Comprehensive analysis of free vibration and bending analysis of porous P- and S- FGM plates with porosity distribution

Vineet Kumar , S.J. Singh , S.P. Harsha

Abstract

This paper aims to study the static and free vibration analysis of porous functionally graded (PFG) plates with different boundary conditions. Two different FGM models for material properties of PFG plate are graded by the rule of mixture (P-FGM) and sigmoidal rule (S-FGM), through the thickness direction of the plate. Plate kinematics are defined by using first-order shear deformation plate theory (FSDPT) to analyze the static behavior based on numerical technique, finite element method (FEM). Also, a four-node quadrilateral plate element with five degrees of freedom at each node has been used during FEM analysis. The governing equations of porous FG plates are developed using variational principles, considering various types of porosity distribution patterns. Moreover, two types of transverse loads including uniformly distributed and sinusoidal loads are considered. The numerical illustrations are presented for static analysis of the PFG plate having two different constituent materials. The accuracy of the present technique is ascertained by comparing the numerical results with available findings in the literature. Then, the effect of aspect ratio, length-to-thickness ratio, porosity parameter, various boundary conditions and power law index on the bending and vibration response of PFG plate are examined to explore the scope of the study. Ultimately, the results of this study provide new avenues for the design and optimisation of novel PFG plate structures and further understanding of the mechanical behaviour of FGMs.

Key Words

FEM; FSDPT; functionally graded material; porosity; power law function; sigmoid law

Address

Vineet Kumar — Mechanical Engineering Department, Engineering College, Bikaner, India
S.J. Singh — Mechanical Engineering Department, NSUT, New Delhi, India
S.P. Harsha — Advance Vibration Laboratory, Mechanical & Industrial Engineering Department, IIT Roorkee, India

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