Acoustic Interactions in a Rectangular Cavity with a Forced Vibrating Top Elastic Plate Filled with a Compressible Fluid

Resumen

Acoustic cavities are founded in many technological applications such as in naval or aerospace engineering. In this paper the vibroacoustic characteristics of a forced vibrating plate at top position of a rectangular cavity filled with an ideal fluid are studied. The velocity potential function is obtained by the method of separation of variables applied to the corresponding wave equation and the pressure field is deduced from the momentum’s linearized equation. After an integration over the surface of the plate of its dynamic motion equation considering the orthogonallity of the functions involved expressed in series expansion of the associated modes, analytical expressions are obtained for the calculus of the plate natural or free frequencies of vibration, and the system frequency response for the case of forced vibration. The frequency response or spectrum of the plate deformation, as well as the sound pressure level at different points of the cavity are obtained, and the influence of various parameters such as container height, fluid density and load position on these spectrums are analyzed. Also the mean quadratic sound pressure level over the plate and the mean quadratic deformation level of the plate in vacuum and with fluid are obtained, and finally the variation of the mean quadratic sensibility with the frequency is calculated. Validation of the method is made by comparing the results with those obtained by other authors and theories.