Effects of the inclination of a rigid wall on the free vibration characteristics of acoustic modes in a trapezoidal cavity.
The coupling between rigid-walled modes of a rectangular cavity (RC modes) is used to obtain the shapes and resonance frequencies of rigid-walled modes of a trapezoidal cavity (TC modes) with an inclined rigid wall. A method is established to identify the TC modes, where the modes can be defined to evolve from individual RC modes. The wall inclination generates two coupling mechanisms, namely, the local coupling where the RC modes couple at the inclined wall, and the global coupling where the RC modes couple throughout the trapezoidal volume. The latter arises from the nonorthogonality of the RC modes in the trapezoidal volume. Both couplings are selective that only RC modes with the same number of nodes in the direction perpendicular to the inclination are coupled to each other. For small inclinations, each TC mode possesses the distorted shape of the RC mode that evolves it. When the inclination is increased, the TC-mode shape becomes complicated and unrecognizable, and extrema can also exist in the resonance frequency of the TC mode. These behaviors are determined by the behaviors of the local and global couplings of the RC mode. This paper provides an understanding of how the free vibration characteristics of TC modes change with the inclination and what determines these changes.