Classical modal analysis and asymptotic modal analysis of structural and acoustic systems

Abstract

The Classical Modal Analysis (CMA) method is commonly used to solve for the vibroacoustic response of large scale structural and acoustic systems. In this method, the modal equations of motion are developed and solved for the modal coefficients to form a modal series solution to predict the structural and acoustic responses. The CMA method generally works well in the low-to-medium frequency range. However, at high frequencies, the large number of modes required in the summation limits the usefulness of the CMA method and alternative methods, such as Statistical Energy Analysis (SEA) and Energy Finite Element Analysis (EFEA) have been developed. As an alternative to SEA and EFEA, the Asymptotic Modal Analysis (AMA) method has been developed in which the modal series summation in the CMA method is asymptotically approximated based on the overall frequency and band averaging of the modal series. The AMA method thereby predicts the band averaged frequency response in the high frequency range and also has the advantage of providing the spatial distribution of the response based on the summed modes in the frequency band. In this paper, an example of coupled cavity-plate system subject to external random white noise pressure load excitation is developed to illustrate the CMA and AMA methods and to address their accuracy.