半无限地基上三维层板受冲击荷载的谱单元解法

Analysis of 3D Stratified Plate Subjected to Impulsive Load over Semi-infinite Foundation Using Spectral Element

提出一类用于三维层板的谱单元,使其解决三维层状夹板在半无限地基上受冲击荷载的动力问题。频域内,结构中的每一层被模拟为两节点谱单元或单节点谱单元。层单元中的波动解采用入射波和反射波解的叠加形式。进而利用快速傅立叶变换技术(FFT),得到时域内三维层状夹板的瞬态响应分析的结果。以半无限地基上双层板为例,对其进行了矩形脉冲荷载下的动力响应分析,并与有限元的计算结果进行了对比,两者的吻合良好。通过对不同夹板厚度和弹模的分析比较,得到对于设计隔振系统的优化思路。

A new type of spectral element was proposed to solve the problems of 3D multi-layer plate on semi-infinite foundation subjected to impulsive load. In frequency domain, each layer in structure was simulated as two-node layer spectral element or one-node spectral element. The wave propagation in each layer element was solved by the superposition of incident wave and reflected wave. The transient time-domain response of 3D layered plate was obtained by fast Fourier transform （FFT）. Both the proposed method and finite element method were applied to analyze the dynamic responses of a two-layer plate subjected to rectangular impulsive load, and the results show a good agreement. Besides, by comparing the solutions of the stratified plates with different thicknesses and elastic moduli, an optimal strategy was obtained for the design of vibration isolation system..