基于尺寸效应的FG-SMA微梁非线性自由振动特性研究

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。本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。

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

Shape Memory Alloys have excellent characteristics, such as low phase transition temperature, high output stress, low energy consumption, low driving voltage, large recoverable strain, and good bio-compatibility. With the further development of the Shape Memory Alloy technology, some scholars proposed that the functional gradient shape memory alloy material used in the micro-electro-mechanical system and other intelligent micro-structure will make it have better characteristics. Therefore, the study of nonlinear free vibration characteristics of electro-mechanical coupling FG-SMA micro-structures is of importance. Based on the von Karman geometric nonlinear theory, considering the influence of electrostatic force, intermolecular force and the size effect, the functional gradient shape memory alloy micro-beam model fixed at both ends is established. The multi-field coupling nonlinear vibration before and after the phase transformation of the alloy micro-beams is studied in depth. The effects of size effect parameters, geometrical parameters and phase-change parameters on the free vibration characteristics of the functional gradient shape memory alloy micro-beams are analyzed.