Multi-modal geometrical non-linear free vibrations of composite laminated plates with the complex shape

Abstract

Geometrically non-linear free vibrations of the composite laminated plates are investigated using new multi modal approach to discretization of motion equations . The non-linear governing equations for laminated plates are derived by Hamilton’s principle using first-order shear deformation theory. Due to proposed algorithm of the discretization all unknown functions except of transverse displacement are eliminated and governing equations are reduced to system of ordinary differential equations in time by the Bubnov-Galerkin procedure. The expansion of all unknown functions in the truncated Fourier series is performed using the eigenfunctions of the linear vibration problems and solutions of the sequence of elasticity problems. All auxiliary problems are solved by RFM (R-functions method).