Flexural wave propagation in beams with periodically attached vibration absorbers: Band-gap behavior and band formation mechanisms

This paper is concerned with flexural wave propagation and vibration transmission in beams with periodically attached vibration absorbers. Such periodic systems feature unique wave filtering characteristics that can find applications in the control of wave propagation in flexural beam structures. The study is performed by using an exact analytical approach based on a combination of the spectral element method and periodic structure theory. Both infinite and finite periodic structures are considered. An explicit expression is provided for the calculation of propagation constants and thus the complex band structures, and it is further developed to examine the effects of various system parameters on the band-gap behavior, including the position, width and wave attenuation performance of all the band gaps. The band formation mechanisms of such periodic systems are explained via both derivations and physical models, yielding explicit equations to enable the prediction of all the band edge frequencies in an exact manner without the need to calculate propagation constants. Based on these equations, explicit formulas are further derived to determine the conditions for the transition and near-coupling between local resonance and Bragg scattering, each being a unique band-gap opening mechanism.