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

A general variational formulation for the determination of natural frequencies and mode shapes of free vibration of symmetric laminated plates of trapezoidal and triangular shapes 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 rotational inertia in the analysis.The developed approach is based on the Ritz method and the plate geometry is approximated by non-orthogonal right triangular co-ordinates. The transverse deflection and two rotations of the laminate are independently approximated by sets of simple polynomials.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.

► A variational model for the dynamic study of trapezoidal/triangular plates is proposed.
► The kinematics corresponding to the first-order shear deformation plate theory (FSDT).
► Approximate analytical solutions for symmetric laminated plate are obtaining.
► The formulation includes edges elastically restrained against rotation and translation.
► New results are presented that can be useful for validation purposes.