Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method

Free vibration analysis of rectangular plates with internal columns and elastic edge supports is presented using the powerful pb-2 Ritz method. Reddy's third order shear deformation plate theory is employed. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken as the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate using the Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. Many numerical results for reasonable natural frequency parameters of rectangular plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

► Accuracy and efficiency of the proposed method are verified by comparison and convergency studies.
► New numerical results are presented.
► Influences of different factors on natural frequency parameters are carefully studied.