Vibro-acoustic response of a simplified residential structure exposed to sonic booms. Part I: Numerical model.

Abstract

This paper presents a numerical model to predict the vibro-acoustic responses of simplified residential structures exposed to sonic booms. The model is validated experimentally in a companion paper. The dynamics of the fluid-structure system, including their interaction, is computed in the time domain using a modal-decomposition approach. In the dynamic equations of the system, the structural displacement is expressed in terms of summations over the in vacuo modes of vibration. The pressures inside the interior volumes are expressed as summations over the acoustic modes of rooms with perfectly reflecting surfaces. The structural modes are computed numerically using the finite element method. A shell element was specifically derived to model the structural components of typical residential buildings, e.g., plaster-wood walls, windows, and doors. The acoustic modes are computed for rectangular geometries using analytical expressions. Using modal decomposition, the dynamics of the fluid-structure system may be formulated by a finite set of ordinary differential equations (modal equations). These equations are then integrated with a Newmark algorithm to solve for the vibro-acoustic response of the system in the time domain. The system response may also be predicted in the frequency domain, by taking the Fourier transform of the time-domain response.