傾斜機能材料平板におけるラム波伝播とその衝撃応答 : 第一報,解析手法
傾斜機能材料平板におけるラム波伝播とその衝撃応答 : 第一報,解析手法
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DOI：
10.1299/kikaia.57.603
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发表时间：
1991-03
期刊：
影响因子：
--
通讯作者：
順二 谷;直 大好
中科院分区：
文献类型：
--
作者：
順二 谷;直 大好
将作者提出的各向异性层合板中Lamb波及其瞬态响应的数值方法推广到功能梯度材料（FGM）板的波传播分析中。板的材料性质沿厚度方向逐渐变化，在板的平面内具有各向异性。将板划分为N个板单元。在单元中，我们假设材料的性质在厚度方向上线性变化，位移场由二阶多项式表示。利用虚功原理建立了近似的动力平衡方程。利用自由边界条件得到了兰姆波的频散关系和模式形状。兰姆波的能量速度与瑞利商的帮助下制定。采用傅立叶变换和模态分析相结合的方法来确定位移响应。本文阐述了该理论的形成过程。
The numerical methods which have been proposed by the present authors for Lamb waves in an anisotropic laminated plate and its transient responses are expanded for the wave propagation analysis of functionally gradient material (FGM) plates. The material properties of the plate change gradually in the thickness direction, and are anisotropic in the plane of the plate. The plate is divided into N plate elements. In the element, we assume that the material properties change linearly in the thickness direction, and that the displacement field is expressed by second-order polynomials. The principle of virtual work is used to develop approximate dynamic equilibrium equations. The dispersion relation and the mode shape of the Lamb waves are obtained by using the free boundary conditions. The energy velocities of the Lamb waves are formulated with the aid of the Rayleigh quotient. The method of Fourier transforms in conjunction with the modal analysis is used to determine the response of displacements. The formulation of the theory is described in this paper.