua University,2005,22(2):23-25.
[86]刘善增,余跃庆等.3-RRC并联柔性机器人的动力学分析[J].振动与冲击,2008,27(2)：157-161.
[87]Liu Zhuyong, Hong Jiazhen, Liu Jinyang. Complete geometric nonlinear formulation for rigid-flexible coupling dynamics[J]. J. Cent. South Univ. Technol,2009,16(1):119-124.
[88]张劲夫,许庆余,张陵.具有粘性摩擦的弹性曲柄滑块机构的动力学建模及计算[J].西安交通大学学报,2000,34(11)：86-89.
[89]拓耀飞,陈建军,徐亚兰等.随机参数连杆机构的静动态运动精度可靠性分析[J].电子机械工程,2004,20(4)：4-8.
[90]陈建军,郜文文等.随机参数弹性连杆机构运动功能的可靠性分析[J].机械设计与研究,2006,22(3)：19-22.
[91]拓耀飞,陈建军,陈永琴.区间参数弹性连杆机构的非概率可靠性分析[J].中国机械工程第2007,18(5)：528-531.
[92]张义民.机械振动[M].北京：清华大学出版社,2007.
[93]刘德贵,费景高.动力学系统数字仿真算法[M].北京：科学出版社,2000.
[94]张铁,闫家斌.数值分析[M].北京：冶金工业出版社,2001.
[95]W. J. T. Daniel. The subcycled newmark algorithm [J]. Computational mechanics,1997,20(3): 272-281.
[96]W. Moser, H. Antes, G. Beer. A Duhamel integral based approach to one-dimensional wave propagation analysis in layered media[J]. Comput Mech,2005,35:115-126.
[97]黄文虎,邵成勋.多柔体系统动力学[M].北京：科学出版社,1996.
[98]张劲夫,贾丽俊,秦卫阳.柔性连杆机构动力学研究进展[J].机械科学与技术,2005,24(2)：199-203.
[99]Eduardo Bayo, Javier Garcia De Jalon, Miguel Angel Serna. A modified lagrangian formulation for the dynamic analysis of constrained mechanical systems [J]. Computer Methods in Applied Mechanics and Engineering,1988,71(2):183-195.
[100]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].西南交通大学博士学位论文,1996.
[101]Shinozuka M, Jan C M. Digtal simulation of random processes and its applications[J]. Journal of Sound and Vibration,1972,25(1):111-128.
[102]Shinozuka, M. Monte Carlo solution of structural dynamics[J]. Computer & Structures,1972, 2:855-874.
[103]Shinozuka M, Wen Y K. Monte Carlo simulation of nonlinear vibrations[J]. AIAA J,1972, 10(1):37-40.
[104]赵雷,陈虬.结构随机分析的Monte Carlo加权残值法[J].计算结构力学及其应用,1996,13(2)：193-200.
[105]Kaminski M. Monte-Carlo simulation of effective conductive for fiber composites[J]. Int. Communications in Heat and Mass Transfer,1999,26(6):801-810.
[106]Bellman R. On the foundations of a theory stochastic variational processes[J]. In:Proc of Symposium on Applied Mathematics,1962,13:275-286.
[107]Hien T D, Kleiber M. Finite element analysis based on stochastic Hamilton variational principle[J]. Computer & Structures,1990,37(6):893-902.
[108]Liu W K, et al. Probabilistic finite element methods in nonlinear dynamics[J]. Compt Meth Appl Mech Eng.,1986,56(1):61-81.
[109]Lee X X. Double random vibration of nonlinear systems[C]. In:Proc Int Conf on Computational Stochastic Mechanics, Corfu, Greeze, Sept,1991.
[110]陈塑衰.随机参数结构的振动理论[M].长春：吉林科学技术出版社,1992.
[111]陈虬,尹志远.随机结构动力分析的随机有限元法[J].西南交通大学学报,1994,29(5)：477-481.
[112]Yamazaki F. Neumann expansion for stochastic finite element analysis[J]. J Eng Mech. ASCE, 1988,114(8):1335-1354
[113]赵雷,陈虬.随机有限元动力分析方法的研究进展[J].力学进展,1999,29(1)：9-18.
[114]Sun T C. A finite element method for random differential equations with random coefficients[J]. Int J Number Analysis,1979,16(6):1019-1035.
[115]Iwan W D, Jensen H. On the dynamic response of continuous systems including model uncertainty[J]. JAppl Mech, ASME,1993,60(2):484-490.
[116]Ghanem R, Spanos P D. Spectral stochastic finite element formulation for realiability analysis[J]. J Eng. Mech, ASCE,1991,117(10):2351-2372.
[117]李杰.随机结构动力分析的扩阶系统方法[J].工程力学,1996,13(1)：93-102.
[118]李杰.复合随机振动分析的扩阶系统方法[J].力学学报,1996,28(1)：66-75.
[119]李杰,魏星.随机结构动力分析的递归聚缩算法[J].固体力学学报,1996,17(3)：263-267.
[120]李杰,陈建兵.随机结构反应的概率密度演化分析[J].同济大学学报(自然科学版),2003,31(12)：1387-1391.
[121]李杰,陈建兵.随机结构动力反应分析的概率密度演化方法[J].力学学报,2003,35(4)：437-441.
[122]李杰,陈建兵.随机结构非线性动力响应的概率密度演化分析[J].力学学报,2003,35(6)：716-722.
[123]陈建兵,李杰.随机结构复合随机振动分析的概率密度演化方法[J].工程力学,2004,21(3)：90-95.
[124]易平,林家浩,赵岩.线性随机结构的非平稳随机响应变异性分析[J].固体力学学报,2002,23(1)：93-97.
[125]高伟,陈建军,刘伟.随机参数智能桁架结构动力特性分析[J].应用力学学报,2003,20(1)：123-127.
[126]陈建军,黄居锋,赵颖颖.随机参数链式结构系统的动力特性分析[J].中国机械工程,2005,16(1)：16-19.
[127]陈建军,黄居锋等.随机参数轴盘扭转结构系统动力特性优化[J].机械工程学报,2005,41(8)：180-184.
[128]王小兵,陈建军,李金平,刘国梁.基于随机因子法的随机结构动力特性分析研究[J].振动与冲击,2008,27(2)：4-8.
[129]戴君,陈建军,马洪波,等.随机参数结构在随机荷载激励下的动力响应分析[J].工程力学,2002,19(3)：64-68.
[130]Gao W., Chen J. J., Ma H. B. Dynamic response analysis of closed loop control system for intelligent truss structures based on probability[J]. Structural Engineering & Mechanics,2003, 15(2):239-248.
[131]高伟,陈建军,刘伟,马洪波,马孝松.随机参数智能桁架结构在随机力下的闭环控制动力响应分析[J].机械科学与技术,2002,21(6)：909-912.
[132]陈建军,王小兵.随机参数智能板结构的动态特性分析[J].西安电子科技大学学报,2004,31(5)：661-665.
[133]陈龙,陈建军,赵岽,李金平.随机参数结构最优控制的闭环响应分析[J].振动与冲击,2010,29(1)：34-37.
[134]陈建军.机械与结构系统的可靠性[M].西安：西安电子科技大学出版社,1994.
[135]胡太彬,陈建军,王小兵.不均匀随机参数桁架结构的随机反应分析[J].工程力学,2007,24(2)：123-131.
[136]王登刚,李杰.计算具有区间参数结构特征值范围的一种新方法[J].计算力学学报,2004,21(1)：56-61.
[137]Moore RE. Interval Analysis[M]. New York:Prentice-Hall, Englewood cliffs,1966.
[138]陈塑寰,邱志平,宋大同等.区间矩阵标准特征值问题的一种解法[J].吉林工业大学学报,1993,23(3)：1-8,
[139]Qiu Z P, Wang X J, Friswell M I. Eigenvalue bounds of structures with uncertain-but-bounded parameters[J]. Journal of Sound and Vibration,2005,282(1/2):297-312.
[140]陈怀海,陈止想.求解实对称矩阵区间特征值问题的直接优化法[J].振动工程学报,2000,13(1)：117-121.
[141]Koylouglu H U, Cakmak A S, Nielsen SRK. Interval algebra to deal with pattern loading and structural uncertainties[J]. Journal of Engineering Mechanics,1995,121(11):1149-1157.
[142]Muhanna R L, Mullen R L. Uncertainty in mechanics problems-interval-based approach[J]. Journal of Engineering Mechanics,2001,127(3):557-566.
[143]吴晓,罗佑新,文会军,李敏.非确定结构系统区间分析的泛灰求解方法[J].计算力学学报,2003,20(3)：329-334.
[144]Chen S H, Lian H D, Yang X W. Interval displacement analysis for structures with interval parameters[J]. Int J Num Methods in Eng,2002,53(2):393-407.
[145]吴杰,陈塑寰.区间参数结构的动力响应优化[J].固体力学学报,2004,25(2)：186-189.
[]46]陈塑寰.结构动态设计的矩阵摄动理论[M].北京：科学出版社,1999.
[147]Hansen Eldon. Global Optimization Using Interval Analysis[C]. New York:Marcel Dekker Inc,1992.
[148]王登刚.计算具有区间参数结构的固有频率的优化方法[J].力学学报,2004,36(3)：364-372.
[149]Ma Juan, Chen Jian-jun, Zhang Jian-guo, Jiang Tao. Interval factor method for interval finite element analysis of truss[J]. Journal Multidiscipline Modeling in Materials and Structures, 2005,1(4):367-376.
[150]王芳林,高伟.区间桁架结构动力特性分析的区间因子法[J].应用力学学报,2007,24(3)：477-481.
[151]林立广,陈建军,马娟等.基于区间因子法的不确定桁架结构动力响应分析[J].应用力 学学报,2008,25(4)：612-616.
[152]李桂青,李秋胜.工程结构时变可靠度理论及其应用[M].北京：科学出版社,2001.
[153]Rice S O. Mathematical Analysis of Random Noise[J]. Bell System Technical Journal,1944, 23:282-332.
[154]Sieget A J. K, Darling, D. A. The first passage problem for a continuous Markov process[J]. Annal of mathematics statistics,1953,24:624.
[155]Helmstrom C W. Note on a Markov a Envelop Process. Institute of Radio Engineers, Transaction on Information Theory, IT-5,1959,139-140.
[156]Coleman J J. Reliability of Aircraft Structures in Resisting Chance Failure Operations. Res, 1959,7(5):639-645.
[157]Miles J. W. On structural Fatigue under random loading[J]. Journal of Aero Science,1954,21: 753-768.
[158]Shinozuka M. Probability of structural failure under random loading[J]. EM. ASSCE,1964 Vol.90.
[159]Shinozuka M, Yao J T P. On the two-sided time dependent barrier problem. Columbia Univinst Study of Fatigue and Reliability, Tech. Rept.21, June,1965
[160]lyenger R N. First passage probability during random vibration[J]. Journal of Sound and Vibration,1973,31(2):185-193.
[161]Roberts J B. Structural fatigue under nonstationary random loading[J], Journal of Mechanical Engineering Science,1966,8(4):392-405.
[162]Gasparini D A. Response of MDOF systems to nonstationary random excitation[J]. Journal of the Engineering Mechanics Division,1979,105(1):13-27.
[163]Iwan W D, Spanos P T. Response envelope statistics for nonlinear oscillators with random excitation. Journal of Applied Mechanics,1978,45(1):170-174.
[164]Iwan W D, Gates N C. Estimations earthquake response of simple hysteretic structures[J]. Journal of Applied Mechanics,1979,105(3),391-405.
[165]刘锡荟.现行规范抗震设计方法安全度的评价及工程参数的确定[J].地震工程与工程振动,1982,2(1)：21-32.
[166]尹之潜,李树帧.结构抗震的可靠度与位移控制设计[J].地震工程与工程振动,1982,2(2)：45-55.
[167]李桂青,曹宏.动力可靠性述评[J].地震工程与工程震动,1983,3(3)：42-61.
[168]欧进萍,干光远.基于模糊破坏准则的抗震结构动力可靠性分析[J].地震工程与工程振动,1986,5(1)：1-11.
[169]朱位秋.随机振动[M].第一版.北京：科学出版社,1992.
[170]李桂青,曹宏,李秋胜,霍达.结构动力可靠性理论及其应用[M].北京：地震出版社,1993.
[171]管昌生,张鹏,刘增夕,李桂青,李国发.时变结构动力可靠性分析的包络过程法[J].广西工学院学报,1995,6(3)：25-30.
[172]李创第,李桂青,黄任常.连续随机结构的动力反应和可靠性分析[J].广西工学院学报,1997,8(1)：25-31.
[173]Chen J J, Duan B Y & Zen Y G.. Study on dynamic reliability analysis of the structures with multidegree-of-freedom system [J]. Computers & Structures,1997,62(5):877-881.
[174]石少卿,姜节胜.非平稳随机激励作用下多自由度体系系统动力可靠性研究[J].应用力 学学报.1999,16(4)：73-77.
[175]郑忠双.结构随机响应分析及其动力可靠性研究现状及趋势[J].福建建筑,2002,76(1)：25-28.
[176]肖梅玲,高春涛,叶燎原.结构地震反应在小波基下的动力可靠性分析[J].世界地震动工程,2002,18(1)：27-33.
[177]Van den NIEUWENHOF B V, COYETTE J P. Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties[J]. Computer Methods in Applied Mechanics and Engineering,2003,192(33-34):3705-3729.
[178]KAPLUNOV J D, NOLDE E V, SHORR B F. A perturbation approach for evaluating natural frequencies of moderately thick elliptic plates[J]. Journal of Sound and Vibration,2005, 281(3-5):905-919.
[179]胡太彬,陈建军等.平稳随机激励下随机桁架结构的动力可靠性分析[J].力学学报,2004,36(2)：241-246.
[180]GAO W, CHEN J J, CUI M T, et al. Dynamic response analysis of linear stochastic truss structures under stationary random excitation[J]. Journal of Sound and Vibration,2005, 281(1-2):311-321.
[181]Abhijit Chaudhuri, Subrata Charkraborty. Reliability of linear structures with parameter uncertainty under non-stationary earthquake[J].Structural Safety,2006,28(3):231-246.
[182]Chen Jianbing, Li Jie. The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters[J]. Structural safety,2007,29(2):77-93.
[183]胡俊,欧进萍.大跨度悬索桥抖振时变动力可靠性分析[J].武汉理工大学学报,2010,32(9)：26-30.
[184]吴震宇,袁惠群.随机载荷下内燃机轴系动力可靠性分析[J].振动、测试与诊断,2010,30(5)：534-538.
[185]唐增宝,钟毅芳,刘伟忠.提高多级齿轮传动系统动态性能的优化设计[J].机械工程学报,1994,30(5)：66-75.
[186]王勇,许蕴梅.随机振动最小为目标的齿轮系统优化[J].山东大学学报(工学版),2003,33(3)：257-260.
[2]Ibrahim R.A. Structural dynamics with parameter uncertainties [J]. Applied Mechanics, Reviews,1987,40(3):309-328.
[3]张圣坤.不确定问题的有限元方法及应用[J].固体力学学报,1987,3：277-281.
[4]李杰.结构动力分析的若干发展趋势[J].世界地震工程,1993,(2)：1-8.
[5]李杰.随机结构系统分析与建模[M].第一版.北京：科学出版社,1996.
[6]王光远.论不确定性结构力学的进展[J].力学进展,2002,32(2)：205-211.
[7]邱志平.不确定参数结构静力响应和特征值问题的区间分析方法[D].吉林工业大学博士论文,1994.
[8]郭书祥,吕震宙.区间运算和静力区间有限元[J].应用数学和力学,2001,22(12)：1249-1254.
[9]Chen J J, Che J W, Sun H A, et al. Probabilistic dynamic analysis of truss structures[J]. Structural-Engineering & Mechanics,2002,13(2):231-239.
[10]Dai J, Chen J J, Li Y G. Dynamic response optimization design for engineering structures based on reliability [J]. Applied Mathematics and Mechanics,2003,24(1):43-52.
[11]胡太彬,陈建军,徐亚兰.随机参数平面刚架结构频率特性分析的随机因子法[J].机械强度,2006,28(2)：196-200.
[12]胡太斌.随机结构动力分析与动力可靠性优化设计[D].西安电子科技大学博士学位论文,2005.
[13]Gao W, Chen J J, Ma H B. Dynamic response analysis of closed loop control system for intelligent truss structures based on probability[J]. Structural Engineering & Mechanics,2003, 15(2):239-248.
[14]高伟,陈建军等.随机钢架结构在平稳随机激励下的动力响应分析[J].振动与冲击,2004,23(2)：88-91.
[15]张策.机械动力学[M].第二版.北京：高等教育出版社,2008.
[16]Erdman A G, Sandor G N. Kineto-elstodynamnic:a review of the state-of-the art and trends[J]. Mechanism and Machine Theory,1972,7(1):19-33.
[17]Hrones J A. Analysis of dynamic force in a cam-driven system[J]. Trans. ASME,1948,70(5): 473-482.
[18]Mitchell D B. Test on dynamic response of cam follower systems. Mechanical. Engineering, 1950,72(6):467-471.
[19]Sunada W, Dubowsky S. On the dynamic analysis and behavior of industrial robotic manipulators with elastic members [J]. AMSE Journal of Mechanisms, Transmissions, and Automation Design,1983,105(1):42-51.
[20]张策,王玉新,杨玉虎,陆锡年.机构动力学最新发展动态综述[J].唐山工程技术学院学报,1993,15(2)：34-43.
[21]李润方,王建军.齿轮系统动力学—振动、冲击、噪声[M].第1版.北京：科学出版社,1997.
[22]张义民,闻邦椿.齿轮的可靠性设计[J].传动技术.1997(2)：34-40.
[23]徐宏伟,成刚虎,黄玉美等.一种圆柱齿轮强度可靠性的现代设计方法[J].西安理工大学学报.2005,21(3)：268-271.
[24]魏任之,张永忠,史兴虹.关于直齿圆柱齿轮轮齿受载变形量的计算[J].机械传动,1980,4：1-8.
[25]张永忠,王洪.齿根动态应力分析[J].机械工程学报,1986,22(3)：58-65.
[26]Kahraman A, Singh R. Non-linear dynamic of a spur gear pair[J]. J Sound Vib,1990,142(1): 49-75.
[27]Nakamura K. Tooth separations and abnormal noise on power transmission gears[J]. Bull JSME,1967,10:846-854.
[28]Blankenship G W, Singh R. A new gear mesh interface dynamic model to predict multi-dimensional force coupling and excitation[J]. Mech Mach Theory,1995,30(1):43-57.
[29]Vaishya M, Houser R. Modeling and analysis of sliding friction in gear dynamics[C]. Proceedings of the 2000ASME Design Engineering Technical Conferences, Baltimore, USA: DETC2000/TG-14430,2000,601-610.
[30]孙月海,张策等.直齿圆柱齿轮传动系统振动的动力学模型[J].机械工程学报,2000,36(8)：47-50.
[31]Kahraman A. Dynamic analysis of a multi-mesh helical gear train[J]. ASME Mech Des,1994, 116:706-712.
[32]Rook T E, Singh R. Dynamic analysis of a rever-idler gear pair with concurrent clearances[J]. J Sound Vib,1995,182(2):303-322.
[33]Vinayak H, Singh R, Padmanabhan C. Linear dynamic analysis of multi-mesh transmissions containing external rigid gears[J]. J Sound Vib,1995,185(1):1-32.
[34]Benton M, Seireg A. Simulation of resonances and instability conditions in pinion-geared system[J]. ASME Mech Des,1978,100:26-32.
[35]Benton M, Seireg A. Factors influencing instability and resonance in geared systems[J]. ASME Mech Des,1981,103:372-378.
[36]Wang K L, Cheng H S. A numerical solution to the dynamiv load, film thickness, and surface temperatures inspur gears, part I analysis[J]. ASME Mech Des,1981,103:177-187.
[37]Kahraman A, Singh R. Interactions between time-varying mesh stiffness and clearance non-linearties in a geared system[J]. J Sound Vib,1991,146(1):135-156.
[38]Cai Y. Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (a new stiffness function of helical involute tooth pair) [J]. ASME Mech Des,1995,117:460-469.
[39]Kahraman A, Blankenship G W. Interactions between commensurate parametric and forcing excitations in a system with clearance[J]. J Sound Vib,1996,194 (3):317-336.
[40]Theodossiades S, Natsiavas S. Non-linear dynamics of gear-pair systems with periodic stiffness and backlash[J]. J Sound Vib,2000,229(2):287-310.
[41]Lee A S Ha J W, Choi D H. Coupled lateral and torsional vibration characteristics of a speed increasing geared rotor-bearing system[J]. Journal of Sound and Vibration,2003,263: 725-742.
[42]欧卫林,王三民,袁茹.齿轮耦合复杂转子系统弯扭耦合振动分析的轴单元法[J].航空动力学报,2005,20(3)：537-538.
[43]庞辉,方宗德,欧卫林.多平行齿轮耦合转子系统的振动特性分析[J].振动与冲击,2007,26(6)：21-25.
[44]方宗德,蒋孝煜,宋镜瀛.用状态空间方法的齿轮传动系统动态分析[J].清华大学学报,1987,5(27)：1-11.
[45]姚文席.渐开线直齿轮单级齿轮传动系统的振动[J].西安交通大学学报,1990,4(24)：39-49.
[46]唐增宝,钟毅芳.直齿圆柱齿轮传动系统的振动分析[J].机械工程学报,1992,28(4)：86-93.
[47]Cai Y. Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (A new stiffness function of helical involute tooth pair)[J]. ASME, Journal of Mechanical Design,1995,117(9):460-468.
[48]LIN Jian, Robert G. Parker. Mesh stiffness variation instabilities in two-stage gear systems[J]. Journal of Vibration and Acoustics,2002,124(1):68-76.
[49]张锁怀,沈允文,董海军等.齿轮时变系统对扭矩激励的响应[J].航空动力学报,2003,18(6)：737-743.
[50]A. Parey, Badaoui M El, Guillet F, Tandon N. Dynamic modelling of spur gear pair and application of empirical mode decomposition-based statistical analysis for early detection of localized tooth defect[J]. Journal of Sound and Vibration,2006,294(3):547-561.
[51]Vaishya M, Houser R. Modeling and analysis of sliding friction in gear dynamics[C]. Proceedings of the 2000ASME Design Engineering Technical Conferences, Baltimore, USA: DETC2000/TG-14430,2000,601-610.
[52]Grzegorz Litak, Michael I. Friswell. Dynamics of a gear system with faults in meshing stiffness[J]. Nonlinear Dynamic,2005,41(4):415-421.
[53]王三民,沈允文,董海军.多间隙耦合非线性动力系统的分叉与混沌[J].西北工业大学学报,2003,21(2)：191-194.
[54]Gang Liu, Robert G Parker. Nonlinear dynamics of idler gear systems[J]. Nonlinear dynamics, 2008,53(4):345-367.
[55]唐进元,陈思雨,钟掘.一种改进的齿轮非线性动力学模型[J].工程力学,2008,25(1)：217-223.
[56]Tobe, T., Sato, K., Takasu, N. Statistical analysis of dynamic loads on spur gear teeth[J]. Bull. of the JSME,1976,19(133):800-813.
[57]Tobe, T., Sato, K., Takasu, N. Statistical analysis of dynamic loads on spur gear teeth[J]. Bull. of the JSME,1977,20(148):1315-1328.
[58]Neriya, S., V., Bhat, R. B., Sankar, T. S. On the dynamic response of a helical geared system subjected to a static transmission error in the form of deterministic and filtered white noise inputs[J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design, Transactions of the ASME,1988,110(4):501-506.
[59]Y. Wang, W. J. Zhang. Modelling of gear stochastic vibration considering non-white noise errors[J]. Chinese science bulletin,1999,44(4):375-378.
[60]刘梦军,沈允文,董海军.随机外激励下齿轮非线性系统的全局分析[J].中国机械工程,2004,15(13)：1182-1185.
[61]孙宜强,温建明,冯奇.随机阻尼拍击振动的二级传动模型[J].力学季刊,2010,31(2)：243-249.
[62]卢剑伟,曾凡灵,杨汉生,刘梦军.随机装配侧隙对齿轮系统动力学特性的影响分析[J].机械工程学报,2010,46(21)：82-86.
[63]袁哲,孙志礼,李国权,牟峰.齿轮随机参数结构固有频率灵敏度分析[J].机械与电子,2009,12：16-17.
[64]张明辉,黄田.Diamond机构的弹性动力分析与实验研究[J].机械设计,2004,21(11)：6-8.
[65]Erdman A G, Imam I, Sandor G N. Applied koneto-elastodynamics:Proceedings of 2ed OSU applied mechanism conference. Oklahoma:Oklahoma State University,1971.
[66]Alexander, R. M., Lawrance, K. L.. Experimentally determined dynamic strains in an elastic mechanism[J]. ASME Journal of Engineering for Industry 102,1975,791-794.
[67]Stamps, F. R., Bagci, C.. Dynamics of planar, elastic, high speed mechanisms considering three dimensional offset geometry:Analytical and experimental investigations[J]. ASME Journal of Mechanisms Transmissions and Automation in Design 105,1983,498-510.
[68]张策,陈树勋等.弹性连杆机构的分析与设计[M].第2版.北京：机械工业出版社,1997.
[69]Imam I, Sandor G N, Kramer S N. Deflection and stress analysis of high-peed mechanisms with elastic links[J]. ASME Journal of Engineering for Industry,1973,95(2):541-548.
[70]Bahgat B M, Willmert K D. Finite element vibration analysis of planar mechanism[J]. Mechanism and Machine Theory,1976,11(1):47-71.
[71]Midha A, Erdman A G., Finite element approach to mathematical modeling of high-speed elastic linkages[J]. Mechanism and Machine Theory,1978,13(6):603-618.
[72]Wang Yuxin. Dynamics of an Elastic Four Bar Linkage Mechanism with Geometric Nonlinearities[J]. Nonlinear Dynamics,1997,14(4):357-375.
[73]Nath P K, Ghosh A. Steady state response of mechanism with elastic links by finite element method[J]. Mechanism and Machine Theory,1980,15(3):199-211.
[74]Turcic D A, Midha A. Generalized equations of motion for the dynamic analysis of elastic mechanism systems[J]. ASME Journal of Dynamic Systems Measurement and Control,1984, 106(4):243-248.
[75]Turcic D A, Midha A. Dynamic analysis of elastic mechanism system[J]. Part 1:Applications ASME Journal of Dynamic Systems Measurement and Control,1984,106(4):249-254.
[76]Cleghom W L, Fenton R G, Tabarrok B. Steady-state vibration response of high-speed mechanisms[J]. Mechanism and Machine Theory,1984,19(4-5):417-423.
[77]Lieh J. Dynamic modeling of a slider-crank mechanism with coupler and joint flexibility[J]. Mechanism and Machine Theory,1994,29(1):139-147.
[78]Fallahi B, Lai S, Venkat C. A finite element formulation of a flexible slider-crank mechanism using local coordinate[J]. ASME J of Dynamic Systems, Measurement & Control,1995, 117(3):329-338.
[79]Makwana K C, Cupta K N. On mathematical modeling for the elastic coupler response of a planar four-bar linkage with possible speed perturbation at crank[J]. Mechanism and Machine Theory,1998,33(8):1105-1115.
[80]Chen J S, Chian C H. Effects of crank length on the dynamic of a flexible connecting rods [J].ASME Journal of Vibration and Acoustics,2001,123(3):318-323.
[81]刘建琴,张策等.变长度曲柄-连杆机构的动力学分析[J].机械工程学报,2000,36(4)：41-44.
[82]陆念力,兰朋,金奕山.弹性连杆机构动力分析的一种新方法[J].中国机械工程学报,2003,1(1)：6-10.
[83]张利,黄文振,周志革.灵敏度方法在连杆机构动态响应重分析中的应用[J].上海交通大学学报,2000,34(3)：378-380.
[84]阎绍泽,季林红等.柔性机械系统动力学的变形耦合方法[J].机械工程学报,2001,37(8)：1-4.
[85]Ren Jiazhi, Yu Chongwen. Influence of Dropping scales of E7/6 Comber on Process Performance[J]. Journal of Donghua University,2005,22(2):23-25.
[86]刘善增,余跃庆等.3-RRC并联柔性机器人的动力学分析[J].振动与冲击,2008,27(2)：157-161.
[87]Liu Zhuyong, Hong Jiazhen, Liu Jinyang. Complete geometric nonlinear formulation for rigid-flexible coupling dynamics[J]. J. Cent. South Univ. Technol,2009,16(1):119-124.
[88]张劲夫,许庆余,张陵.具有粘性摩擦的弹性曲柄滑块机构的动力学建模及计算[J].西安交通大学学报,2000,34(11)：86-89.
[89]拓耀飞,陈建军,徐亚兰等.随机参数连杆机构的静动态运动精度可靠性分析[J].电子机械工程,2004,20(4)：4-8.
[90]陈建军,郜文文等.随机参数弹性连杆机构运动功能的可靠性分析[J].机械设计与研究,2006,22(3)：19-22.
[91]拓耀飞,陈建军,陈永琴.区间参数弹性连杆机构的非概率可靠性分析[J].中国机械工程第2007,18(5)：528-531.
[92]张义民.机械振动[M].北京：清华大学出版社,2007.
[93]刘德贵,费景高.动力学系统数字仿真算法[M].北京：科学出版社,2000.
[94]张铁,闫家斌.数值分析[M].北京：冶金工业出版社,2001.
[95]W. J. T. Daniel. The subcycled newmark algorithm [J]. Computational mechanics,1997,20(3): 272-281.
[96]W. Moser, H. Antes, G. Beer. A Duhamel integral based approach to one-dimensional wave propagation analysis in layered media[J]. Comput Mech,2005,35:115-126.
[97]黄文虎,邵成勋.多柔体系统动力学[M].北京：科学出版社,1996.
[98]张劲夫,贾丽俊,秦卫阳.柔性连杆机构动力学研究进展[J].机械科学与技术,2005,24(2)：199-203.
[99]Eduardo Bayo, Javier Garcia De Jalon, Miguel Angel Serna. A modified lagrangian formulation for the dynamic analysis of constrained mechanical systems [J]. Computer Methods in Applied Mechanics and Engineering,1988,71(2):183-195.
[100]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].西南交通大学博士学位论文,1996.
[101]Shinozuka M, Jan C M. Digtal simulation of random processes and its applications[J]. Journal of Sound and Vibration,1972,25(1):111-128.
[102]Shinozuka, M. Monte Carlo solution of structural dynamics[J]. Computer & Structures,1972, 2:855-874.
[103]Shinozuka M, Wen Y K. Monte Carlo simulation of nonlinear vibrations[J]. AIAA J,1972, 10(1):37-40.
[104]赵雷,陈虬.结构随机分析的Monte Carlo加权残值法[J].计算结构力学及其应用,1996,13(2)：193-200.
[105]Kaminski M. Monte-Carlo simulation of effective conductive for fiber composites[J]. Int. Communications in Heat and Mass Transfer,1999,26(6):801-810.
[106]Bellman R. On the foundations of a theory stochastic variational processes[J]. In:Proc of Symposium on Applied Mathematics,1962,13:275-286.
[107]Hien T D, Kleiber M. Finite element analysis based on stochastic Hamilton variational principle[J]. Computer & Structures,1990,37(6):893-902.
[108]Liu W K, et al. Probabilistic finite element methods in nonlinear dynamics[J]. Compt Meth Appl Mech Eng.,1986,56(1):61-81.
[109]Lee X X. Double random vibration of nonlinear systems[C]. In:Proc Int Conf on Computational Stochastic Mechanics, Corfu, Greeze, Sept,1991.
[110]陈塑衰.随机参数结构的振动理论[M].长春：吉林科学技术出版社,1992.
[111]陈虬,尹志远.随机结构动力分析的随机有限元法[J].西南交通大学学报,1994,29(5)：477-481.
[112]Yamazaki F. Neumann expansion for stochastic finite element analysis[J]. J Eng Mech. ASCE, 1988,114(8):1335-1354
[113]赵雷,陈虬.随机有限元动力分析方法的研究进展[J].力学进展,1999,29(1)：9-18.
[114]Sun T C. A finite element method for random differential equations with random coefficients[J]. Int J Number Analysis,1979,16(6):1019-1035.
[115]Iwan W D, Jensen H. On the dynamic response of continuous systems including model uncertainty[J]. JAppl Mech, ASME,1993,60(2):484-490.
[116]Ghanem R, Spanos P D. Spectral stochastic finite element formulation for realiability analysis[J]. J Eng. Mech, ASCE,1991,117(10):2351-2372.
[117]李杰.随机结构动力分析的扩阶系统方法[J].工程力学,1996,13(1)：93-102.
[118]李杰.复合随机振动分析的扩阶系统方法[J].力学学报,1996,28(1)：66-75.
[119]李杰,魏星.随机结构动力分析的递归聚缩算法[J].固体力学学报,1996,17(3)：263-267.
[120]李杰,陈建兵.随机结构反应的概率密度演化分析[J].同济大学学报(自然科学版),2003,31(12)：1387-1391.
[121]李杰,陈建兵.随机结构动力反应分析的概率密度演化方法[J].力学学报,2003,35(4)：437-441.
[122]李杰,陈建兵.随机结构非线性动力响应的概率密度演化分析[J].力学学报,2003,35(6)：716-722.
[123]陈建兵,李杰.随机结构复合随机振动分析的概率密度演化方法[J].工程力学,2004,21(3)：90-95.
[124]易平,林家浩,赵岩.线性随机结构的非平稳随机响应变异性分析[J].固体力学学报,2002,23(1)：93-97.
[125]高伟,陈建军,刘伟.随机参数智能桁架结构动力特性分析[J].应用力学学报,2003,20(1)：123-127.
[126]陈建军,黄居锋,赵颖颖.随机参数链式结构系统的动力特性分析[J].中国机械工程,2005,16(1)：16-19.
[127]陈建军,黄居锋等.随机参数轴盘扭转结构系统动力特性优化[J].机械工程学报,2005,41(8)：180-184.
[128]王小兵,陈建军,李金平,刘国梁.基于随机因子法的随机结构动力特性分析研究[J].振动与冲击,2008,27(2)：4-8.
[129]戴君,陈建军,马洪波,等.随机参数结构在随机荷载激励下的动力响应分析[J].工程力学,2002,19(3)：64-68.
[130]Gao W., Chen J. J., Ma H. B. Dynamic response analysis of closed loop control system for intelligent truss structures based on probability[J]. Structural Engineering & Mechanics,2003, 15(2):239-248.
[131]高伟,陈建军,刘伟,马洪波,马孝松.随机参数智能桁架结构在随机力下的闭环控制动力响应分析[J].机械科学与技术,2002,21(6)：909-912.
[132]陈建军,王小兵.随机参数智能板结构的动态特性分析[J].西安电子科技大学学报,2004,31(5)：661-665.
[133]陈龙,陈建军,赵岽,李金平.随机参数结构最优控制的闭环响应分析[J].振动与冲击,2010,29(1)：34-37.
[134]陈建军.机械与结构系统的可靠性[M].西安：西安电子科技大学出版社,1994.
[135]胡太彬,陈建军,王小兵.不均匀随机参数桁架结构的随机反应分析[J].工程力学,2007,24(2)：123-131.
[136]王登刚,李杰.计算具有区间参数结构特征值范围的一种新方法[J].计算力学学报,2004,21(1)：56-61.
[137]Moore RE. Interval Analysis[M]. New York:Prentice-Hall, Englewood cliffs,1966.
[138]陈塑寰,邱志平,宋大同等.区间矩阵标准特征值问题的一种解法[J].吉林工业大学学报,1993,23(3)：1-8,
[139]Qiu Z P, Wang X J, Friswell M I. Eigenvalue bounds of structures with uncertain-but-bounded parameters[J]. Journal of Sound and Vibration,2005,282(1/2):297-312.
[140]陈怀海,陈止想.求解实对称矩阵区间特征值问题的直接优化法[J].振动工程学报,2000,13(1)：117-121.
[141]Koylouglu H U, Cakmak A S, Nielsen SRK. Interval algebra to deal with pattern loading and structural uncertainties[J]. Journal of Engineering Mechanics,1995,121(11):1149-1157.
[142]Muhanna R L, Mullen R L. Uncertainty in mechanics problems-interval-based approach[J]. Journal of Engineering Mechanics,2001,127(3):557-566.
[143]吴晓,罗佑新,文会军,李敏.非确定结构系统区间分析的泛灰求解方法[J].计算力学学报,2003,20(3)：329-334.
[144]Chen S H, Lian H D, Yang X W. Interval displacement analysis for structures with interval parameters[J]. Int J Num Methods in Eng,2002,53(2):393-407.
[145]吴杰,陈塑寰.区间参数结构的动力响应优化[J].固体力学学报,2004,25(2)：186-189.
[]46]陈塑寰.结构动态设计的矩阵摄动理论[M].北京：科学出版社,1999.
[147]Hansen Eldon. Global Optimization Using Interval Analysis[C]. New York:Marcel Dekker Inc,1992.
[148]王登刚.计算具有区间参数结构的固有频率的优化方法[J].力学学报,2004,36(3)：364-372.
[149]Ma Juan, Chen Jian-jun, Zhang Jian-guo, Jiang Tao. Interval factor method for interval finite element analysis of truss[J]. Journal Multidiscipline Modeling in Materials and Structures, 2005,1(4):367-376.
[150]王芳林,高伟.区间桁架结构动力特性分析的区间因子法[J].应用力学学报,2007,24(3)：477-481.
[151]林立广,陈建军,马娟等.基于区间因子法的不确定桁架结构动力响应分析[J].应用力 学学报,2008,25(4)：612-616.
[152]李桂青,李秋胜.工程结构时变可靠度理论及其应用[M].北京：科学出版社,2001.
[153]Rice S O. Mathematical Analysis of Random Noise[J]. Bell System Technical Journal,1944, 23:282-332.
[154]Sieget A J. K, Darling, D. A. The first passage problem for a continuous Markov process[J]. Annal of mathematics statistics,1953,24:624.
[155]Helmstrom C W. Note on a Markov a Envelop Process. Institute of Radio Engineers, Transaction on Information Theory, IT-5,1959,139-140.
[156]Coleman J J. Reliability of Aircraft Structures in Resisting Chance Failure Operations. Res, 1959,7(5):639-645.
[157]Miles J. W. On structural Fatigue under random loading[J]. Journal of Aero Science,1954,21: 753-768.
[158]Shinozuka M. Probability of structural failure under random loading[J]. EM. ASSCE,1964 Vol.90.
[159]Shinozuka M, Yao J T P. On the two-sided time dependent barrier problem. Columbia Univinst Study of Fatigue and Reliability, Tech. Rept.21, June,1965
[160]lyenger R N. First passage probability during random vibration[J]. Journal of Sound and Vibration,1973,31(2):185-193.
[161]Roberts J B. Structural fatigue under nonstationary random loading[J], Journal of Mechanical Engineering Science,1966,8(4):392-405.
[162]Gasparini D A. Response of MDOF systems to nonstationary random excitation[J]. Journal of the Engineering Mechanics Division,1979,105(1):13-27.
[163]Iwan W D, Spanos P T. Response envelope statistics for nonlinear oscillators with random excitation. Journal of Applied Mechanics,1978,45(1):170-174.
[164]Iwan W D, Gates N C. Estimations earthquake response of simple hysteretic structures[J]. Journal of Applied Mechanics,1979,105(3),391-405.
[165]刘锡荟.现行规范抗震设计方法安全度的评价及工程参数的确定[J].地震工程与工程振动,1982,2(1)：21-32.
[166]尹之潜,李树帧.结构抗震的可靠度与位移控制设计[J].地震工程与工程振动,1982,2(2)：45-55.
[167]李桂青,曹宏.动力可靠性述评[J].地震工程与工程震动,1983,3(3)：42-61.
[168]欧进萍,干光远.基于模糊破坏准则的抗震结构动力可靠性分析[J].地震工程与工程振动,1986,5(1)：1-11.
[169]朱位秋.随机振动[M].第一版.北京：科学出版社,1992.
[170]李桂青,曹宏,李秋胜,霍达.结构动力可靠性理论及其应用[M].北京：地震出版社,1993.
[171]管昌生,张鹏,刘增夕,李桂青,李国发.时变结构动力可靠性分析的包络过程法[J].广西工学院学报,1995,6(3)：25-30.
[172]李创第,李桂青,黄任常.连续随机结构的动力反应和可靠性分析[J].广西工学院学报,1997,8(1)：25-31.
[173]Chen J J, Duan B Y & Zen Y G.. Study on dynamic reliability analysis of the structures with multidegree-of-freedom system [J]. Computers & Structures,1997,62(5):877-881.
[174]石少卿,姜节胜.非平稳随机激励作用下多自由度体系系统动力可靠性研究[J].应用力 学学报.1999,16(4)：73-77.
[175]郑忠双.结构随机响应分析及其动力可靠性研究现状及趋势[J].福建建筑,2002,76(1)：25-28.
[176]肖梅玲,高春涛,叶燎原.结构地震反应在小波基下的动力可靠性分析[J].世界地震动工程,2002,18(1)：27-33.
[177]Van den NIEUWENHOF B V, COYETTE J P. Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties[J]. Computer Methods in Applied Mechanics and Engineering,2003,192(33-34):3705-3729.
[178]KAPLUNOV J D, NOLDE E V, SHORR B F. A perturbation approach for evaluating natural frequencies of moderately thick elliptic plates[J]. Journal of Sound and Vibration,2005, 281(3-5):905-919.
[179]胡太彬,陈建军等.平稳随机激励下随机桁架结构的动力可靠性分析[J].力学学报,2004,36(2)：241-246.
[180]GAO W, CHEN J J, CUI M T, et al. Dynamic response analysis of linear stochastic truss structures under stationary random excitation[J]. Journal of Sound and Vibration,2005, 281(1-2):311-321.
[181]Abhijit Chaudhuri, Subrata Charkraborty. Reliability of linear structures with parameter uncertainty under non-stationary earthquake[J].Structural Safety,2006,28(3):231-246.
[182]Chen Jianbing, Li Jie. The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters[J]. Structural safety,2007,29(2):77-93.
[183]胡俊,欧进萍.大跨度悬索桥抖振时变动力可靠性分析[J].武汉理工大学学报,2010,32(9)：26-30.
[184]吴震宇,袁惠群.随机载荷下内燃机轴系动力可靠性分析[J].振动、测试与诊断,2010,30(5)：534-538.
[185]唐增宝,钟毅芳,刘伟忠.提高多级齿轮传动系统动态性能的优化设计[J].机械工程学报,1994,30(5)：66-75.
[186]王勇,许蕴梅.随机振动最小为目标的齿轮系统优化[J].山东大学学报(工学版),2003,33(3)：257-260.