## 1 Introduction
[PERSON] and [PERSON] [9] developed analytical models of the wave and sound propagation characteristics of two sets of orthogonal stiffened laminated structures subjected to convective fluid pressure. They checked the accuracy of the analytical model by comparing its predictions to previous findings. [PERSON] and [PERSON] [10] established an analytical model of the sound transmission loss of orthogonal stiffened plate structures under a diffuse sound field. They validated the effectiveness and feasibility of the model by comparing it with experimental results. [PERSON] [11] conducted a study on the sound excitation of uniformly stiffened plates using an approximate model and compared it with the joint acceptance formula of plane wave harmonic sound excitation. In summary, while numerous studies have explored the vibro-acoustic characteristics of the coupled system between a composite laminated stiffened plate and acoustic cavities, most of these studies have focused on rectangular stiffened plates. There has been limited research on the coupled system between a composite laminated rotationally stiffened plate and acoustic cavities. Even in cases where rotationally stiffened plates or other complex structures are involved [12], the analysis is often confined to finite element method (FEM) simulations, which may not be conducive to design and practical implementation. This article aims to utilize the modified Fourier series method and first-order shear deformation theory to construct a unified analysis model of the vibro-acoustic characteristics of the coupling system between a composite laminated rotationally stiffened plate and acoustic cavities. Firstly, displacement and sound pressure functions of the coupling system are established by using the modified Fourier series method [13; 14]. Subsequently, energy functionals are formulated for both the structural and acoustic domains. Leveraging the coupling characteristics between a composite laminated rotationally stiffened plate and acoustic cavities, a coupling potential energy of the plate-cavity coupling system is defined. This coupling potential energy is then integrated into the energy functional of the coupled system between a composite laminated rotationally stiffened plate and the acoustic cavities to derive the total energy functional of the coupled system. Finally, utilizing the Rayleigh-Ritz energy technique, the extremal values of the coupled system's energy functional are determined to solve for the vibro-acoustic characteristics. Upon verifying the correctness and convergence of the established coupled system, the correlative parameterization research is carried out. It investigates the effects of crucial parameters such as height of the cylindrical cavity, the apex angle of the spherical cavity, the rotation angle, the cone apex angle of the conical cavity, and the boundary spring stiffness values on the coupling system's vibro-acoustic characteristics. Furthermore, it examines the impact of external excitation amplitude, the impedance value, and material parameters on steady-state response. This research offers a theoretical direction for the design, vibration control, and noise reduction of similar engineered structures.