Vibration response of a geometrically discontinuous bi-directional functionally graded plate resting on elastic foundations in thermal environment with initial imperfections

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.