Vibration, Buckling and Dynamic Instability Studies on Fgm Plates Under Conservative and Non-Conservative System of Forces

Abstract

The present study investigates the vibration and buckling behaviour of porous Functionally Graded Sandwich Plates (FGSP) with and without cutouts subjected to Non-uniform Inplane Edge Loads (NIELs) and localised in-plane edge loads in nonthermal (mechanical) and thermal environment (thermo-mechanical) using Finite Element (FE) method. Additionally, the study explores dynamic instability characteristics of the FGSP under a non-thermal environment. The study is carried out by selecting different kinds of sandwich configurations such that there is no material mismatch along the thickness directions. Due to the material asymmetry occurring in the sandwich configurations, a physical neutral surface is incorporated in the formulation. The porosity imperfections that occur during the manufacturing process of FGSPs are accounted for in this study by considering different types of porosity distribution models and are modelled as the criteria of stiffness reduction. The plate members made up of FGSPs commonly features cutouts due to practical requirements and experience flutter due to a non-conservative system of forces. As a result, structural responses such as vibration, buckling and dynamic instability of porous FGSP are affected. Therefore, this work aims to examine the vibration, buckling and dynamic instability characteristics of porous FGSP with and without geometric discontinuity subjected to NIELs and localised edge loads under non-thermal and thermal environments. The material properties of porous FGSPs are evaluated using modified power law and sigmoid function and are assumed to be temperature-dependent for plates studied in a thermal environment. The application of different cases of NIELs on the plate with cutouts in thermal and non-thermal environments results in non-uniform stress distribution. Hence a novel dynamic approach has been proposed to evaluate buckling loads by implementing two sets of boundary conditions. The first set of the boundary conditions calculates pre-buckling stress, while the second set calculates critical buckling loads. The study includes a convergence analysis of the proposed FE formulations and further validation through comparisons with numerical results available in the published literature. After verifying the theoretical formulations and solution methodologies, parametric studies are conducted by varying aspect ratios, layer schemes, support conditions, side-to-thickness ratios, sandwich configurations, cutout ratios, and more. The numerical solutions based on the current First-order Shear Deformation Theory (FSDT) can serve as a benchmark for future reference when dealing with porous FGSPs containing cutouts. It is expected that the findings from this study will offer valuable insights for the analysis and design of Functionally Graded Material (FGM) plates in practical engineering applications.