基于尺寸效应的FG-SMA微梁非线性自由振动特性研究

Nonlinear Vibration Characteristics of FG-SMA Micro-beams Based on Size Effect

形状记忆合金具有相变温度低、输出应力高、能耗小、驱动电压低、可恢复应变大、生物相容性好等特性.随着形状记忆合金制备技术的进一步发展,有学者提出将功能梯度形状记忆合金材料用于微机电系统等智能微结构,将使其具有更优良的特性.因此开展机电多场耦合功能梯度形状记忆合金微结构的非线性自由振动特性研究具有重要研究价值.论文基于冯卡门几何非线性理论,综合考虑静电力和分子间作用力的影响,考虑尺寸效应,基于修正偶应力理论,建立两端固定的功能梯度形状记忆合金微梁模型,对功能梯度形状记忆合金微梁相变前后的机电耦合非线性自由振动问题进行深入研究,分析了尺寸效应参数、几何结构参数和相变参数等对功能梯度形状记忆合金微梁自由振动特性的影响.

Shape memory alloys(SMA)have the characteristics of low phase transition temperature,high output stress,low energy consumption,low driving voltage,large recoverable strain,and good biocompatibility.Functionally graded(FG)materials are a new type of composite materials,whose compositions,structures,physical parameters,chemical parameters,biological parameters and other single or composite properties change continuously in gradient to adapt to different environments and achieve a special function.Recently,the FG-SMA was proposed to be used as smart micro-structures by some scholars,such as in the micro-electro-mechanical system(MEMS)to enhance the performances of the system.Therefore,it is of great research value to study the mechanical characteristics of FG-SMA micro-structures in the MEMS.In this paper,based on von Kármán geometric nonlinearity and modified couple stress theory,and considering the effects of electrostatic forces and intermolecular forces,an electromechanical multi-field coupled nonlinear mechanical model for FG-SMA microbeams considering size effect is established.Then the differential quadrature(DQ)method is used to predict the dynamic pull-in voltages and nonlinear free vibration frequencies of FG-SMA microbeams in the high-temperature austenitic state and low-temperature martensite state,respectively.Furthermore,the effects of size effect parameters,slenderness ratio,fixed electrode shape parameters,and gap ratio of FG-SMA microbeam on nonlinear free vibration are analyzed.The results show that:(1)The nonlinear free vibration frequency and dynamic pull-in voltage of the FG-SMA microbeam are relatively large in the high-temperature austenite state.However,the nonlinear free vibration frequency and the dynamic pull-in voltage are significantly reduced when the martensite phase transition occurs.(2)The FG-SMA microbeam considering size effect has a high equivalent stiffness.As a result,the nonlinear free vibration frequency and the dynamic pull-in voltage are larger than those obtained by the classical microbeam model.(3)The nonlinear free vibration frequency and dynamic pull-in voltage of FG-SMA microbeams increase with the increase of size effect parameter,fixed electrode shape parameter,and gap ratio,but decrease with the increase of slenderness ratio.