Size-dependent natural frequencies of functionally graded plate with out of plane material inhomogeneity using Eringen’s theory of nonlocal elasticity

Abstract

Nonlocal effect is one of the critical reasons which cause an extraordinary vibration response in small-scale structures. In the present work, vibration characteristics of functionally graded nonlocal plate are studied using Eringen’s nonlocal classical elasticity theory. A computationally efficient numerical method has been proposed in this study by reformulating the classical plate theory and Rayleigh–Ritz method using nonlocal differential relationship of Eringen’s theory in conjugation with algebraic polynomial displacement functions. The reformulated method helps to evaluate the natural frequencies of functionally graded nonlocal plates subjected to all possible combinations of edge conditions. The material properties are assumed to vary through the thickness of the plate following the power law. The computed results of natural frequencies are first tested for convergence and then validated with the published one. A parametric study has been thoroughly conducted focusing on the effects of aspect ratio, nonlocal parameter, material property index and Young’s modulus ratio on the natural frequency parameters of the functionally graded nonlocal plate. It has been observed that the material property index and aspect ratio affect the vibration behaviour of the functionally graded plate. The study also establishes that nonlocal effect has a pronounced influence on the higher modes of vibration of functionally graded plate. 3D mode shapes of functionally graded material nonlocal plate have also been reported.