A weak formulation for interior acoustic analysis of enclosures with inclined walls and impedance boundary

A weak variational principle based approach is presented in this paper to study the sound field inside the acoustic enclosures with walls in arbitrary inclination and impedance conditions. The whole acoustic domain is firstly divided into several sub-cavities with trapezoidal and rectangular faces, and each sub-cavity is coupled with adjacent ones by matching the required continuity constraints on the interfaces on the basis of a modified variational principle and least-squares weighted residual method. By using this domain partitioning strategy, high-order acoustic modes and responses can be easily achieved. Chebyshev orthogonal polynomials of the first kind are employed as the wholly admissible unknown sound pressure functions for each sub-cavity without meshing process like FEM/BEM does, and then each physical domain is mapped into a square spectral domain. To demonstrate the convergence, accuracy and stability of the approach, the modal and sound response analyses of several configurations of cavities are examined and compared with available analytical solutions, or those obtained by using FEM. Effects of the weighted parameters together with the number of truncated polynomial terms and the divided cavity segments on the accuracy of present solutions are investigated. Key parametric studies concerning the influences of the geometrical properties as well as the impedance boundary of enclosing walls are also performed. It is demonstrated that the present method is a computationally efficient way to achieve interior sound predictions in mid-frequency range with a satisfactory accuracy of solutions.