Modal Analysis of an Enclosure Acoustic Space Based on Spectro-Geometric Method

The Spectro-Geometric Method (SGM) has shown great efficiency in solving solid mechanics problems. In this investigation, acoustic eigenproblems of an enclosure space are solved using the SGM method. Under this solution framework, the sound pressure is invariantly expressed as a new trigonometric series in the form of the superposition of a Fourier cosine series supplemented by two sine terms. The use of the two sine terms is to ensure the series expansion converges uniformly and polynomially over the entire solution domain including the boundary surfaces. The Rayleigh-Ritz method is employed to derive the final characteristic equation for the acoustic system. The modal characteristics for an enclosure acoustic space can be directly obtained from solving a standard matrix eigenvalue problem. Several numerical examples have been presented to demonstrate the effectiveness and reliability of the SGM.