On the formation of a super stop-band in finite mono-coupled periodic structures using an array of vibration absorbers: Controlling parameters and physical insight

Abstract

There are two fundamental strategies in the design of metamaterials used for noise and vibration control. The first uses structural periodicity and explores the Bragg scattering to produce frequency ranges where waves do not propagate or are severely attenuated (stop-bands). This condition is usually limited by the constitutive size of the structural elements and tends to occur at higher frequencies. A second strategy consists of adding vibration absorbers to produce a resonance(s), and this can occur at much lower frequencies. The addition of periodically attached vibration absorbers alone creates a periodic medium, and Bragg stop-bands also occurs in this situation. There is a particular condition where the Bragg and local resonance stop-bands can be combined to produce an ultra-wide or a super stop-band. This paper investigates the conditions required to produce a super stop-band in a finite mono-coupled periodic system composed of symmetric cells, each with a vibration absorber attached. Using a lumped parameter system, the dynamic features and the transmissibility of a single cell are determined, and the physical mechanisms behind the super stop-band formation are investigated, including the absorber tuning frequency and the influence of damping. Two experimental setups to support the theoretical findings are described. One involves a lumped-parameter system and the other involves a rod, both with a vibration absorber attached. The results show that a smooth super stop-band only occurs when the vibration absorber is tuned to the free-free natural frequency of the single host cell, creating a union between the Bragg stop-bands due to mass and stiffness of the absorber, and that the damping in the absorber should be equal to the damping in the host cell.