Cross-scale energy transfer of chaotic oscillator chain in stiffness-dominated range

Abstract

The investigations on the dynamics of hierarchical oscillator chains provide basic theories for the elds of acoustic metamaterial and passive guidance of energy ow. In the present study, the characteristics of stiffness-dominated energy transfer of a reduced cross-scale oscillator chain that generates chaotic vibrations are studied. The semi-analytical solutions are obtained by the complexi cation-averaging method and the least-square method for thoroughly searching the branches of responses. Then the energy transfer patterns of the oscillator chain are analyzed based on Runge-Kutta method. Moreover, chaotic responses are determined using the displacements and Lyapunov exponents of the system. The average energy and normalized energy ux are de ned to evaluate the energy distribution in each oscillator and the energy transfer between oscillators, respectively. The semi-analytical results show that the oscillator chain produces complex unstable branches of response around the resonance frequency of the linear oscillator. It is found that the detached higher branches of response of the chain are similar to that of a system consisting of one linear oscillator and one cubic oscillator. When chaotic responses occur, the energy transfer patterns that re ected by average energy and normalized energy ux are similar in the same branch of response for different excitation frequencies. However, energy transfer patterns in different branches of response are quite different even at the same excitation frequency, and the higher branch generates the lower energy transfer. Furthermore, analyses of the input energy and the scale between cubic oscillators demonstrate that variations of the two parameters slightly affect the normalized energy ux.

Energy transfer mechanisms in binary tree-structured oscillator with nonlinear energy sinks

“…Systems having multiple NESs attached are even capable of exhibiting chaotic dynamics. In recent works of Chen et al [7,8], a chain of NESs were attached to a primary linear oscillator and the system was subjected to the harmonic forcing of the linear oscillator. They showed that for sufficiently high excitation amplitude the response of the system can be chaotic for specific frequency bands that depend on the excitation amplitude.…”

Energy transfer mechanisms in binary tree-structured oscillator with nonlinear energy sinks

“…Systems having multiple NES' attached are even capable of exhibiting chaotic dynamics. In a recent work of Chen et al [7,8] a chain of NES' were attached to a primary linear oscillator and the system was subjected to the harmonic forcing of the linear oscillator. They showed that for sufficiently high excitation amplitude the response of the system can be chaotic for specific frequency bands that depend on the excitation amplitude.…”