Vibration analysis of rectangular Mindlin plates with internal line supports using static Timoshenko beam functions

In this paper, the vibration characteristics of rectangular Mindlin plates with internal line supports in one or two directions are studied by using the Rayleigh–Ritz method. The static Timoshenko beam functions are employed as admissible functions, which are composed of a set of transverse deflection functions and a set of rotation-angle functions due to bending. The static Timoshenko beam functions are derived from a point-supported strip of unit width taken from the particular plate under consideration in a direction parallel to the edge of the plate and acted upon by a series of static sinusoidal loads distributed along the length of the strip. It can be seen that the suggested approach is very simple mathematically, and each of the beam functions is only a sine or cosine function plus a polynomial function of not more than the third order. A unified program can be easily prepared, because the changes in boundary conditions, number and locations of internal line supports and thickness ratio of the plate will result in a corresponding change of only the coefficients of the polynomials. Both high accuracy and low computational cost have been verified by convergence and comparison studies. In addition, it can be seen that the admissible functions presented in this paper can also properly describe the discontinuity conditions of the shear forces at the line supports. Therefore, accurate results can be expected for the analysis of dynamic response and internal force distribution of the plate.