形状记忆合金变刚度结构振动控制仿真研究

Simulation Study on Vibration Control of VariableStiffness Structure with Shape Memory Alloy

关键词:  形状记忆合金  本构模型  变刚度振动控制  非线性振动  仿真研究

Key words:  Shape memory alloy  Constitutive model  Variable stiffness vibration control  Nonlinear vibration  Simulation research

摘要:

为了实现Ti50Ni41Cu9形状记忆合金(SMA)用于复杂结构振动控制的动力学分析，掌握变刚度振动控制的机理和控制规律，基于Kelvin-Voigt粘弹性本构关系，建立了适用于动力学分析的SMA本构模型，并通过ABAQUS编写材料本构程序，形成有效的SMA结构动力学有限元仿真方法，实现了多参数影响下SMA结构的非线性稳态和瞬态动力学仿真计算。计算结果表明:SMA的宏观本构模型能够较好地反映材料动力学性能的变化特征，编制的UMAT子程序与试验数据吻合较好；变刚度控制可以有效降低定频激励引起的稳态响应，对于悬臂板结构响应降幅在40%以上；控制速率与响应的最终变化程度无关，但会引起系统非线性特征，从而影响控制过程需要的时间；采用对向变刚度控制可以降低跨越主频的瞬态振动响应，变温速率越快，系统的峰值响应越小，快速变温时会产生自发频带现象，其对主频能量有显著分散作用，可以一定程度上抑制最大响应峰值。

Abstract:

In order to realize the dynamic analysis of the complex structure with shape memory alloy (SMA)Ti50Ni41Cu9 and obtain the mechanism and control law of variable stiffness vibration abatement， the constitutive equation of SMA is established based on the Kelvin-Voigt model. And through compiling the material constitutive program with the ABAQUS， an effective dynamic simulation method is developed to realize the nonlinear steady state and transient dynamic simulation of the SMA structure under the influence of multiple parameters. The calculation results show that the macroscopic constitutive model of SMA can better reflect the dynamic characteristics of the material and the user-defined material mechanical behavior (UMAT) subroutine is in good agreement with the experimental data. The variable stiffness control can effectively reduce the steady-state response caused by constant-frequency excitation， such as a more than 40% decrease of amplitude for cantilever plate and the control rate of the SMA is independent of the final response， but it will cause the non-linear characteristic of the system and affect the time required for the control process. For the transient vibration response through the main frequency， the faster the temperature change rate， the smaller the peak response of the system because spontaneous frequency band induced by rapid temperature change has significant dispersion effect on vibration energy of the main frequency， to some extent， which can inhibit the maximum response peak.