Wideband vibration attenuation of a metamaterial beam via integrated hardening and softening nonlinear resonators

Nonlinear metamaterials (NLMs) have recently garnered significant interest for their abilities to achieve wide bandwidth in vibration attenuation and wave manipulation. However, NLMs proposed have been predominantly theoretical and conceptual due to nonlinearity being introduced through discrete spring models rather than the practically achievable components. To overcome this shortcoming, this paper proposes an original integrated design strategy leveraging a mono-slender beam configuration to tailor nonlinear stiffness and form quasi-linear, hardening and softening resonators. By adjusting only one geometric parameter of the beam, transitions between different nonlinear types can be realized. The nonlinear behaviors of resonators are verified through static force–displacement curves and frequency-amplitude responses. Subsequently, a metamaterial beam comprising a linear host beam and periodically distributed integrated hardening and softening nonlinear resonators is constructed. The dispersion relation for an infinite-size beam is derived using the transfer matrix method. The resulting complex band structure and nonlinear frequency response reveal that the bandgap is amplitude-dependent and more importantly, broadened due to the introduced nonlinearities. Furthermore, vibration attenuation in a finite NLM beam is demonstrated in a broad nonlinear-dependent frequency region which aligns well with the predicted bandgap. The analysis of the power spectral density within this region indicates that the attenuation is due to frequency dissipation caused by the nonlinear interaction between the resonators and the host beam. This study presents a promising solution for advancing the practical application of nonlinear metamaterials.