复杂边界下功能梯度微结构多场耦合准三维建模及振动特性分析

With the application of functionally graded materials (FGMs) in micro electro mechanical system (MEMS), size dependent dynamic analysis of FGM micro-structures has increasingly been the focus of attention. However, due to the spatial variation of material properties and the existence of size effects, it is difficult to establish the reliable model for vibration analysis of FGM micro-structures. For the electrically actuated FGM micro-structures, electromechanical fluid coupling exists in their operation. At present, there is lacking of efficient models and computational methods to analyze the multi-physical fields coupling vibration problems for FGM micro-structures, which restricts the theoretical research of MEMS. The attempt of the study is to establish a reliable and efficient quasi-three dimensional model for multi-physical fields coupling vibration analysis of FGM micro-structures considering electrical actuation and squeeze film damping which also capture the size effects. The proposed model is suitable for the arbitrarily thick FGM micro-structures with general boundary conditions. Based on this model, systemic theoretical investigations and experimental studies are carried out to demonstrate the influence of size effects, boundary conditions, material distributions, thickness stretching, damping effects and electrical parameters on the vibration behaviors of FGM micro-structures, hoping to provide effective guidance for design and optimization of FGM micro-structures.

随着功能梯度材料在微机电系统中的应用，计及尺度效应的功能梯度微结构动力学问题逐渐成为关注的焦点。然而，由于材料特性的空间变化以及尺度效应的存在，功能梯度微结构振动模型的建立要复杂困难得多。对于静电驱动微结构而言，常涉及机-电-流体多物理场耦合问题，而目前对微尺度效应下功能梯度微结构多场耦合振动问题尚缺乏有效的建模分析方法，理论研究相对滞后。本课题旨在建立微尺度效应下，考虑静电力和阻尼效应，适用复杂边界条件的功能梯度微结构机-电-流体多物理场耦合振动的准三维理论模型和分析方法，并结合理论分析和实验研究等手段深入探究尺度效应、边界条件、材料分布、横向变形、阻尼效应、电场参数等因素对微结构振动行为的影响，以期为功能梯度微结构的设计、优化提供准确可靠的理论分析模型及机理性数据参考。

随着材料科学和制造技术的发展，功能梯度材料已开始应用于微机电器件中以满足特定的设计要求。计及尺度效应的功能梯度微结构动力学问题逐渐成为关注的焦点和难点。本项目以功能梯度微结构为研究对象，开展了复杂边界条件下功能梯度微结构的准三维动力学模型以及多场耦合振动特性的研究。首先，在非局部理论的框架下建立了可以满足不同精度要求的准三维本构关系，通过变分法以及广义谱方法建立了复杂边界下功能梯度微结构的准三维动力学模型。其次，在此基础上进一步考虑温度场、电场等因素的影响，建立了功能梯度微结构在多物理场耦合作用下动力学模型。最后，基于上述模型开展了功能梯度微结构的振动特性以及机理研究，深入探究尺度效应、边界条件、材料分布、横向变形、温度参数等因素对功能梯度微结构振动行为的影响规律。本项目的实施揭示了复杂边界下功能梯度微结构的振动特性，为微机电系统中功能梯度微结构的设计、优化提供准确可靠的理论分析模型及机理性数据参考。