Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets

Abstract

Nonlinear forced vibration of graphene platelet reinforced metal foam (GPLRMF) rectangular plates is investigated. Attention is focused on the primary, superharmonic, and subharmonic resonances of this novel nanocomposite structure. Three kinds of graphene platelet (GPL) pattern and three kinds of porosity distribution are taken into account. Based on the von Kármán nonlinear plate theory, governing equations and general boundary conditions of the GPLRMF plates are obtained via Hamilton’s principle. By introducing stress functions, nonlinear ordinary differential equations of the plates are obtained by using the Galerkin method. Then, frequency–response and force–response relationships of the GPLRMF plates are solved by applying the multiple scale method. A validation study is conducted to verify the present method. Results show that GPLRMF plates exhibit hardening nonlinearity in primary and superharmonic resonances. Dispersing more small-size pores or more GPLs near the middle surface will lead to the larger vibration amplitude and resonance domain of the plates in primary and superharmonic resonances. While uniformly distributed pores or uniformly distributed GPLs will result in the larger vibration amplitude in the case of subharmonic. Moreover, change of porosity coefficient or GPL weight fraction can significantly alter the nonlinear dynamic behavior of GPLRMF plates.