Accurate analysis of steady state response of fully clamped orthotropic functionally graded rectangular plates

Abstract

Abstract A Hamiltonian-based method is introduced to find exact solutions for steady state forced vibration of a fully clamped orthotropic functionally graded (FG) rectangular plate. The proposed method has two major steps. Firstly, the steady state response for an FG rectangular plate with Naiver-type boundary conditions is analytically derived by a wave-based symplectic method. Subsequently, exact solutions of the fully clamped FG rectangular plate are obtained by a symplectic superposition technique. The overall procedure is systematic with a clearly defined, step-by-step derivation. The accuracy of the obtained exact solutions is highlighted in comparison with reference data. Numerical results are presented to reveal the effects of the material properties.