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http://hdl.handle.net/2122/13024
Authors: | Zivieri, Roberto* Garesci, Francesca* Azzerboni, Bruno* Chiappini, Massimo* Finocchio, G.* |
Title: | Nonlinear dispersion relation in anharmonic periodic mass-spring and mass-in-mass systems | Journal: | Journal of Sound and Vibration | Series/Report no.: | /462 (2019) | Issue Date: | 2019 | DOI: | 10.1016/j.jsv.2019.114929 | Keywords: | Physics - Geophysics Physics - Geophysics physics.app-ph |
Abstract: | The study of wave propagation in chains of anharmonic periodic systems is of fundamental importance to understand the response of dynamical absorbers of vibrations and acoustic metamaterials working in nonlinear regime. Here, we derive an analytical nonlinear dispersion relation for periodic chains of anharmonic mass-spring and mass-in-mass systems resulting from considering the hypothesis of weak anharmonic energy and a periodic distribution function as ansatz of a general solution of the nonlinear equations of motion. Numerical simulations show that this expression is valid for anharmonic potential energy up to 50% of the harmonic one. This work provides a simple tool to design and study nonlinear dynamics for a class of seismic metamaterials. |
Appears in Collections: | Article published / in press |
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