Existing analytical methods for sandwich panel-cavity vibroacoustic analysis are limited to specific configurations and fixed coupling positions, and lack universal capability for arbitrary-layer systems with variable coupling positions. This paper presents a comprehensive analytical framework addressing these limitations through a novel “decoupling-solving-inverse decoupling” strategy. The approach combines matrix theory with modal coupling methods, transforming complex multilayer coupling systems into solvable independent “generalized” single-layer plate-cavity systems via eigenvalue decomposition. Validation demonstrates excellent agreement with finite element solutions while achieving significant computational efficiency, reducing analysis time from 16 minutes to under 10 seconds. Parametric studies reveal critical design insights: resilient layer stiffness significantly affects sound transmission performance, plate thickness enhancement improves sound insulation following classical mass law, and cavity geometric parameters directly affect resonance characteristics. The framework provides engineers with a universal, computationally efficient tool for vibroacoustic design of multilayer structures.
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