Vibroacoustic analysis of periodic structures using a wave and finite element method

Abstract

In this paper, a modelling approach is developed for predicting the vibroacoustic response of infinite, plane, 1- or 2-dimensionally periodic structures, including the forced response, sound transmission and radiation. This method combines a wave and finite element method with a space-harmonic assumption. A periodic cell of the structure is modelled using a conventional finite element method to find the mass and stiffness matrices. Wave propagation in the fluids is modelled analytically. The response at the interface between structure and fluid is represented in terms of a series of space harmonics. The effects of the fluids on the structure are modelled as a series of equivalent nodal forces. By post-processing the mass and stiffness matrices along with the applied forces using periodicity theory and equilibrium conditions, a spectral dynamic stiffness matrix is derived to calculate the response to a convected harmonic pressure. Excitation of the structure by oblique plane waves and a diffuse sound field are considered, together with the consequent sound transmission. The response to general excitation and the consequent radiation are also determined. For complex structures, model reduction using component mode synthesis is suggested. Various numerical examples are presented to illustrate this method. For simple structures, analytical solutions are available for comparison with the predictions made using the proposed method. For complicated structures, vibroacoustic analysis using analytical methods is difficult. However, the method developed in this paper provides a straightforward and efficient approach for estimating the vibroacoustic response of general plane periodic structures.