Frequency-Energy Analysis of Coupled Oscillator With Nonsmooth Asymmetrical Nonlinear Energy Sink

Abstract

The underlying nonlinear dynamical behavior of the linear oscillator (LO) attached with a nonlinear energy sink (NES) in which asymmetrical coupling force is employed is investigated here on the frequency-energy plot (FEP). Accordingly, the configuration of this asymmetrical nonlinear energy sink (ANES) incorporates a purely cubic-stiffness element on one side of the equilibrium position, while a linear restoring coupling stiffness acts on the other side. This configuration is capable to approximate the single-sided vibro-impact NES (SSVI NES) dynamics by employing a weak linear force in one side of the equilibrium position and strong nonlinear coupling force at the other side. The obtained FEP of the system under consideration reveals different kinds of backbone curves when the LO is attached to this ANES. Six continuous backbones of unsymmetrical nonlinear normal modes (NNMs) of 1:1 resonance between the LO and the ANES are obtained. The ANES has two fundamental backbones for in phase and antiphase periodic oscillations, respectively. The in phase backbone curve is associated with several subharmonic resonance branches which further assists resonance captures during the targeted energy transfer (TET) process. Therefore, the ANES merges significant linear and nonlinear dynamical properties in one configuration. Accordingly, an enhanced capability in TET is achieved by the ANES compared with the purely cubic-stiffness NES.