Forced vibration of porous functionally graded nanoplates under uniform dynamic load using general nonlocal stress–strain gradient theory

Abstract

Forced vibration analysis of porous functionally graded nanoplates under uniform dynamic loads is performed based on generalized nonlocal strain gradient theory. In this model, both stiffness-softening and stiffness-hardening effects are considered for more reliable forced vibration analysis of nanoplates. The present model is based on a vibrating higher order nanoscale plate subjected to transverse uniform dynamic load. Nanopores or nanovoids are incorporated to the model based on a modified rule of mixture. According to t Hamilton’s principle, the formulation of dynamically loaded nanoplate is derived. Applying Galerkin’s method, the resonance frequencies and dynamic deflections are obtained. It is indicated that the forced vibration characteristics of the nanoplate are significantly influenced by the porosities, excitation frequency, nonlocal parameter, strain gradient parameter, material gradation, elastic foundation and dynamic load location.