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- 2020
基于正弦剪切变形理论的功能梯度材料三明治微梁的静动态特性
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Abstract:
基于修正的偶应力理论和正弦剪切变形梁理论，研究了功能梯度材料三明治微梁的静态弯曲和自由振动行为。考虑两种不同类型的功能梯度材料三明治微梁，根据哈密顿变分原理建立其静动态力学行为的控制方程，应用Navier解法，得到了简支边界条件下弯曲变形和振动频率的解析解，同时，给出了固支等边界条件时的里兹法求解过程。数值算例表明，功能梯度三明治微梁的静动态力学行为具有明显的尺度效应，微梁的无量纲厚度、功能梯度指数、长厚比和结构形式等因素对其静动态响应有很大影响，相关结果和规律对功能梯度材料三明治微梁的结构设计和性能优化等实际工程应用具有一定的指导意义。 The static bending and free vibration of functionally graded (FG) sandwich microbeams were investigated based on the modified couple stress theory (MCST) and the sinusoidal shear deformation theory. The two types of FG sandwich microbeams were taken into consideration. Governing equations were derived by using the Hamilton' principle. Analytical solutions of bending and vibration with simply supported boundary condition were obtained in the basis of the Navier's solution procedure. The results with general boundary conditions were obtained by using the Ritz method. The numerical results demonstrate that the static and dynamic behavior of FG sandwich microbeams is size-dependent and affected by the microbeam's nondimensional thickness, FG index, the ratio of length to thickness and the structure type. This study may be helpful for the design and performance optimization of the FG sandwich structures. 重庆市教育委员会科学技术研究计划青年项目（KJQN201803802）；国家自然科学基金（11802101
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