ANALYSIS OF BENDING VIBRATION OF RECTANGULAR PLATES USING 2D PLATE MODES

A higher order assumed modes (Ritz) method is developed for rectangular plate analysis using two dimensional plate mode shape functions. These two dimensional plate mode shape functions were determined using the extended Kantorovich-Krylov method. The rectangular plate is assumed isotropic and uniform, which has each edge of its span (root and tip) clamped, and remaining edges free (clamped-free-clamped-free or CFCF boundary conditions). Natural frequencies, mode shape functions, and frequency responses of the plate were calculated and compared to the results of traditional analysis using one dimensional beam modes to approximate plate modes in both x and y directions. The updated two dimensional plate mode shape functions substantially reduce the computational cost compared to the case of using one dimensional beam mode shape functions. Fewer number of modes are needed in the our proposed method to yield the same accuracy. Experiments were conducted to validate our predictions and the data agree with our predictions.