Dynamic Response and Parametric Analysis of Geometrically Nonlinear Functionally Graded Plate With Arbitrary Constraints Under Moving Mass

Abstract

A comprehensive method is presented to investigate nonlinear dynamic responses of functionally graded rectangular plate with arbitrary boundary conditions under a moving mass, based on Rayleigh–Ritz solutions together with the penalty method (PM) and the Newmark with inverse Broyden quasi-Newton method. Different from the existing methods, all inertial effects associated with the moving mass, which affect the mass, damping, and stiffness matrices of system, are taken into account. The formulations are derived based on classical plate theory and von Karman geometric nonlinearity, which considers large deformation without violating stress failure criteria. Material properties of FG plate vary continuously in the thickness direction according to the power law. The PM is employed to deal with the troublesome arbitrary constraints, which excludes an orthonormalization process for determining these admissible functions, and where only one set of admissible functions is used for arbitrary boundary conditions. The Newmark method together with the rank-one inverse Broyden quasi-Newton method is adopted to solve the nonlinear coupled differential equations of second order in time with more computational efficiency and avoiding numerical instability. Formulation and method of solution are validated by studying their convergence behavior and performing the comparison studies with existing results in the literature in the limit cases. In addition, influences of different material distribution, velocity of moving mass, different conventional, and unconventional boundary conditions on forced and free vibration responses are discussed.