超弹性形状记忆合金丝对结构减震控制的研究
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摘要
超弹性形状记忆合金(Shape Memory Alloy,简称SMA)是实施结构被动控制的理想材料。国内外学者致力于SMA在结构振动控制中的研究,取得了一些成果,但在材料本构、阻尼器的研制开发、减震结构振动分析及优化设计等方面,还存在一些问题,有待于进一步研究。在此背景下,本论文在以下几方面进行了系统的理论分析和试验研究:
(1)试验测试了超弹性NiTi丝的力学性能,研究了循环次数、加载速率、应变幅值、环境温度等因素对SMA滞回曲线及其力学参数(临界应力、单位循环耗能量、模量、残余应变)的影响。在此基础上,对Lagoudas多线性模型进行改进,分别考虑模型参数随加载速率和循环次数的变化规律,建立了多线性动态本构模型和循环现象模型。针对Graesser模型不能反应加、卸载过程中材料力学性能变化的缺陷,提出了改进方法。
(2)设计并制作了新型自复位SMA阻尼器,兼有耗能和复位功能,且构造简单紧凑、丝材受力均匀。力学试验研究了循环次数、位移幅值和加载频率对阻尼器滞回曲线及其力学参数(最大输出力、残余变形、割线刚度、单位循环耗能量和等效阻尼比)的影响。在SMA多线性动态本构模型和受力分析基础上,建立了阻尼器的力学模型。数值模拟分析了不同功能丝组合(复位丝与耗能丝面积比)对阻尼器力学性能的影响。
(3)对自复位SMA阻尼器控制下的对称结构弹塑性地震时程反应及其能量分析进行研究,以一三层钢筋混凝土框架结构为算例,分别针对总用丝量相同和控制最大层间位移角相同两种工况,计算比较不同功能丝组合时阻尼器的减震功效和总用丝量,结果表明:当复位丝与耗能丝面积比在0.67～2时,能同时满足减震控制和经济性要求。通过对一二层模型钢框架进行模拟地震振动台试验,验证了自复位阻尼器的减震及复位功能,并证实了理论分析的可靠性。
(4)对自复位SMA阻尼器控制下的均匀偏心结构在双向地震输入时的时程反应及其能量分析进行研究,以一单自由度偏心体系为算例,分别针对总用丝量相同和控制最大层间位移角相同两种工况,计算比较了不同功能丝组合时阻尼器的减震功效和总用丝量,建议复位丝与耗能丝面积比取0.67～2,以有效抑制结构的平-扭耦联振动并满足经济性要求。另外,假定复位丝与耗能丝面积比为2,计算了不同地震输入下阻尼器对多自由度偏心结构的振动控制。
(5)为了改善多目标优化算法的计算效率和效果以实现耗能减震结构的优化设计,在二元锦标赛遗传算法基础上改进提出了新的一轮锦标赛遗传算法,该算法采用无回放随机联赛选择机制,根据Pareto支配关系复制个体,每一代选择过程在一轮循环中完成;为了将约束优化问题转化为无约束问题,依据Pareto优于准则建立了能体现约束信息的约束子目标函数。测试函数的比较计算证明该算法能够在较短时间内搜索到更多均匀分布的Pareto解。分别针对对称结构和均匀偏心结构,建立了基于Pareto思想的减震结构多目标优化模型,实现了阻尼器数量、位置和减震效果的共同优化。
Superelastic shape memory alloy (SMA) is a perfect material for passive control of structures. Numerous studies have been conducted in using SMA for structural vibration control, and some developments have been attained. However, there still exist some problems in modeling and application of SMA. Further investigations are carried out in this thesis, concering constitutive model, damper design, vibration analysis and optimization design of damped structures.
(1) Experiments on the mechanical behaviors of the superelastic NiTi wires are performed. Cyclic number, loading rate, strain amplitude, and temperature are considered to investigate their effects on the hysteretic curves and the mechanical parameters of SMA (such as critical stress, energy dissipation per cycle, modulus and residual strain). Based on the experimental results, the Lagoudas' multilinear model is modified to reflect the dynamic hysteretic hehaviors or the cyclic mechanical behaviors of SMA, considering loading rate or cyclic number's effects on the parameters of the model, respectively. In addition, the Graesser's model is improved to reflect the variations of the hysteretic behaviors of SMA during loading and unloading.
(2) An innovative recentering damping device (RDD) is designed and manufactured, which provides a perfect energy dissipation compatible with a negligible residual displacement, and has such advantages as the simple configuration and the uniform stresses of the wires. Extensive experiments are carried out to investigate the influences of cyclic number, displacement amplitude and loading frequency on the damper's hysteretic curves and the mechanical behaviors (such as maximum output force, residual deflection, secant stiffness, dissipated energy per cycle and equivalent viscous damping ratio). By analyzing the working mechanism of the RDD, a theoretical model is set up on the basis of the multilinear dynamic model of SMA. Some numerical simulations are taken to compare the mechanical behaviors of the damper with different ratio of cross-sectional area of recentering wires to dissipating wires.
(3) Seismic nonlinear response time histories and energy analyses of a symmetric structure with the RDD are simulated. Taken a three-story RC frame as an example, some comparisons of the seismic response of the controlled structure and the amount of gross SMA wires are executed, given the same amount of gross wires and the same maximum inter-story displacement ratio of the controlled structure, respectively, and a combination (ratio of cross-sectional area of recentering wires to dissipating wires) of 0.67～2 is suggested to satisfy the desired seismic response of the RDD structure and the economical efficiency. A two-story steel frame model with the RDD is tested on the shaking table, and the results approve that the RDD can decrease the structural vibration and mitigate the residual displacement effectively, which agrees with the theoretical results.
(4) Seismic response time histories and energy analyses of an eccentric structure with the RDD excited by bi-directional earthquakes are simulated. Taken an eccentric single-story structure as an example, some comparisons of the seismic response of the controlled structure and the amount of gross wires are executed, given the same amount of gross wires and the same maximum inter-story displacement ratio of the controlled structure, respectively. The results show that the damper with a combination of 0.67～2 can eliminate the coupled lateral-torsional response of the structure at a low cost. Moreover, the seismic response of a three-story eccentric structure controlled by the RDD with a combination of 2 is simulated, considering different earthquakes.
(5) To improve computational efficiency of multiobjective optimization algorithms for optimal design of damped structures, a novel one-round tournament genetic algorithm is advanced on the basis of the two-branch tournament genetic algorithm. Using stochastic tournament selection without replacement, the individuals are copied according to the Pareto relationships, and selections in each generation are accomplished in one-round repetition. In order to transfer a constrainted problem into an unconstrainted one, each objective function is revised as a constrainted objective function, according to the precedence rules. Test functions testify that the novel algorithm can search more Pareto optima stretching along the Pareto front in a shorter time. Based on the Pareto optimization theory, the multiobjective optimization models of controlled symmetric and eccentric structures are established to achieve the Pareto optima of the number and the placement of dampers and the seismic response of controlled structures.
(1)试验测试了超弹性NiTi丝的力学性能,研究了循环次数、加载速率、应变幅值、环境温度等因素对SMA滞回曲线及其力学参数(临界应力、单位循环耗能量、模量、残余应变)的影响。在此基础上,对Lagoudas多线性模型进行改进,分别考虑模型参数随加载速率和循环次数的变化规律,建立了多线性动态本构模型和循环现象模型。针对Graesser模型不能反应加、卸载过程中材料力学性能变化的缺陷,提出了改进方法。
(2)设计并制作了新型自复位SMA阻尼器,兼有耗能和复位功能,且构造简单紧凑、丝材受力均匀。力学试验研究了循环次数、位移幅值和加载频率对阻尼器滞回曲线及其力学参数(最大输出力、残余变形、割线刚度、单位循环耗能量和等效阻尼比)的影响。在SMA多线性动态本构模型和受力分析基础上,建立了阻尼器的力学模型。数值模拟分析了不同功能丝组合(复位丝与耗能丝面积比)对阻尼器力学性能的影响。
(3)对自复位SMA阻尼器控制下的对称结构弹塑性地震时程反应及其能量分析进行研究,以一三层钢筋混凝土框架结构为算例,分别针对总用丝量相同和控制最大层间位移角相同两种工况,计算比较不同功能丝组合时阻尼器的减震功效和总用丝量,结果表明:当复位丝与耗能丝面积比在0.67～2时,能同时满足减震控制和经济性要求。通过对一二层模型钢框架进行模拟地震振动台试验,验证了自复位阻尼器的减震及复位功能,并证实了理论分析的可靠性。
(4)对自复位SMA阻尼器控制下的均匀偏心结构在双向地震输入时的时程反应及其能量分析进行研究,以一单自由度偏心体系为算例,分别针对总用丝量相同和控制最大层间位移角相同两种工况,计算比较了不同功能丝组合时阻尼器的减震功效和总用丝量,建议复位丝与耗能丝面积比取0.67～2,以有效抑制结构的平-扭耦联振动并满足经济性要求。另外,假定复位丝与耗能丝面积比为2,计算了不同地震输入下阻尼器对多自由度偏心结构的振动控制。
(5)为了改善多目标优化算法的计算效率和效果以实现耗能减震结构的优化设计,在二元锦标赛遗传算法基础上改进提出了新的一轮锦标赛遗传算法,该算法采用无回放随机联赛选择机制,根据Pareto支配关系复制个体,每一代选择过程在一轮循环中完成;为了将约束优化问题转化为无约束问题,依据Pareto优于准则建立了能体现约束信息的约束子目标函数。测试函数的比较计算证明该算法能够在较短时间内搜索到更多均匀分布的Pareto解。分别针对对称结构和均匀偏心结构,建立了基于Pareto思想的减震结构多目标优化模型,实现了阻尼器数量、位置和减震效果的共同优化。
Superelastic shape memory alloy (SMA) is a perfect material for passive control of structures. Numerous studies have been conducted in using SMA for structural vibration control, and some developments have been attained. However, there still exist some problems in modeling and application of SMA. Further investigations are carried out in this thesis, concering constitutive model, damper design, vibration analysis and optimization design of damped structures.
(1) Experiments on the mechanical behaviors of the superelastic NiTi wires are performed. Cyclic number, loading rate, strain amplitude, and temperature are considered to investigate their effects on the hysteretic curves and the mechanical parameters of SMA (such as critical stress, energy dissipation per cycle, modulus and residual strain). Based on the experimental results, the Lagoudas' multilinear model is modified to reflect the dynamic hysteretic hehaviors or the cyclic mechanical behaviors of SMA, considering loading rate or cyclic number's effects on the parameters of the model, respectively. In addition, the Graesser's model is improved to reflect the variations of the hysteretic behaviors of SMA during loading and unloading.
(2) An innovative recentering damping device (RDD) is designed and manufactured, which provides a perfect energy dissipation compatible with a negligible residual displacement, and has such advantages as the simple configuration and the uniform stresses of the wires. Extensive experiments are carried out to investigate the influences of cyclic number, displacement amplitude and loading frequency on the damper's hysteretic curves and the mechanical behaviors (such as maximum output force, residual deflection, secant stiffness, dissipated energy per cycle and equivalent viscous damping ratio). By analyzing the working mechanism of the RDD, a theoretical model is set up on the basis of the multilinear dynamic model of SMA. Some numerical simulations are taken to compare the mechanical behaviors of the damper with different ratio of cross-sectional area of recentering wires to dissipating wires.
(3) Seismic nonlinear response time histories and energy analyses of a symmetric structure with the RDD are simulated. Taken a three-story RC frame as an example, some comparisons of the seismic response of the controlled structure and the amount of gross SMA wires are executed, given the same amount of gross wires and the same maximum inter-story displacement ratio of the controlled structure, respectively, and a combination (ratio of cross-sectional area of recentering wires to dissipating wires) of 0.67～2 is suggested to satisfy the desired seismic response of the RDD structure and the economical efficiency. A two-story steel frame model with the RDD is tested on the shaking table, and the results approve that the RDD can decrease the structural vibration and mitigate the residual displacement effectively, which agrees with the theoretical results.
(4) Seismic response time histories and energy analyses of an eccentric structure with the RDD excited by bi-directional earthquakes are simulated. Taken an eccentric single-story structure as an example, some comparisons of the seismic response of the controlled structure and the amount of gross wires are executed, given the same amount of gross wires and the same maximum inter-story displacement ratio of the controlled structure, respectively. The results show that the damper with a combination of 0.67～2 can eliminate the coupled lateral-torsional response of the structure at a low cost. Moreover, the seismic response of a three-story eccentric structure controlled by the RDD with a combination of 2 is simulated, considering different earthquakes.
(5) To improve computational efficiency of multiobjective optimization algorithms for optimal design of damped structures, a novel one-round tournament genetic algorithm is advanced on the basis of the two-branch tournament genetic algorithm. Using stochastic tournament selection without replacement, the individuals are copied according to the Pareto relationships, and selections in each generation are accomplished in one-round repetition. In order to transfer a constrainted problem into an unconstrainted one, each objective function is revised as a constrainted objective function, according to the precedence rules. Test functions testify that the novel algorithm can search more Pareto optima stretching along the Pareto front in a shorter time. Based on the Pareto optimization theory, the multiobjective optimization models of controlled symmetric and eccentric structures are established to achieve the Pareto optima of the number and the placement of dampers and the seismic response of controlled structures.
引文
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