Band gap analysis of a locally resonant meta-beam with a low-frequency, stiffness-adjustable buckled beam–spring–mass resonator

Abstract

This study analyzes the bandgap characteristics of a locally resonant meta-beam (LRMB) incorporating buckled beam-spring-mass (BSM) low-frequency resonators. These resonators are strategically positioned on the top and bottom surfaces of the foundational beam, enabling adjustable stiffness. The BSM is implemented using a horizontally arranged Euler-Bernoulli buckled beam, a vertically installed positive stiffness linear spring, and a mass block. The axially compressed buckling beam provides variable negative stiffness by adjusting the compression levels within the first buckling mode shape. The subsequent sections address the static characteristics, stiffness adjustment methods, and the performance of the BSM resonator. Analyzing the real band structures for the infinite meta-beam utilizes the governing equations and the metamaterial beam model. This investigation employs the plane wave expansion method and Bloch's theorem to examine the low-frequency band gap. Finite element analyses on a restricted set of BSM resonators show significant suppression of vibration propagation within the band gap, particularly near the natural frequency of the BSM. The bending wave's propagation characteristics are also presented to validate the theoretical bandgap meta-beam. The discussion focuses on assessing the influence of lattice constant, resonator damping, and mass block on the band gap feature.