Structural-acoustic interaction of a three-dimensional panel-cavity-duct system with non-uniform boundary restraints

Plate drum-silencer has received a lot of research attention due to its excellent low frequency noise attenuation and flow-through characteristics. The majority of existing studies are limited to the classical or uniform elastic boundary conditions, while there is little effort devoted to the study of boundary restraint non-uniformity effect on the vibro-acoustic behavior of such silencing system. Motivated by the current limitation, the structural-acoustic coupling model of a three-dimensional panel-cavity-duct silencer is established, in which the elastic boundary restraint can be set as arbitrary distribution function. Energy principle is formulated to describe the vibro-acoustic dynamics of such 3-D panel-cavity-duct silencing system, with the admissible field functions constructed as the superposition of standard Fourier series and the auxiliary edge/interface smoothed terms. All the coupled system response information can be derived in conjunction with Rayleigh-Ritz procedure. Numerical examples are presented to validate the proposed model through the comparison with those from other approaches. The coupling effects of boundary restraining coefficient and plate bending stiffness on sound attenuation performance of such cavity-backed plate-duct silencer are then discussed and analyzed. The results show that the relationship of translational restraints at the duct entrance and exit, kx0 and kxLx, can be obtained through property inverse proportional functions to achieve the optimal sound attenuation. There will be significant improvement in some special frequency band compared with the uniform restraints distribution, especially for the plate with lower bending stiffness The experimental study is also performed to verify the theoretical prediction from current model. In reality, the arbitrary non-uniform elastic edge restraints represent the most general class of boundary conditions, and can provide more optimal space for such drum silencer design.