On the Formation of a Super Attenuation Band in a Mono-coupled Finite Periodic Structure Comprising Asymmetric Cells

Abstract

Metamaterials are employed to reduce vibration levels by exploiting the effects of structural periodicity. When structural elements are arranged in a periodic pattern, they act as mechanical filters, creating stop-bands. The term stop-band is often used for infinite structures, but a more appropriate term for a finite structure is attenuation band. A way of obtaining this effect is by attaching vibration absorbers, which create a local resonance stop-band plus a Bragg stop-band. The local resonance stop-band is controlled only by the properties of the attached device. The Bragg stop-band depends on the interaction between the host cell and the device. The combination of these two effects can create an attenuation zone – the so-called super attenuation band. Recent works on finite mono-coupled metamaterials have shown that asymmetric periodic structures have better attenuation properties when compared to the symmetric ones, if they are correctly orientated. This paper investigates the formation of a super attenuation band in a finite mono-coupled structure using vibration absorbers. The system is defined by the formation of a cell, which repeats along with the whole structure. The cell can be divided into sub-cells with equal or different dynamic properties. The dynamic features to form the super attenuation band are determined from the displacement transmissibility of a single cell. This analysis is extended to several cells. The results show that a super attenuation band can only occur when each attached vibration absorber is optimally tuned to its corresponding host cell in a structure comprising cells with dynamical asymmetry.