Influence of geometric discontinuities and geometric/microstructural defects on the temperature-dependent vibration response of functionally graded plates on elastic foundation

In the present article, the vibrational behaviour of a functionally graded plate (FGP) resting on elastic foundations under a thermal environment with geometric discontinuities and microstructural defects (porosity) has been investigated. The structural kinematics is based on the trigonometric shear-strain function with only four unknowns. The transverse shear stress varies nonlinearly along the thickness. The FGP has geometric discontinuities in the form of a circular cut-out of different dimensions at the centre. The various geometric imperfections are modelled using a generic function, whereas the microstructural defects (porosity) have been included using modified power law. The temperature variation between the surfaces is nonlinear along the thickness direction. The FEM-based solutions are presented using C(0)continuous iso-parametric element. Convergence and validation study have been carried out to demonstrate the efficacy and reliability of the presented results. The effect of porosity inclusion, circular cut-out, elastic foundation, thermal environment, geometric imperfection modes and the volume fraction index have been analysed under conventional and unconventional boundary constraints. It is observed that after a specific dimension of circular cut-out, vibrational behaviour of FGPs exhibits nonlinearity in nature.