Local resonance and Bragg bandgaps in sandwich beams containing periodically inserted resonators

TL;DR

This paper investigates wave propagation in sandwich beams with embedded resonators, revealing how local resonance and Bragg bandgaps coexist and interact, with implications for controlling low-frequency vibrations.

Contribution

It provides a closed-form expression for the propagation constant and analyzes the interaction between local resonance and Bragg bandgaps in such systems.

Findings

Local resonance and Bragg bandgaps coexist in the system.

The width of the bandgaps depends on resonator parameters and periodicity.

Bragg bandgaps transition into sub-wavelength bandgaps when local resonance frequency exceeds classical Bragg frequency.

Abstract

We study the low frequency wave propagation behavior of sandwich beams containing periodically embedded internal resonators. A closed form expression for the propagation constant is obtained using a phased array approach and verified using finite element simulations. We show that local resonance and Bragg bandgaps coexist in such a system and that the width of both bandgaps is a function of resonator parameters as well as their periodicity. The interaction between the two bandgaps is studied by varying the local resonance frequency. We find that a single combined bandgap does not exist for this system and that the Bragg bandgaps transition into sub-wavelength bandgaps when the local resonance frequency is above their associated classical Bragg frequency.