Inertial amplification stiffened meta-panels for low-frequency sound insulation

Abstract

Stiffened structures have been widely employed in various engineering fields, including aerospace, large aircrafts, and underwater vehicles, due to their high specific stiffness and specific strength. However, improving their low-frequency sound insulation using local resonance metamaterials is challenging, particularly when additional mass is constrained. This study introduces an inertial amplification (IA) stiffened meta-panel to enhance the low-frequency sound insulation of stiffened structures. A semi-analytical method is developed to model the proposed structure and to calculate the band structures and transmission loss (TL). To impose periodic boundary conditions, a collocation-based Lagrange multiplier method is introduced, using a series of pre-selected collocation points along unit-cell boundaries. Numerical validations of the proposed model and method demonstrate their feasibility and accuracy in computing both band structures and TL. Theoretical results reveal that the IA effect contributes to the formation of bandgaps in the band structures and the TL peaks within the low-frequency range. Parametric studies further show that as the IA ratio increases, IA and Bragg bandgaps are reversed—a trend also observed with variations in the length of cantilever beams and the height of stiffeners. However, increasing the height of stiffeners enhances the bending stiffness of the unit cell, leading to a high-frequency shift of Bragg bandgaps. Laboratory measurements of TL, conducted using the reverberation chamber method and the sound box method, confirm the effectiveness of the proposed meta-panel and the computational method, revealing their potential for engineering applications in low-frequency sound insulation.