SMA超弹性特性的分段线性化及其结构稳态响应研究
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摘要
当温度 T TAF时 ,在 SMA的加—卸载循环内 ,应力和应变之间形成无残余变形的迟滞环 ,这种称之为超弹性的行为在振动被动控制中具有广泛的应用前景。但是 ,由于材料内部发生的正、逆相变 ,使得应力、应变、温度以及马氏体百分数之间存在强耦合非线性关系 ,给分析和计算造成很大的困难。从 Tanaka系列的 SMA本构关系出发 ,建立 SMA超弹性应力和应变之间的分段线性化模型。该模型的本构方程形式简洁、参数确定方便 ,消除了应力、应变和马氏体百分数之间的耦合性 ,因此易于应用。为了研究具有超弹性 SMA元件的结构的稳态振动响应 ,将分段线性化处理的应力应变关系展成傅里叶级数 ,用于揭示具有 SMA丝约束的悬臂梁在支座扰动下的稳态响应特性。并定义了 SMA超弹性迟滞阻尼的等效阻尼因子。
In the case of temperature TA f ,a hysteresis loop without plastic strain occurs during each loading—unloading cycle of SMA.The unique property which is often referred to as superelastic can be widely used in passive vibration control of structures.However,strongly coupled nonlinear relations among stress,strain,temperature and transformation volume fraction make analysis and numerical approach extremely difficult.This paper develops the piecewise linear model of SMA superelastic hysteresis stress—strain relation based on the model of Tanaka.The constitutive equations proposed by the authors having simply and uncoupled form,are convenient for applications.Fourier series of the restoring stress is obtained.The model is empolyed in the analysis of the steady state response characteristics of a cantilever beam with constraint of SMA wires excited by sinusoidally base motion.The equivalent damping factor of the system is also presented in the paper.
In the case of temperature TA f ,a hysteresis loop without plastic strain occurs during each loading—unloading cycle of SMA.The unique property which is often referred to as superelastic can be widely used in passive vibration control of structures.However,strongly coupled nonlinear relations among stress,strain,temperature and transformation volume fraction make analysis and numerical approach extremely difficult.This paper develops the piecewise linear model of SMA superelastic hysteresis stress—strain relation based on the model of Tanaka.The constitutive equations proposed by the authors having simply and uncoupled form,are convenient for applications.Fourier series of the restoring stress is obtained.The model is empolyed in the analysis of the steady state response characteristics of a cantilever beam with constraint of SMA wires excited by sinusoidally base motion.The equivalent damping factor of the system is also presented in the paper.
引文
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[8] 王社良 ,苏三庆 .形状记忆合金的超弹性恢复力模型及其结构抗震控制 [J] .工业建筑 ,1999,2 9( 3 ) :49～ 5 2 .
[9] L iang C,Rogers C A.One-dimensional thermomechanical constitutive relations for shape memory materials[J] .JIntell MaterSyst Struct,1990 ,1:2 0 7～ 2 3 4 .
[2 ] 王益槐 ,任勇生 .用于振动、冲击和噪声控制的 SMA智能复合材料结构 [J] .力学与实践 ,1999,2 1( 2 ) :1～ 13 .
[3 ] 吴波 ,李惠 .形状记忆合金在土木工程中的应用 [J] .世界地震工程 ,1999,15 ( 3 ) :1～ 13 .
[4] Birman V.Effect of SMA dam pers on nonlinear vibrations of elastic sturctures[J] .SPIE,1997,3 0 3 9:2 68～ 2 76.
[5 ] Feng Z C,L i D Z.Dynamics of a mechanical system with a shape memory alloy bar[J] .JIntell Mater Syst Struct,1996,7:3 99～ 410 .
[6] Graesser E J,Cozzarelli F A.A proposed three-dim ensional constitutive model for shape memory alloys[J] .JIntell MaterSyst Struct,1994,5 :78～ 89.
[7] Thomson P,Balas G J.Pseudoelastic hysteresis models of shape-memory wires and effects on passive structural damping[J] .SPIE,1999,2 445 :188～ 189.
[8] 王社良 ,苏三庆 .形状记忆合金的超弹性恢复力模型及其结构抗震控制 [J] .工业建筑 ,1999,2 9( 3 ) :49～ 5 2 .
[9] L iang C,Rogers C A.One-dimensional thermomechanical constitutive relations for shape memory materials[J] .JIntell MaterSyst Struct,1990 ,1:2 0 7～ 2 3 4 .
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