Free vibration analysis of orthotropic rectangular Mindlin plates with general elastic boundary conditions

In this investigation, a modified Fourier solution based on the Mindlin plate theory is developed for the free vibration problems of orthotropic rectangular Mindlin plates subjected to general boundary supports. In this solution approach, regardless of the boundary conditions, the plate transverse deflection and rotation due to bending are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown coefficients are treated as the generalized coordinates and determined using the Raleigh-Ritz method. The change of the boundary conditions can be easily achieved by only varying the stiffness of the three sets of the boundary springs at the all boundaries of the orthotropic rectangular Mindlin plates without the need of making any change to the solutions. The excellent accuracy of the current result is validated by comparison with those obtained from other analytical approach as well as the Finite Element Method (FEM). Numerical results are presented to illustrate the current method is not only applied to the classical homogeneous boundary conditions but also other interesting and practically important boundary restraints on free vibrations of the orthotropic rectangular Mindlin plates with varying stiffness of boundary springs.