This work attempts to present approximate results for the free and forced vibration of the rectangular plate with a diagonal line mass in the condition of four clamped edges. This type of the model may be simulated to the piano sound board, where one of two bridges in the actual pianos is slightly curved and placed in the diagonal direction.
Series assumed mode functions and Rayleigh-Ritz method are used to determine the natural frequencies, the corresponding mode shape of the plate and the response to the sinusoidal excitation. As the assumed mode functions, use is made of the functions which define the natural mode of vibration of a uniform beam. To investigate the effects of the line mass, solutions are obtained for three specific cases of line mass and compared with the solution of a uniform plate. In the forced vibration analysis, the excitation frequencies and the exciting positions are given according to the actual pianos, and the compliances due to the excitations of keys in the range of #30 - #51 are computed.
Result shows that for the keys of #30, #31, #34, #35, #36, #40, #42, #44, #48 compliances of the plate with bridge are larger than those of a plate without bridge.
