Influence of microstructural defects on vibration characteristics of sandwich double FGM layer under mixed boundary conditions

The influence of porosity inclusion and geometric imperfections on the vibrational frequency of sandwich functionally graded material (SFGM) plates under conventional and unconventional boundary conditions has been investigated in this article. The generalised governing equations for free vibration are formulated for the SFGM plates based on the Lagrangian approach using power law distribution. The non-polynomial higher-order shear deformation theory (HSDT) is employed for the vibration analysis of SFGM plate structure. A new porosity modal function has been used for SFGM plate analysis, and microstructural imperfections are incorporated as porosity inclusions. The various geometric imperfections are modelled using the generic function. Convergence and validation have been carried out and results are validated with the literatures. The influence of volume fraction exponent, porosity volume fractions, geometric imperfections, even, mixed, and uneven porosity distribution on the vibrational frequency of SFGM plates under the unconventional boundary conditions have been investigated. The current findings are achieved based on the Lagrangian approach using finite element method (FEM) with four-nodes and seven-degrees of freedom (DOF) per node. The mentioned influences have a significant impact on the vibrational characteristics of the SFGM plates with double FGM layer under the various boundary conditions using higher-order shear deformation theory (HSDT).