自复位记忆合金阻尼器的数值模拟及工程应用
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摘要
形状记忆合金（Shape Memory Alloy）的超弹性是指材料在外力作用下会发生马氏体相变，产生较大的变形，应力去除后会发生马氏体逆相变，并恢复到原来的形状。利用记忆合金的超弹性可以耗能，开发出了多种自复位记忆合金阻尼器，部分记忆合金阻尼器也在实际工程中得到了应用。利用自复位的记忆合金阻尼器进行耗能减震时，不需要外部能量的输入，结构没有残余侧移，值得重视。
为推广记忆合金阻尼器的工程应用，本文利用记忆合金材料的Brinson本构模型，通过MATLAB编程进行阻尼器的力学性能模拟，并在此基础上通过时域积分进行SMA阻尼器减震效果分析与评价。本文具体工作如下：
1.介绍了对记忆合金的超弹特性，并对直径1mm的NiTi SMA丝进行了力学试验，研究了加载速率、应变幅值及循环次数等因素对SMA超弹特性的影响。同时，介绍了记忆合金的唯象本构模型的发展演变过程，并利用Brinson本构模型在MATLAB中编程得到材料的相变运动方程的数值解，从而描述SMA材料的应力-应变关系。实验与理论分析结果表明采用Brinson模型的数值模拟能很好的反映SMA材料的超弹性。
2.介绍了三种典型的自复位SMA阻尼器构造，通过将阻尼器元件分为回位组和耗能组，并在此基础上研究了阻尼器发生相对位移时各功能组元件的内力变化。针对利用预张拉的SMA丝组耗能、弹簧提供回位力的自复位SMA阻尼器，建立了力学平衡方程，并在Brinson本构模型的基础上，根据阻尼器内部相对位移推算出耗能组反力，叠加弹簧反力，借助MATLAB编程从而计算出整个阻尼器的力-位移滞回曲线。
3.利用记忆合金本构模型，通过MATLAB编程，对布置自复位SMA阻尼器进行减震的三层钢框架结构进行了结构动力响应分析。具体分析过程如下：首先将结构模型简化为层间剪切模型，并提取出主结构的刚度矩阵、质量矩阵和阻尼矩阵；建立被动结构的动力方程，利用Wilson-θ法并考虑阻尼器提供的控制力，在MATLAB软件中编制了结构的动态仿真分析程序。选取El Centro(NS)波、Northridge(NS)波和Taft波作为地震激励，对结构分别进行了有控和无控的动力响应分析，对比了两种情况下结构的层间位移响应、楼层最大加速度与最大楼层剪力。
4.为评价自复位SMA阻尼器的振动控制效果，对自复位SMA阻尼器进行了Benchmark结构分析，具体为：针对高、中、低层三种Benchmark结构，在SAP2000中建立了有限元模型，分析了有控与无控结构的地震动响应，评价了自复位SMA阻尼器对不同结构的减震作用。另外，对采用自复位SMA阻尼器加强的某6层宿舍楼加固工程，分析了阻尼器布置方式对结构减震效果的影响。
For shape memory alloys (SMAs) in their austenitic state, stress induced martensitetransformation occurs upon loading, resulting in large deformations. Reverse transformationsfrom martensite to austenite occurs when withdrawing applied loads. This results in thealloys restoring their initial shape. This is called the super elastic effect of SMA. Manytypes of SMA based self-centering dampers were presented recently with using superelasticity,and some dampers were applied in the real conditions. When using the self-centering SMAdampers for vibration controlling during earthquake event, there are no needs for outer energyinputs and no residual interstorey drifts. This attracts more attentions of the engineers.
To extend the applications of the SMA damper, this paper investigates the numeralsimulations of the mechanical behavior of the SMA damper by programing in MATLABenvironments based on the material constitutive models. Moreover, the vibration controleffects of the SMA damper are evaluated by time history analysis of passive structures. Theworks of this paper are listed in details as follows:
1. The superelastic behavior of SMAs are introduced. The tensional experiments of1mm diameter NiTi SMA wires were conducted, and the effects of loading rate, strainamplitude and loading cycles on superelasticity are studied. The evolution process of severalphenomenologital constitutive models are introduced. Among these models, the Brinsonconstitutive model is selected to describe the strain-stress relationship of the superelastic SMAby programming in MATLAB environments. Good agreement between the experimental andnumerical results is observed.
2. The configurations are introduced and summarized based on three types ofself-centering SMA dampers. These dampers consists of two functional groups, recentring andenergy dissipating groups. The damper working principle is studied by figuring out theinternal force changement with relative displacement of both ends of the damper. For theSMA damper with springs offering restore force and two groups of SMA wires dissipatingenergy, the force equilibrium equations are presented. With using the Brinson model, theforce-displacement relationships of the damper are described by programming in MATLABenvironments.
3. For a three-storey steel frame equipped with the SMA damper, the structural responseis simulated by time history analysis program in MATLAB environments based on materialconstitutive model. The simulation is conducted as follows: The main frame is simplied as a inter-story shearing structure. Then, the mass, stiffness matrix together with the dampingmatrix of the main structure are presented. The dynamic equations with considering thecontrolling force offered by the SMA damper are founded. With using Wilson-θ method, theequations are solved and the structural responses are simulated by time history analysisprogram in MATLAB environments. The earthquake waves, such as El-Centro(NS)、Northridge(NS) and Taft waves, are selected as earthquake excitations, the structuralresponses including inter-storey drift, floor accelerations, inter-storey shear force withconsidering the damper effect are contrasted with those without the damper.
4. To assess the vibration control effect of the SMA damper, the Benchmark structuresare analyzed as follows: For high, medium and lower Benchmark frames, the finite elementmodels are set up in SAP2000environments, the structural responses with equipped the SMAdamper and without the damper are contrasted. The vibration control effects of the damper areevaluated. In addition, the SMA dampers was applied to strengthen a6-storey frame. Thestructural vibration control effects are analyzed with considering the damper distributions
为推广记忆合金阻尼器的工程应用，本文利用记忆合金材料的Brinson本构模型，通过MATLAB编程进行阻尼器的力学性能模拟，并在此基础上通过时域积分进行SMA阻尼器减震效果分析与评价。本文具体工作如下：
1.介绍了对记忆合金的超弹特性，并对直径1mm的NiTi SMA丝进行了力学试验，研究了加载速率、应变幅值及循环次数等因素对SMA超弹特性的影响。同时，介绍了记忆合金的唯象本构模型的发展演变过程，并利用Brinson本构模型在MATLAB中编程得到材料的相变运动方程的数值解，从而描述SMA材料的应力-应变关系。实验与理论分析结果表明采用Brinson模型的数值模拟能很好的反映SMA材料的超弹性。
2.介绍了三种典型的自复位SMA阻尼器构造，通过将阻尼器元件分为回位组和耗能组，并在此基础上研究了阻尼器发生相对位移时各功能组元件的内力变化。针对利用预张拉的SMA丝组耗能、弹簧提供回位力的自复位SMA阻尼器，建立了力学平衡方程，并在Brinson本构模型的基础上，根据阻尼器内部相对位移推算出耗能组反力，叠加弹簧反力，借助MATLAB编程从而计算出整个阻尼器的力-位移滞回曲线。
3.利用记忆合金本构模型，通过MATLAB编程，对布置自复位SMA阻尼器进行减震的三层钢框架结构进行了结构动力响应分析。具体分析过程如下：首先将结构模型简化为层间剪切模型，并提取出主结构的刚度矩阵、质量矩阵和阻尼矩阵；建立被动结构的动力方程，利用Wilson-θ法并考虑阻尼器提供的控制力，在MATLAB软件中编制了结构的动态仿真分析程序。选取El Centro(NS)波、Northridge(NS)波和Taft波作为地震激励，对结构分别进行了有控和无控的动力响应分析，对比了两种情况下结构的层间位移响应、楼层最大加速度与最大楼层剪力。
4.为评价自复位SMA阻尼器的振动控制效果，对自复位SMA阻尼器进行了Benchmark结构分析，具体为：针对高、中、低层三种Benchmark结构，在SAP2000中建立了有限元模型，分析了有控与无控结构的地震动响应，评价了自复位SMA阻尼器对不同结构的减震作用。另外，对采用自复位SMA阻尼器加强的某6层宿舍楼加固工程，分析了阻尼器布置方式对结构减震效果的影响。
For shape memory alloys (SMAs) in their austenitic state, stress induced martensitetransformation occurs upon loading, resulting in large deformations. Reverse transformationsfrom martensite to austenite occurs when withdrawing applied loads. This results in thealloys restoring their initial shape. This is called the super elastic effect of SMA. Manytypes of SMA based self-centering dampers were presented recently with using superelasticity,and some dampers were applied in the real conditions. When using the self-centering SMAdampers for vibration controlling during earthquake event, there are no needs for outer energyinputs and no residual interstorey drifts. This attracts more attentions of the engineers.
To extend the applications of the SMA damper, this paper investigates the numeralsimulations of the mechanical behavior of the SMA damper by programing in MATLABenvironments based on the material constitutive models. Moreover, the vibration controleffects of the SMA damper are evaluated by time history analysis of passive structures. Theworks of this paper are listed in details as follows:
1. The superelastic behavior of SMAs are introduced. The tensional experiments of1mm diameter NiTi SMA wires were conducted, and the effects of loading rate, strainamplitude and loading cycles on superelasticity are studied. The evolution process of severalphenomenologital constitutive models are introduced. Among these models, the Brinsonconstitutive model is selected to describe the strain-stress relationship of the superelastic SMAby programming in MATLAB environments. Good agreement between the experimental andnumerical results is observed.
2. The configurations are introduced and summarized based on three types ofself-centering SMA dampers. These dampers consists of two functional groups, recentring andenergy dissipating groups. The damper working principle is studied by figuring out theinternal force changement with relative displacement of both ends of the damper. For theSMA damper with springs offering restore force and two groups of SMA wires dissipatingenergy, the force equilibrium equations are presented. With using the Brinson model, theforce-displacement relationships of the damper are described by programming in MATLABenvironments.
3. For a three-storey steel frame equipped with the SMA damper, the structural responseis simulated by time history analysis program in MATLAB environments based on materialconstitutive model. The simulation is conducted as follows: The main frame is simplied as a inter-story shearing structure. Then, the mass, stiffness matrix together with the dampingmatrix of the main structure are presented. The dynamic equations with considering thecontrolling force offered by the SMA damper are founded. With using Wilson-θ method, theequations are solved and the structural responses are simulated by time history analysisprogram in MATLAB environments. The earthquake waves, such as El-Centro(NS)、Northridge(NS) and Taft waves, are selected as earthquake excitations, the structuralresponses including inter-storey drift, floor accelerations, inter-storey shear force withconsidering the damper effect are contrasted with those without the damper.
4. To assess the vibration control effect of the SMA damper, the Benchmark structuresare analyzed as follows: For high, medium and lower Benchmark frames, the finite elementmodels are set up in SAP2000environments, the structural responses with equipped the SMAdamper and without the damper are contrasted. The vibration control effects of the damper areevaluated. In addition, the SMA dampers was applied to strengthen a6-storey frame. Thestructural vibration control effects are analyzed with considering the damper distributions
引文
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