Abstract
Three nonlinearly elastic extended mass-in-mass metamaterial models are asymptotically studied using their long wavelength continuum limits. The governing nonlinear equations with dispersion are obtained for longitudinal strain including dispersion effects. Both nonlinear stiffness of the main chain spring and those of the attached masses are taken into account. It is shown that the nonlinearities and dispersion differently affect the dynamics of the longitudinal strain waves for the models considered.
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Acknowledgements
The work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the state assignment under contract No. 12112500318-1.
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Porubov, A.V. (2023). Nonlinearity and Dispersion in Extended Mass-in-Mass Metamaterials. In: Altenbach, H., Eremeyev, V. (eds) Advances in Linear and Nonlinear Continuum and Structural Mechanics. Advanced Structured Materials, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-031-43210-1_21
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DOI: https://doi.org/10.1007/978-3-031-43210-1_21
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