Abstract

The present study includes the free vibration analysis of geometrically imperfect and discontinuous porous functionally graded bi-directional plate (B-FGP) resting on an elastic foundation in a thermal environment. The geometric discontinuity is present in the form of a circular cutout at the center of the plate whereas initial imperfections have been incorporated in terms of geometric as well as porosity inclusions. The kinematic formulation is based on the refined non-polynomial trigonometric higher-order shear deformation theory (HSDT). A new porosity model has been developed to incorporate the influence of the microstructure defect on the effective material properties of the B-FGP. The gradation of properties is done along the thickness (z-direction) as well as the length (x-direction) of the plate using the power-law distribution. A new expression has been given to obtain the solution of the non-linear temperature rise along the thickness of the B-FGP. A $C^0$ continuous Lagrangian four-noded quadrilateral element has been used to perform the finite element formulation with eight degrees of freedom per node. The equations of motion have been derived using a variational approach. The validation and comparative study have been done to authenticate the present formulation. The influence of the cutout radius, elastic foundation parameters, porosity, thermal environment, geometric imperfection, and volume fraction indexes has been discussed in detail.

摘要

本研究包括在热环境中基于弹性地基的几何缺陷和不连续多孔功能梯度双向板 (B-FGP) 的自由振动分析。几何不连续性以板中心的圆形切口的形式存在，而初始缺陷已在几何和孔隙夹杂物方面合并。运动学公式基于改进的非多项式三角高阶剪切变形理论 (HSDT)。开发了一种新的孔隙率模型，以纳入微观结构缺陷对 B-FGP 有效材料特性的影响。属性的渐变是沿着厚度（z方向）以及长度（x-方向）的板块使用幂律分布。给出了一个新的表达式来获得沿 B-FGP 厚度的非线性温升的解。A$C^0$连续拉格朗日四节点四边形单元已用于执行每个节点具有八个自由度的有限元公式。已经使用变分方法导出了运动方程。已经进行了验证和比较研究以验证本制剂。详细讨论了切口半径、弹性地基参数、孔隙率、热环境、几何缺陷和体积分数指数的影响。