Nonlinear Dynamic Response of Functionally Graded Rectangular Plates under Different Internal Resonances

Abstract EN

The nonlinear dynamic response of functionally graded rectangular plates under combined transverse and in-plane excitations is investigated under the conditions of 1 : 1, 1 : 2 and 1 : 3 internal resonance.

The material properties are assumed to be temperature-dependent and vary along the thickness direction.

The thermal effect due to one-dimensional temperature gradient is included in the analysis.

The governing equations of motion for FGM rectangular plates are derived by using Reddy's third-order plate theory and Hamilton's principle.

Galerkin's approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4th-order Runge-Kutta algorithm.

The effects of in-plane excitations on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied.