## 1 Introduction  
Noise issues are widely present in both living and working environments and are now considered the second largest environmental concern after air pollution [1]. The sound radiation resulting from mechanical vibrations can cause physical and psychological harm to users or people in proximity and can also impact the functionality of the machinery itself, for example, the stealth capability of submarines or the effectiveness of sonar systems [2, 3]. Reinforced double-layer panel structures, as a basic type of structure, are widely used in various fields such as vehicles, ships, aviation, agriculture, construction, and defense. These panels offer better sound and vibration performance than plate structures with the same volume or weight. Additionally, they decrease sound radiation effectively if the internally reinforced cavity is filled with foam. Its advantages include high strength, high rigidity, light weight, excellent damping performance, energy absorption performance, sound insulation performance, thermal insulation performance, etc. [4, 5, 6]. However, it has a relatively high manufacturing cost, and several factors need to be considered during the design and manufacturing process [7]. As a result, the sound control concerns of foam-filled reinforced sandwich panel structures are gaining greater attention and are of great research importance. Advanced sandwich panels come in various types, including polyurethane core, mineral wool core, and polystyrene core [8]. Currently, [PERSON] et al. [9] conducted theoretical analysis and finite element simulations to investigate the optimization of anisotropic sandwich beams. They found that parameters such as the thickness, density, and elastic modulus of anisotropic cores significantly impact sound transmission performance. Through optimization design, they achieved maximum transmission loss within a specified frequency range. [PERSON] [10] examined the acoustic and vibration characteristics of sandwich panel structures with a wood core and polyurethane foam filling by means of numerical research and simulation analysis in his master's thesis. The findings suggest that the panels filled with polyurethane foam demonstrated excellent sound insulation capabilities. [PERSON] et al. [11] performed a simulation analysis exploring the effects of polyurethane foam filling on the acoustic and vibration characteristics of truss sandwich panels. The results of the study indicated that this approach reduced the resonance amplitudes of both vibration and acoustic responses significantly. [PERSON] et al. [12] provided an overview of basic polyurethane foam core structures, advanced polyurethane foam core composite materials with various reinforcing materials, and complex structures such as hybrid core panels. In recent years, these have found extensive applications and commercial prospects in fields such as mechanics, electrical engineering, dynamics, thermodynamics, and acoustics. [PERSON] et al. [13] carried out both theoretical and experimental investigations on the acoustic and vibration properties of fiber-reinforced polymer laminates featuring porous foam cores when subjected to planar acoustic excitation. [PERSON] et al. [14] conducted a series of simulation studies to investigate how foam filling affects the acoustic radiation performance of circumferentially ribbed double-layer cylindrical shells. Their findings show that both ribbing and foam filling improve the sound insulation performance of the double-layer cylindrical shells. The recent literature suggests that polyurethane foam has garnered significant attention in the field of acoustics owing to its superior vibration damping and noise reduction capabilities. However, the integration of porous materials in reinforced sandwich panels, though effective in minimizing structural vibration and lowering radiated sound pressure levels, increases the complexity of the mechanical and acoustic responses of composite sandwich panels.