## 1 Introduction  
The composite laminated rotationally stiffened plate has found extensive applications in the aerospace industry. These stiffened plates vibrate under loading, and this vibration interacts with the surrounding airflow, making them a significant source of noise. In practical engineering, creatin a coupled system between composite laminated rotationally stiffened plates and acoustic cavities is unavoidable. The coupling potential energy between the structural domain and the acoustic field domain makes the study of the coupled system's vibro-acoustic characteristics exceedingly difficult. Simultaneously, a deeper understanding of the structural-acoustic coupling in such coupled systems is crucial for systematic structural optimization and noise control. This is why it is necessary to further study the vibro-acoustic characteristics of the coupled system between a composite laminated rotationally stiffened plate and acoustic cavities. Currently, some progress has been made in the research of structural-acoustic coupled systems between composite material structures and infinite acoustic fields. [PERSON] et al. [1] developed an analytical model of the coupled system between piezoelectric laminated plate and acoustic cavities under a simply supported boundary using the classical laminated plate theory and the eigenfunction expansion method. [PERSON] et al. [2] proposed a modelling methodology according to the wave superposition method. They unified the analysis of near-field and far-field regions as a single system, providing a quantitative analysis of how the marine acoustic environment affects the acoustic radiation field of an elastic shell structure, using the example of an elastic spherical shell. [PERSON] and [PERSON] [3] employed an improved variational principle and a multi-level partitioning method to investigate the nonlinear vibration and acoustic radiation responses of laminated plates with skin-core debonding under time-varying loads in an unlimited fluid. [PERSON] et al. [4] proposed a statistical energy analysis method for complex structural acoustic systems, including point, line, and area connections. This method was used for mid- to high-frequency vibrations and acoustic analysis of box-model-basing modal impedances. Structural-acoustic coupled systems composed of an infinite sound field cannot analyze specific product objects in engineering practice. As a result, more study on the vibro-acoustic characteristics of coupling systems with finite-sized sound fields is required. In such studies, some researchers have started to establish theoretical models of the coupled system between composite material structures and acoustic cavities using finite element or energy methods. [PERSON] and [PERSON] [5] investigated the modal, structural-acoustic coupling properties of plates with different composite material parameters, studying the impact of material properties, layer angles, and the number of layers on the vibro-acoustic characteristics of a composite material plate-cavity coupling system and comparing them to isotropic plate-cavity coupling system. [PERSON] and [PERSON] [6] proposed a novel and advanced finite element formulation for structural-acoustic problems and studied the coupling problem between rectangular composite-material plates and cavities. [PERSON] et al. [7] studied the vibration and sound responses of hyperbolic laminated plate structures under harmonic point loads and established a structural response simulation model that considered different geometric shapes, such as cylinders, ellipsoids, spheres, and hyperboloids. [PERSON] et al. [8] numerically evaluated the vibro-acoustic performance of metal-fiber laminated plates with the mid-plane as the center and used finite element methods to study fluid-structure coupling problems. With the widespread application of stiffened plates in various fields, there is an increasing amount of research on the vibro-acoustic characteristics of the coupled system between a composite laminated stiffened plate and acoustic cavities.