中文摘要：

在对叠层板状元件的固有振动特性的理论分析中，提出了单梁与多梁对接的力学模型；在研究叠层板状元件湿模态固有频率与振型的理论分析与计算中，采用了以干模态振型函数序列作为试函数对复模态振型方程进行变分求解的方法；在研究叠层板状元件的稳定性时，采用直接法和变分法对其临界流速和失稳挠曲线进行分析和计算，二者的计算结果吻合较好；此外，对结构在非线性支承下的流致振动与稳定性作了初步研究。

英文摘要：

A model of multi-parallel-beam joined with single-beam is adopted in the theoretical analysis of the natural vibration characteristics of the parallel-plate assembly. In the study of theoretical calculation and analysis of the wet-modal natural frequencies and modes, the dry-modal mode functions are used as trial functions to solve the complex-modal mode equation by variational method. In the study of stability of the parallel-plate assembly, its critical flow velocity and destabilizing deflection are analyzed and calculated by direct method and variational method, and the results of the two methods agree with each other. In addition, this thesis preliminarily studies the flow-induced vibration and stability of the parallel-plate assembly with nonlinear support.