Enhanced wave attenuation through inertial amplification in periodic beam-rigid body structure

Abstract

We address the fundamental challenge of achieving low-frequency wave attenuation in periodic structures without increasing system mass - a critical limitation in current design of metastructures. Traditionally, low-frequency attenuation has been achieved through the use of local resonators, which can be tuned to a specific low-frequency range by increasing their mass. To overcome this trade-off, we investigate the influence of two inertial amplifiers with distinct configurations: one with auxiliary masses connected to both beam and main mass and another with auxiliary masses suspended between the main mass and a fixed support. The transfer matrix method, combined with the spectral element method, is employed to analyze how design parameters influence the dispersion properties of each system. Our findings show that purposeful structural design of these inertial amplifiers can lead to as much as 50% broader attenuation bands across both high and low-frequency ranges. We also demonstrate near-coupling phenomena between local resonance and Bragg scattering mechanisms, which result in an ultra-wide low-frequency band gap. This study provides a method for robust wave control in periodic structures made of elastic and rigid segments such as buildings and bridges, particularly for low-frequency, lightweight acoustic and seismic isolation.