A unified hybrid Ritz-SEA acoustic vibration coupling method of a rectangular plate coupled with fast multipole boundary integration

Abstract

The Ritz method, based on a segmental strategy, is known for its fast convergence and ability to handle arbitrary boundary conditions while maintaining accuracy comparable to benchmark solutions. It is particularly effective in calculating vibrations in composite laminates, functionally graded plates, and other novel plate types. However, this method faces challenges in accurately calculating the mid-frequency problems that arise between plate structures and acoustic cavities. To fill this gap, this paper proposes a Ritz and statistical energy analysis (Ritz-SEA) hybrid method for calculating rectangular plate acoustic vibration coupling in the mid-frequency range for both deterministic and random loads. This method utilizes the fast multi-pole boundary element integral equation and region segmentation mapping as the governing equation for the coupling boundaries. The power flow equation of the statistical energy analysis (SEA) method is incorporated to solve for the average sound pressure level and sound power level of the coupled acoustic cavity. A method that combines the CHIEF and Burton-Miller methods has been proposed to address the issue of non-unique solutions. Validation and parametric studies are conducted. The results demonstrate that this approach can effectively filter out random fluctuations in mid-frequency domains while exhibiting exceptional stability and precision.