A three-dimensional modeling method for the trapezoidal cavity and multi-coupled cavity with various impedance boundary conditions

A three-dimensional modified Fourier series method is applied to study the acoustic characteristics of the trapezoidal cavity and coupled cavity with various impedance boundary conditions. The formulation is constructed to describe the cavity systems based on the energy principle. The admissible sound pressure function is set to a Fourier cosine series and supplementary functions. These supplementary functions can eliminate the discontinuous or jumping phenomenon in the boundaries. The trapezoidal cavity can be transformed into regular rectangular cavity by coordinate transformation. The triangular cavity can be obtained by changing the dimensions of the trapezoidal cavity. The coupled cavity consists of two irregular triangular cavities and the coupling interface is regarded as a non-dissipative surface. The accuracy and convergence of the present results are verified by comparison with the results obtained by finite element calculation and experiment. The natural frequencies and mode shapes of the trapezoidal cavity and coupled cavity are studied. Besides, the sound pressure response under monopole sound source excitation is obtained. What's more, some results are obtained in the basis of effects of various factors on acoustic characteristics, such as shapes, geometric parameters and impedance values. These results provide a benchmark for the future researches. (C) 2019 Elsevier Ltd. All rights reserved.