Since proposed, the perforated honeycomb-corrugation sandwich panel has attracted a lot of attention due to its superior broadband sound absorption at low frequencies and excellent mechanical stiffness/strength. However, most existing studies have assumed a structure made of high-strength materials and studied its performance based on the ideal rigid-wall model with little consideration for acoustic-structure interaction, thereby neglecting the structural vibrations caused by the material’s elasticity. In this paper, we developed a more realistic model considering the solid structural dynamics using the finite element method (FEM) and by applying aluminum and rubber as the structural material. The enhancement of the low-frequency performance and inhibition of broadband absorption coexisted in low-strength rubbers, implying a compromise in the selection of Young's modulus to balance these two influences. Further analysis on thermal-viscous dissipation, mechanical energy, and average structural stress indicated that the structure should work right below the resonant frequency for optimization. Based on these findings, we designed a novel aluminum-rubber composite structure possessing enhanced low-frequency absorption, high resistance to shear load, normal compression, and thermal expansion. Our research is expected to shed some light on noise control and the design of multifunctional acoustic metamaterials.