Size-dependent nonlinear vibration problem of piezoelectric graphene origami auxetic metamaterial sandwich microplates under coupled thermo-fluid-viscoelastic multi-physics

Abstract

This paper investigates the nonlinear dynamic behavior of a microplate combining functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAM) in sandwich architecture with piezoelectric layers on a viscoelastic substrate under fluid-structure interaction and thermal loading. Accordingly, the primary objective is to develop a unified analytical framework to model and predict the intricate, size-dependent nonlinear dynamics of this multi-physics system. Graded graphene origami (GOri) elements are dispersed through the plate thickness to achieve negative Poisson’s ratio and improved thermal conductivity. First-order shear deformation theory (FSDT) with von Kármán geometric nonlinearity models large-amplitude deflections, while modified couple stress theory (MCST) captures size dependency. Thermal effects include uniform, linear, and nonlinear temperature distributions, and fluid-plate interaction is modeled via Navier-Stokes equations. Hamilton’s principle derives the governing equations, discretized using the Galerkin method into nonlinear time-dependent ordinary differential equations. The harmonic balance technique solves these equations to obtain nonlinear frequency-amplitude relationships for forced vibration. Effects of strain-gradient length-scale parameter, thermal field properties, piezoelectric actuation voltage, fluid layer depth, viscoelastic foundation stiffness and damping, GOri content, folding, and distribution patterns are parametrically examined using nonlinear frequency response curves.