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Tunable nonlinear band gaps in a sandwich-like meta-plate

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Abstract

This paper aims to explore the working mechanism of sandwich-like meta-plates by periodically attaching nonlinear mass-beam-spring resonators for low-frequency wave attenuation. The nonlinear MBS resonator consists of a mass, a cantilever beam, and a spring to provide negative stiffness in the transverse vibration of the resonator; this stiffness is tunable by changing the parameters of the spring. Considering the nonlinear stiffness of the resonator, the energy method is applied to obtain the dispersion relation of the sandwich-like meta-plate, and the band-gap bounds related to the amplitude of the resonator are derived by dispersion analysis. For a finite-sized sandwich-like meta-plate with a fully free boundary condition subjected to external excitations, its dynamic equation is established by the Galerkin method. The frequency response analysis of the meta-plate is carried out by numerical simulation, with the band-gap range obtained in good agreement with that of the theoretical one. Results show that the band-gap range of the present meta-plate is tunable by designing the structural parameters of the MBS resonator. Furthermore, by analyzing the vibration suppression of the finite-sized meta-plate, it is observed that the nonlinearity of the resonators can widen the wave attenuation range of the meta-plate.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 12072084, 11902093 and 11761131006), the Ph.D. Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities (No. 3072020GIP0206) and Fundamental Research Funds for the Central Universities.

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  1. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China

    Yu Xue, Jinqiang Li, Yu Wang & Fengming Li

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  1. Yu Xue
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Xue, Y., Li, J., Wang, Y. et al. Tunable nonlinear band gaps in a sandwich-like meta-plate. Nonlinear Dyn 106, 2841–2857 (2021). https://doi.org/10.1007/s11071-021-06961-8

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