Vibration Response Analysis of Tapered Porous FGM Plate Resting on Elastic Foundation

This paper attempts to demonstrate the vibration response of porous Functionally Graded Material (FGM) plate with variable thickness. For the first time, the porous tapered FGM plate being considered is mathematically modeled and assumed to be resting on a linear, parabolic, sinusoidal, and exponential varying Winkler's elastic foundation. The even and uneven porosity distribution as a micro-defect is assumed in a tapered FGM plate that varies according to well-defined mathematical rules. The tapered FGM plate, across the edges, is supported with various boundary conditions. Simple Power (P-) and Sigmoid (S-) Law have been chosen for the homogenization of material properties that are tailored in the thickness direction. First-order shear deformation theory (FSDT) is applied to describe the displacement function for computing the strain field. The variational approach has been used to establish the formulation for free vibration response. The equation of motion has been derived using Hamilton's principle and solved by implementing Galerkin Vlasov's method. Parametric studies on elastic foundations have been done to explore the results and relevance to the real problems. It was observed that variable foundation has a significant effect on the tapered FGM plate rather than the tapered homogenous plate. In addition, it was witnessed that the effect of variable foundation effect diminishes as a constraint on the edges of the tapered FGM plate increases. Also, some benchmark results based on the porosity effect and the influence of variable elastic foundations are exhibited in this study for future reference.