Abstract
Abstract In this paper, a local resonant (LR) rod with high-static-low-dynamic-stiffness (HSLDS) resonators is proposed to create a very low-frequency band gap for longitudinal wave propagation along the rod. The HSLDS resonator is devised by employing geometrical nonlinearity, and attached onto a periodic rod composed of rigid frames and rubbers to construct a LR rod. To reveal the band gaps, the LR rod is modeled as a lumped mass-spring chain. The effects of damping and nonlinearity of the HSLDS resonator on the dispersion relation is studied analytically by the Harmonic Balance method. The analytical results indicate that the damping mainly affects the width and depth of the band gap, while the nonlinearity can influence the central frequency and width of the band gap. In addition, both multi-body dynamic analyses and numerical simulations are conducted to predict longitudinal wave propagation along the LR rod, and thus to validate the very low-frequency band gap. The results show that the periodic rod with HSLDS resonators can create a very low-frequency band gap for longitudinal waves propagating along the rod.
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