Noureddine Atalla
Alain Berry
GAUS, Mech. Eng., Univ. of Sherbrooke, Sherbrooke, PQ J1K 2R1, Canada
A mathematical model is derived to address the vibrations and sound radiations into a dense fluid, of a coupled system consisting of two semicomplex plates (i.e., supporting added mass, stiffeners, and having arbitrary elastic boundary conditions) linked in four points through multistage suspensions elements. The top plate is subjected to point, line, or surface harmonic excitation, while the radiating plate is excited through the suspensions. Both plates are assumed to be baffled, and the radiating plate is fluid loaded. The model is based on a variational approach for the plates, and a matrix transfer approach is used to handle the coupling between the two plates. The solution is sought using a Rayleigh--Ritz expansion in terms of polynomial trial functions which are shown to allow for the arbitrary elastic boundary conditions and to facilitate the calculation of the radiation impedance matrix. The vibrations and noise design of the system is discussed. The main design indicators are the force transmissibilities between the different excitation and attachment points, the ratio of mean-square velocities of the two plates, the mean-square velocity, the radiated power, and the radiation efficiency of the radiating plate. Numerical examples are presented to show the effects of different design parameters (plates thickness, boundary conditions, added mass, stiffeners,...) on the radiated sound. [Work supported by DREA.]