（1）粘弹性材料线性本构方程及动力学应用 （2）旋转导向钻井工具有关力学问题研究
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摘要
粘弹性结构或粘弹性复合结构的振动分析必然要涉及到粘弹性材料的本构方程及其形式,粘弹性材料本构方程的形式对粘弹性结构或粘弹性复合结构的动力学分析具有决定性影响。对于同一种材料,采用不同形式的松弛模量函数,粘弹性材料的本构方程也将呈现出不同的具体形式。综述了近年来粘弹性材料线性本构方程的研究成果,介绍和讨论了复常数模量模型、标准流变学模型、分数阶导数模型、分数指数模型、微振子模型等典型和常用的五种模型,同时简单介绍了这些模型的动力学应用。
粘弹性复合结构动力学方程是一组线性的二阶Volterra 型微分积分方程,直接利用这样的一组二阶Volterra 型微分积分方程来进行复合结构的模态分析很不方便。为了方便复合结构动力学问题的分析研究,给出了粘弹性复合结构动力学方程的扩阶状态形式。对于三参数标准流变学模型,粘弹性复合结构动力学方程还可以化为一般三阶微分方程的形式。对于由扩阶状态形式和一般三阶微分方程形式表示的粘弹性复合结构动力学方程,可以利用常规的模态分析理论和状态空间法来分析求解粘弹性复合结构的特征值问题。
利用扩阶状态形式的粘弹性复合结构动力学方程,把微分方程数值积分的Runge-Kutta 方法和精细积分法引入到粘弹性复合结构动力响应的计算中来,使这个复杂的问题得到简便的解决。通过计算实例,并同现有的计算方法比较,说明了该方法的有效性和精确性。
利用扩阶状态形式的粘弹性复合结构动力学方程分析求解特征值问题和计算结构动力响应具有理论简单、思路清晰、编程容易、计算速度快等优点,特别适合于工程实际问题的计算。
在粘弹性结构动力学分析中,对于同一种粘弹性材料可以选用不同的本构方程模型。当本构方程模型确定之后,如何针对具体的粘弹性材料来估计本构方程的模型参数是一个非常重要的问题。分析了用曲线拟合估计粘弹性材料线性本构方程模型参数的原理和方法。根据粘弹性材料储能模量和损耗因子在频域的实测数据,依据不同的本构方程模型构造出不同的加权优化目标函数。这是一个具有约束条件的非线性优化问题,应用最优化方法拟合出本构方程模型的本构参数。具体分析了三种常用的本构方程模型:标准流变学模型、分数阶导数模型和微振子模型,利用MATLAB 编制了相应的拟合程序,给出算例说明方法的可行性。
稳定平台的闭环控制是调制式旋转导向钻井系统的关键。稳定平台控制轴安装在旋转导向钻井工具的内部,承担着传递扭矩、承载巨大横向动态载荷的重任。由于旋转导向钻井工具本身狭小细长,发电机轴又是控制轴的一部分,所以对控制轴的外形尺寸有特殊要求,要求尽可能的细。因此旋转导向钻井工具稳定平台控制轴的强度和刚度分析十分重要,直接关系到稳定平台能否正常工作和寿命大小。针对作者研究设计的稳定平台控制轴的强度分析和刚度分析分别建立了不同的控制轴力学模型,利用
Viscoelastic material constitutive equations and its forms must be taken into account for analyzing vibration of visco-elastic composite structure. The forms of viscoelastic material constitutive equations are very important to the dynamic characteristics of visco-elastic composite structure. For different relaxation modulus, the viscoelastic material constitutive equations are of different forms. The study on linear constitutive equations of viscoelastic material is summarized. The five typical models in common use are recommended and discussed. They are complex modulus model, the standard model, fractional derivative model, fractional exponential model and mini-oscillator model, respectively. The dynamic applications of these models are briefly discussed.
The dynamic equations of visco-elastic composite structure are second order linear Volterra differential-integral equations. It is difficult to analyze the modes of composite structure by using Volterra differential-integral equations. The extended order state variable forms of dynamic equations of visco-elastic composite structure are given. For three parameters standard model, the dynamic equations of visco-elastic composite structure are transformed into third order ordinary differential equations. The eigenvalue of visco-elastic composite structure can be calculated based on ordinary modal analysis theory and state space method.
An analysis method for dynamic response of visco-elastic composite structure is presented by using extended order state variable method. By introducing Runge-Kutta integration method and the high-precision integration, the complicated problems of dynamic responses can be solved simply. By comparing the obtained results with the results of existing method, it is shown that the present method is accurate enough and efficient.
The extended order state variable forms of dynamic equations of visco-elastic composite structure have many advantages, such as simple in formulation, easy in programming, and fast in calculating. In particular, the method can be applied easily to practical engineering problems.
The estimation of model parameters of a viscoelastic material constitutive equations is a key problem in analyzing visco-elastic composite structure dynamics. The principle and method for fitting and estimation of constitutive equation model parameters are discussed. Based on the experimental data of energy storage module and loss factor for viscoelastic materials in a given frequency span, the model parameters of three constitutive equations, the standard model, the fractional derivative model, and the mini-oscillator model, are confirmed in using an optimization algorithm. Numerical examples are given to show the effectiveness of the present method.
The closed loop control of stabilized platform is a key problem of modulated rotary steering drilling system. The stabilized platform control axes, which must be longer and slender, is subject to larger dynamic loads. The mechanical strength and stiffness of control axes are very important. The mechanical models of control axes designed by authors are established for mechanical strength and stiffness analysis .The mechanical strength and stiffness of the control axes are calculated by means of ANSYS, finite element analytical software. The theoretic basis for designing correctly a stabilized platform for a modulated rotary steering drilling system is put forward. The one of key problems of designing the control valve of a modulated rotary steering drilling tool (MRST) is the design of high pressure hole of upside disk valve. The work principle and mechanical model of the control valve of MRST are investigated. The best central angle parameters of high pressure hole of upside disk are given by theory analysis and simulation. The influence of the liquid lag on the force of palms is discussed. The theoretic basis for designing correctly the control valve of MRST is provided. The mechanical model of drilling string with modulated rotary steering drilling tool and resolving methods are new mechanical problems. In order to realize designing exactly and operating the down-hole closed-loop control system of well bore trajectory, the mechanical problems of bottom hole assembly (BHA) with modulated rotary steering drilling tool must be studied. The actual forces on BHA with modulated rotary steering drilling tool are investigated. Calculating formulas for the steering forces of bit are derived. The steering forces of bit are the summation of two parts. The one is called deformation steering force that is created by the elastic deformation of whole BHA, the other is called tool steering force that is created by rotary steering drilling tool. The application for calculating steering forces is programmed based on MATLAB. Numerical examples are given. The analysis results may be as theoretic basis for calculating the steering forces of bit and the prediction or control of well bore trajectory.
粘弹性复合结构动力学方程是一组线性的二阶Volterra 型微分积分方程,直接利用这样的一组二阶Volterra 型微分积分方程来进行复合结构的模态分析很不方便。为了方便复合结构动力学问题的分析研究,给出了粘弹性复合结构动力学方程的扩阶状态形式。对于三参数标准流变学模型,粘弹性复合结构动力学方程还可以化为一般三阶微分方程的形式。对于由扩阶状态形式和一般三阶微分方程形式表示的粘弹性复合结构动力学方程,可以利用常规的模态分析理论和状态空间法来分析求解粘弹性复合结构的特征值问题。
利用扩阶状态形式的粘弹性复合结构动力学方程,把微分方程数值积分的Runge-Kutta 方法和精细积分法引入到粘弹性复合结构动力响应的计算中来,使这个复杂的问题得到简便的解决。通过计算实例,并同现有的计算方法比较,说明了该方法的有效性和精确性。
利用扩阶状态形式的粘弹性复合结构动力学方程分析求解特征值问题和计算结构动力响应具有理论简单、思路清晰、编程容易、计算速度快等优点,特别适合于工程实际问题的计算。
在粘弹性结构动力学分析中,对于同一种粘弹性材料可以选用不同的本构方程模型。当本构方程模型确定之后,如何针对具体的粘弹性材料来估计本构方程的模型参数是一个非常重要的问题。分析了用曲线拟合估计粘弹性材料线性本构方程模型参数的原理和方法。根据粘弹性材料储能模量和损耗因子在频域的实测数据,依据不同的本构方程模型构造出不同的加权优化目标函数。这是一个具有约束条件的非线性优化问题,应用最优化方法拟合出本构方程模型的本构参数。具体分析了三种常用的本构方程模型:标准流变学模型、分数阶导数模型和微振子模型,利用MATLAB 编制了相应的拟合程序,给出算例说明方法的可行性。
稳定平台的闭环控制是调制式旋转导向钻井系统的关键。稳定平台控制轴安装在旋转导向钻井工具的内部,承担着传递扭矩、承载巨大横向动态载荷的重任。由于旋转导向钻井工具本身狭小细长,发电机轴又是控制轴的一部分,所以对控制轴的外形尺寸有特殊要求,要求尽可能的细。因此旋转导向钻井工具稳定平台控制轴的强度和刚度分析十分重要,直接关系到稳定平台能否正常工作和寿命大小。针对作者研究设计的稳定平台控制轴的强度分析和刚度分析分别建立了不同的控制轴力学模型,利用
Viscoelastic material constitutive equations and its forms must be taken into account for analyzing vibration of visco-elastic composite structure. The forms of viscoelastic material constitutive equations are very important to the dynamic characteristics of visco-elastic composite structure. For different relaxation modulus, the viscoelastic material constitutive equations are of different forms. The study on linear constitutive equations of viscoelastic material is summarized. The five typical models in common use are recommended and discussed. They are complex modulus model, the standard model, fractional derivative model, fractional exponential model and mini-oscillator model, respectively. The dynamic applications of these models are briefly discussed.
The dynamic equations of visco-elastic composite structure are second order linear Volterra differential-integral equations. It is difficult to analyze the modes of composite structure by using Volterra differential-integral equations. The extended order state variable forms of dynamic equations of visco-elastic composite structure are given. For three parameters standard model, the dynamic equations of visco-elastic composite structure are transformed into third order ordinary differential equations. The eigenvalue of visco-elastic composite structure can be calculated based on ordinary modal analysis theory and state space method.
An analysis method for dynamic response of visco-elastic composite structure is presented by using extended order state variable method. By introducing Runge-Kutta integration method and the high-precision integration, the complicated problems of dynamic responses can be solved simply. By comparing the obtained results with the results of existing method, it is shown that the present method is accurate enough and efficient.
The extended order state variable forms of dynamic equations of visco-elastic composite structure have many advantages, such as simple in formulation, easy in programming, and fast in calculating. In particular, the method can be applied easily to practical engineering problems.
The estimation of model parameters of a viscoelastic material constitutive equations is a key problem in analyzing visco-elastic composite structure dynamics. The principle and method for fitting and estimation of constitutive equation model parameters are discussed. Based on the experimental data of energy storage module and loss factor for viscoelastic materials in a given frequency span, the model parameters of three constitutive equations, the standard model, the fractional derivative model, and the mini-oscillator model, are confirmed in using an optimization algorithm. Numerical examples are given to show the effectiveness of the present method.
The closed loop control of stabilized platform is a key problem of modulated rotary steering drilling system. The stabilized platform control axes, which must be longer and slender, is subject to larger dynamic loads. The mechanical strength and stiffness of control axes are very important. The mechanical models of control axes designed by authors are established for mechanical strength and stiffness analysis .The mechanical strength and stiffness of the control axes are calculated by means of ANSYS, finite element analytical software. The theoretic basis for designing correctly a stabilized platform for a modulated rotary steering drilling system is put forward. The one of key problems of designing the control valve of a modulated rotary steering drilling tool (MRST) is the design of high pressure hole of upside disk valve. The work principle and mechanical model of the control valve of MRST are investigated. The best central angle parameters of high pressure hole of upside disk are given by theory analysis and simulation. The influence of the liquid lag on the force of palms is discussed. The theoretic basis for designing correctly the control valve of MRST is provided. The mechanical model of drilling string with modulated rotary steering drilling tool and resolving methods are new mechanical problems. In order to realize designing exactly and operating the down-hole closed-loop control system of well bore trajectory, the mechanical problems of bottom hole assembly (BHA) with modulated rotary steering drilling tool must be studied. The actual forces on BHA with modulated rotary steering drilling tool are investigated. Calculating formulas for the steering forces of bit are derived. The steering forces of bit are the summation of two parts. The one is called deformation steering force that is created by the elastic deformation of whole BHA, the other is called tool steering force that is created by rotary steering drilling tool. The application for calculating steering forces is programmed based on MATLAB. Numerical examples are given. The analysis results may be as theoretic basis for calculating the steering forces of bit and the prediction or control of well bore trajectory.
引文
1. 杨挺青.粘弹性力学[M].华中理工大学出版社,1990
2. Christensen R M.Theory of viscoelasticity[M]. New York: Academic Press, 1982
3. 陈前,朱德懋.粘弹结构动力学分析[J]. 振动工程学报,1989, Vol.2(3):42-51
4. 张阿舟,姚起航.振动控制工程[M] 北京:航空工业出版社,1989: 290-295
5. 孙庆鸿,张启军,姚慧珠.振动与噪声的阻尼控制[M].北京:机械工业出版社,1993: 77-81
6. Scanlan R H. Linear damping models and causality in vibrations[J]. Sound and Vibration, Vol.13(4), 1970,499-509
7. Bert C.W. Material Damping: An Introductory Review of Mathematical Models, Measures and Experimental techniques[J]. J. Sound & Vib, 1973,Vol.29: 129-135
8. Minle H K. The impulse response function of a single degree of freedom system with hysteretic hysteretic damping[J]. Sound and Vibration, Vol.100(4), 1985,590-593
9. 胡海岩.结构阻尼模型及系统时域动响应[J].振动工程学报,1992,Vol.5(1):8-15
10.丁海平,刘长河.复阻尼理论的一点注记[J].地震工程与工程振,2001,Vol.21(1): 61-63
11.何钟怡,廖振鹏,王小华.关于复阻尼理论的几点注记[J].地震工程与工程振动, Vol.2(1):1-6
12.陈前,朱德懋.弹性-粘弹性复合结构模态理论[J].固体力学学报,1990, Vol.11(1):23-33
13.陈前,朱德懋.复合结构振动分析的数值方法[J].计算结构力学及应用,1990, Vol.7(3):27-35
14.任建亭,邱阳.粘弹复合结构特征问题的迭代算法[J].计算力学学报,1997, Vol.14(3):353-359
15.Lesieufre G A, Bianchini E. Time domain modeling of linear viscoelasticity using anelastic displacement fields[J]. Journal of Vibration and Acoustics, 1995, Vol.117 (4) : 424-430
16.李军强.粘弹性复合结构动力响应的实用数值算法[J].机械,2001,Vol.28(2): 25-26
17.李军强,刘宏昭.粘弹性复合结构动力响应的精细积分解法[J].机械设计,2003, Vol.20(10):8-9,13
18.Gement A. On fractional differences [J]. Phi Mag, 1938, Vol.25(1): 92-96
19.Bagley R L, Torvik P J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures[J].AIAA J,1983, Vol.21(5):741-748
20.黄文虎,王心清,张景绘等.航天柔性结构振动控制的若干进展[J].力学进展,1997,Vol.27(1):5-18
21.陈前,朱德懋.关于复合结构振动分析中粘弹性材料本构方程的形式[J].应用力学学报,1987,Vol.4(1):39-51
22.Joseph P, Yuehua G. General response of viscoelastic systems modeled by fractional operators[J]. Franklin Institute ,1988, Vol.325(2): 247-275
23.李卓,徐秉业.粘弹性分数阶导数模型的有限元法[J].工程力学,2002,Vol.19(3): 40-44
24.Bagley Ronald L, Torvik Peter J. Fractional calculus in the transient analysis of viscoelastically damped structures[J]. AIAA, J ,1985, Vol.23(6): 918-925
25.李根国,朱正佑,程昌钧.具有分数导数型本构关系的粘弹性柱的动力稳定性[J]. 应用数学和力学.2001,Vol.22(3):250-258
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2. Christensen R M.Theory of viscoelasticity[M]. New York: Academic Press, 1982
3. 陈前,朱德懋.粘弹结构动力学分析[J]. 振动工程学报,1989, Vol.2(3):42-51
4. 张阿舟,姚起航.振动控制工程[M] 北京:航空工业出版社,1989: 290-295
5. 孙庆鸿,张启军,姚慧珠.振动与噪声的阻尼控制[M].北京:机械工业出版社,1993: 77-81
6. Scanlan R H. Linear damping models and causality in vibrations[J]. Sound and Vibration, Vol.13(4), 1970,499-509
7. Bert C.W. Material Damping: An Introductory Review of Mathematical Models, Measures and Experimental techniques[J]. J. Sound & Vib, 1973,Vol.29: 129-135
8. Minle H K. The impulse response function of a single degree of freedom system with hysteretic hysteretic damping[J]. Sound and Vibration, Vol.100(4), 1985,590-593
9. 胡海岩.结构阻尼模型及系统时域动响应[J].振动工程学报,1992,Vol.5(1):8-15
10.丁海平,刘长河.复阻尼理论的一点注记[J].地震工程与工程振,2001,Vol.21(1): 61-63
11.何钟怡,廖振鹏,王小华.关于复阻尼理论的几点注记[J].地震工程与工程振动, Vol.2(1):1-6
12.陈前,朱德懋.弹性-粘弹性复合结构模态理论[J].固体力学学报,1990, Vol.11(1):23-33
13.陈前,朱德懋.复合结构振动分析的数值方法[J].计算结构力学及应用,1990, Vol.7(3):27-35
14.任建亭,邱阳.粘弹复合结构特征问题的迭代算法[J].计算力学学报,1997, Vol.14(3):353-359
15.Lesieufre G A, Bianchini E. Time domain modeling of linear viscoelasticity using anelastic displacement fields[J]. Journal of Vibration and Acoustics, 1995, Vol.117 (4) : 424-430
16.李军强.粘弹性复合结构动力响应的实用数值算法[J].机械,2001,Vol.28(2): 25-26
17.李军强,刘宏昭.粘弹性复合结构动力响应的精细积分解法[J].机械设计,2003, Vol.20(10):8-9,13
18.Gement A. On fractional differences [J]. Phi Mag, 1938, Vol.25(1): 92-96
19.Bagley R L, Torvik P J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures[J].AIAA J,1983, Vol.21(5):741-748
20.黄文虎,王心清,张景绘等.航天柔性结构振动控制的若干进展[J].力学进展,1997,Vol.27(1):5-18
21.陈前,朱德懋.关于复合结构振动分析中粘弹性材料本构方程的形式[J].应用力学学报,1987,Vol.4(1):39-51
22.Joseph P, Yuehua G. General response of viscoelastic systems modeled by fractional operators[J]. Franklin Institute ,1988, Vol.325(2): 247-275
23.李卓,徐秉业.粘弹性分数阶导数模型的有限元法[J].工程力学,2002,Vol.19(3): 40-44
24.Bagley Ronald L, Torvik Peter J. Fractional calculus in the transient analysis of viscoelastically damped structures[J]. AIAA, J ,1985, Vol.23(6): 918-925
25.李根国,朱正佑,程昌钧.具有分数导数型本构关系的粘弹性柱的动力稳定性[J]. 应用数学和力学.2001,Vol.22(3):250-258
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