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

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