Tailoring resonator-induced attenuation bands for finite elastic rods

Abstract The study of vibration suppression in periodic structures owing to Bragg scattering, local resonance or the coupling between the two is well established. Conventionally, resonators are placed periodically along a one-dimensional structure, suppressing energy transmission at and around their tuning frequency but presenting additional amplification to the system’s response at other frequencies. This work shows that broadband attenuation can be achieved without additional amplification. Our method concerns spatially aperiodic, non-uniform, undamped and damped resonators. We demonstrate how attenuation bands (ABs) in a bare uniform finite rod can be expanded by tuning resonators to an anti-resonance or resonance frequency while placing the resonators at the corresponding operational deflection shape’s (ODS’s) nodal points. The mechanism behind this phenomenon is the resonator mass-like and stiffness-like behaviour below and above its natural frequency, respectively, shifting the system’s resonance and anti-resonance frequencies. Physically, the resonators are utilized as added lumped mass and ground spring to the system below and above their natural frequencies, respectively. The wave approach is utilized to analyse the displacement of the structure, considering the reflection and transmission coefficients for each point discontinuity. Analytical expressions for the AB bounding frequencies and peaks flanking it are derived using the small parameter expansion method.