Modeling and acoustic analysis of irregular sound enclosure by using Chebyshev-variational method

A modeling method for irregular sound enclosure is proposed based on the Chebyshev-variational theory. A rectangular space is firstly assumed to bound the irregular sound space and the sound pressure in the rectangular space is expressed as triple-Chebyshev series. Next, the coordinate transformation is performed and the Lagrangian functional of the irregular sound space is obtained. At last, the Lagrangian functional is solved under the frame work of Ritz method.The acoustic characteristic equation of the enclosure is deduced and the eigenpairs are obtained. The accuracy of the present method is validated according to the agreement between the present results and the finite element results for an enclosure with curved surface. Furthermore, the acoustic characteristics of trapezoidal enclosure and enclosure with inner groove are investigated. The results show that the mode shapes of trapezoidal sound space will change with the increase of inclination angle and the natural frequencies(except the first order) of sound space with rectangular inner groove will decrease with the increase of groove depth.