Free propagation of resonant waves in nonlinear dissipative metamaterials

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Alessandro Fortunati, Andrea Arena, Marco Lepidi, Andrea Bacigalupo, Walter Lacarbonara
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引用次数: 0

Abstract

This paper deals with the free propagation problem of resonant and close-to-resonance waves in one-dimensional lattice metamaterials endowed with nonlinearly viscoelastic resonators. The resonators' constitutive and geometric nonlinearities imply a cubic coupling with the lattice. The analytical treatment of the nonlinear wave propagation equations is carried out via a perturbation approach. In particular, after a suitable reformulation of the problem in the Hamiltonian setting, the approach relies on the well-known resonant normal form techniques from Hamiltonian perturbation theory. It is shown how the constructive features of the Lie Series formalism can be exploited in the explicit computation of the approximations of the invariant manifolds. A discussion of the metamaterial dynamic stability, either in the general or in the weak dissipation case, is presented.

非线性耗散超材料中共振波的自由传播
本文讨论了共振波和接近共振波在装有非线性粘弹性谐振器的一维晶格超材料中的自由传播问题。谐振器的构成和几何非线性意味着与晶格的立方耦合。非线性波传播方程的分析处理是通过扰动方法进行的。特别是,在哈密顿设置中对问题进行适当重述后,该方法依赖于哈密顿扰动理论中著名的共振法线形式技术。研究表明,在显式计算不变流形的近似值时,如何利用列数列形式主义的构造特征。此外,还讨论了超材料在一般或弱耗散情况下的动态稳定性。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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