Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals

E. G. Charalampidis, F. Li*, C. Chong, J. Yang, P. G. Kevrekidis

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

9 引用 (Scopus)

摘要

We consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2: 1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modes and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualization of the time-periodic structures.

源语言英语
文章编号830978
期刊Mathematical Problems in Engineering
2015
DOI
出版状态已出版 - 2015
已对外发布

指纹

探究 'Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals' 的科研主题。它们共同构成独一无二的指纹。

引用此