波在不同组分功能梯度材料介质中的传播特性

摘要

采用有限体积法构造了功能梯度材料中波动方程的显式差分方程,结合冻结系数方法和Fourier方法证明了差分方程是条件稳定的,并得到了差分方程的稳定性条件,然后通过与已有结果的对比证明了差分方程的正确性；计算了不同组分功能梯度材料板在瞬态位移激励下的动态响应,分析了组分幂函数变化对波到达末端时间、波幅、应力等的影响.%The dynamic response of functionally graded material plates with different material component distributions under transient excitations are analyzed using finite volume method. First,a differential equation of quadratic convergence is constructed to do analysis. Then,a detailed convergence analysis is conducted to ascertain the stability criteria of the differential equation. To validate the numerical scheme,we calculated an identical problem to that in a reference. And both the results agree well with each other. Finally,the dynamic responses of functionally graded material plates with different material component distributions under transient excitations are analyzed. It is known from the results that different material component distributions have a significant influence on the dynamic response of functionally graded material plate.