Abstract

In the present article, the vibration response of geometrically imperfect functionally graded material (FGM) plates with geometric discontinuities and microstructural defects have been investigated. The structural kinematics used in the present study is based on logarithmic shear-strain function. A refined generalized porosity model has been developed to encompass even and uneven types of porosity models available in the literature. The geometric discontinuities have been assimilated in terms of a circular cutout of different sizes at the center of the plate. To incorporate the geometric imperfection, a generic function has been used. A C⁰ continuous iso-parametric finite element formulation has been used to attain the results whereas the accuracy of the present solution has been confirmed by comparing the results with the available literature. The analysis reveals that after a specific cutout radius, the FGM plates exhibit the nonlinear vibration characteristics. It has been observed that the influence of boundary conditions, cutout dimensions, geometric imperfections, and porosity inclusions on frequency parameters are significant. Most of the results presented in this paper are novel and may be treated as benchmark results for future reference.

摘要

在本文中，研究了具有几何不连续性和微结构缺陷的几何缺陷功能梯度材料 (FGM) 板的振动响应。本研究中使用的结构运动学基于对数剪切应变函数。已经开发了一种改进的广义孔隙率模型，以涵盖文献中可用的均匀和不均匀类型的孔隙率模型。几何不连续性已被同化为在板中心的不同尺寸的圆形切口。为了合并几何缺陷，使用了通用函数。交流电⁰连续等参数有限元公式已被用于获得结果，而本解决方案的准确性已通过将结果与现有文献进行比较得到证实。分析表明，在特定的切口半径后，FGM 板表现出非线性振动特性。据观察，边界条件、切口尺寸、几何缺陷和孔隙率夹杂物对频率参数的影响是显着的。本文中的大部分结果都是新颖的，可以作为基准结果以备将来参考。