A general Ritz formulation for the free vibration analysis of thick trapezoidal and triangular laminated plates resting on elastic supports

Abstract

A general variational formulation for the determination of natural frequencies and mode shapes of free vibration of laminated trapezoidal and triangular plates is presented in this work. The kinematics corresponding to the first order shear deformation plate theory (FSDT) is used to take into account the effects of shear deformation and rotary inertia in the analysis. This theory allows obtaining greater accuracy of frequency coefficients corresponding to higher modes vibration, even for the thin plates. The developed approach is based on the Ritz method and the plate geometry is approximated by nonorthogonal right triangular co-ordinates. The transverse deflection and two rotations of the laminate are independently approximated by sets of simple polynomials automatically generated. The algorithm allows obtaining approximate analytical solutions for laminated plates with different shapes, aspect ratio, number of layers, stacking sequence, angle of fiber orientation and boundary conditions including translational and rotational elastically restrained edges. The algorithm is simple to program and numerically stable. Additionally, triangular plates can be generated as a special case.