Structural acoustics of semi-infinite simply supported baffled plate using analogy with infinite plate

The acoustic radiation of vibrating plates has received considerable attention in the research literature. There are numerical, experimental as well as analytical solution approaches towards this problem. In the analytical literature, the infinite plate problem using wave propagation techniques has been extensively studied. It turns out that the infinite domain problem, in comparison to the finite domain problem, is easier to solve. Finiteness induces additional reflections into the structure and thus complicates the analytical solution process. In this work, we develop an analytical procedure for determining the sound radiation characteristics of semi-infinite plate (viz. infinite in one direction and finite in the other direction) mounted on a rigid baffle. The end conditions in the finite direction of the plate are taken to be simply-supported. This serves as a model for different applications such as loud speaker design, automotive panels, etc. A harmonic line forcing is applied at the mid-span along the infinite direction. The problem is turned equivalent to an infinite plate subjected to two additional forces and moments arising from the end conditions. While the existence of reaction forces at the simple support is natural, the moments induced at the supports enforce a zero displacement condition beyond the finite extent of the plate. The infinite plate response obtained due to the applied loading with the inclusion of the reaction forces and moments as additional loads is verified to correspond to that of the simply supported beam response. Well-known wave solutions for the acoustic radiation due line forcing and line moments on an infinite plate are then applied to determine the acoustic radiation characteristics for the semi-infinite plate. In particular, we investigate the contrasting aspects of the semi-infinite and infinite plate acoustic radiation characteristics. This is quantified in terms of the two reaction forces and moments.