Multi-frequency nonlinear energy transfer from linear oscillators to mdof essentially nonlinear attachments

Abstract

We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multidegree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous resonance interactions of both linear modes with a set of nonlinear normal modes (NNMs) of the attachment, and is studied utilizing numerical wavelet transforms. The multi-frequency nonlinear energy transfer discussed herein differs from multi-frequency energy transfer caused by resonance capture cascading where sequential energy transfer from a set of linear modes to single-dof nonlinear attachments takes place. r

Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments

“…In the limit ε → 0, the system decomposes into two uncoupled oscillators: a 2-DOF linear primary system with natural frequencies ω 1 = ω 2 0 + 2α and ω 2 = ω 0 < ω 1 , corresponding to out-of-phase and in-phase linear modes, respectively; and a 3-DOF essentially nonlinear oscillator with a rigid-body mode and two flexible nonlinear normal modes, NNMs [12].…”

Control of primary and subharmonic resonances of a Duffing oscillator via non-linear energy sink

“…Multi-d.o.f. nonlinear control devices and multi-frequency energy exchanges are analyzed in [28]. The effect of NES on a Duffing oscillator under impulsive force is analyzed in [29], picking up information on the energy transfer phenomenon from the underlying Hamiltonian system and, consequently, from the Non-linear Normal Modes.…”

Targeted energy transfer efficiency in a low-dimensional mechanical system with an essentially nonlinear attachment

“…Hence, the WTMM can be potentially applied to describe more complex energy transfer pattern in higher-dimensional systems. In recent years, the field of TET has advanced rapidly into applications [16,[22][23][24][25]. It would be of interest to apply the WTMM technique to these sophisticated systems to examine the intricate modal interactions in TET.…”