A GENERALIZED-MODEL FOR PREDICTING THE SOUND-TRANSMISSION PROPERTIES OF GENERALLY ORTHOTROPIC PLATES WITH ARBITRARY BOUNDARY-CONDITIONS

Sound transmission is of significant concern in practical situations, such as building noise insulation or quietening of mechanical products. If the medium- and high-frequency response are well mastered, it is not the case in the low-frequency range where some discrepancies between experiments and theory remain sometimes unexplained. In view of these limitations, the scope of this work is to develop a generalized model which focuses on aspects particularly important in the low-frequency range, namely (1) the finite size of the panel, (2) the orthotropy properties, and (3) the boundary conditions. A variational approach is adopted. The Hamilton functional is built starting with the general tensor relationships between stresses and strains for a generally orthotropic plate. The extremalization is performed using the Rayleigh-Ritz method in conjunction with a nonorthogonal polynomial basis in order to deal with general boundary conditions. The excitation is an acoustic plane wave of any incidence and the radiated field is calculated with an impedance matrix including the cross coupling terms. The different vibroacoustic indicators are the quadratic velocity of the plate, its radiation efficiency, and the transmission loss. The importance of including the intermodal interaction is clearly pointed out. It produces narrow peaks of transmission loss well above the classical mass law. The effect of the dimensions of the panels is shown rigorously and suggests that experimental results should be given in narrow-band if one wants to get usable data. The model also allows, probably for the first time, the effect of the boundary conditions to be fully analyzed. Interestingly enough, the free-free case gives a much bigger transmission loss in the low-frequency range which gives an insight, when possible, for improving the transmission loss. © 1995, Acoustical Society of America. All rights reserved.