Transmission of a Shock Wave into a Room with a Window using a Modal-Interaction Model

As a first step in the development of a model for predicting the noise transmission of sonic booms inside buildings, an analytical formulation was carried for the transmission of a shock wave with an arbitrary time history into a single room with a window. In this model, only the window can vibrate and the remaining portion of the structure enclosing the room is assumed to be rigid. The dynamics of this fluid-structure interaction is computed in the time domain by expressing the structural and acoustic dynamic equations in terms of the “in vacuo” modes of a simply-supported plate and the acoustic modes of a hard-walled rectangular room. Results for illustrative cases are presented, demonstrating that the system response is insensitive of the external wave orientation. It is also shown that the fluid-structure system must be considered as fully-coupled for the solution to be truly representative.