A fast vibro-acoustic modeling method of plate-open cavity coupled systems

In this paper, a fast Chebyshev-Ritz method for vibro-acoustic analytical modeling of plate-open cavity coupled systems is developed for the first time. Based on the Chebyshev spectral method and the Rayleigh-Ritz solution procedure, the vibro-acoustic model of the open cavity coupled with a rectangular plate is established. The exterior acoustic field of the open cavity is expressed by the Rayleigh integral. Additionally, the Rayleigh integral is divided into a frequency-independent singular integral and a frequency-dependent non-singular integral, accelerating the calculation process. Furthermore, the Gauss-Chebyshev-Lobato sampling method is first developed for the plate-open cavity coupling model. By converting the integrals into tensor products, the method avoids complex quadruple integrals, increasing the efficiency of the entire integral operation. The vibration and acoustic responses from the proposed method agree well with existing literature and FEM analysis results, demonstrating the convergence and correctness of the current methodology. The mechanism of cavity depth on vibro-acoustic features of plate-open cavity systems is studied, which is less focused in the published literature. Other factors governing the plate-open cavity coupled model encompassed boundary conditions, fluid mediums, and plate thickness are fully examined. The results provide a theoretical foundation for the design and future research of plate-open cavity structures.