Effects of viscous damping on the bandgaps of multi-frequency periodic structure

Abstract Locally resonant elastic metamaterials (EMMs) have the ability to mitigate or even completely suppress the propagation of vibration within bandgaps, holding promising potential in the field of vibration control. However, achieving broadband vibration suppression remains a significant challenge for EMMs based on single resonance. To address this issue, we propose a scheme employing multiple resonators and introduce a damping mechanism to attenuate vibrations outside the bandgap frequency domain, aiming at wideband vibration control. The effectiveness of this approach is verified through a combination of analytical modeling and numerical analysis. By adjusting the damping characteristics of the internal resonators, we successfully extend the frequency range of vibration attenuation beyond the limitations of traditional designs. Using a mass–spring model coupled with a Kelvin–Voigt type oscillator damping model, an analytical framework is established for the dissipative multi-resonator unit and validated against published experimental data. Further parametric studies reveal the influence of additional loss coefficients on vibration attenuation performance. By optimizing the damping coefficients, the vibration attenuations are enhanced within 0–7500 Hz while maintaining a high attenuation rate near the resonance frequencies. This research provides new theoretical insights and practical guidance for the design and application of dissipative multi-resonator EMMs, holding promise for advancing broadband vibration and elastic wave suppression technologies.