Low-to-high frequency targeted energy transfer using a nonlinear energy sink with softening-hardening nonlinearity

Abstract

This paper investigates the performance of a nonlinear energy sink (NES) equipped with a softening–hardening (SH) element for mitigating vibrations that occur below its linear, low-energy frequency. First, an SH elastic struct is constructed, tested quasi-statically, and the resulting restoring force is modeled using a polynomial. Next, the SH polynomial is non-dimensionalized and a theoretical system composed of a linear oscillator (LO) and NES is studied where the NES has a linear, low-energy frequency above that of the LO. The underlying nonlinear normal modes (NNMs) of the system are studied by using harmonic excitation and tracking the changes in the frequency response functions. The transient performance of the NES is investigated and compared with that of a NES with the same linear stiffness but only a cubic nonlinearity. The theoretical performance of the NES is verified using a comparable experimental system that incorporates the SH elastic struct built in the beginning of the paper. The results of this work demonstrate that an SH NES is capable of mitigating vibrations that occur at frequencies below its own linear, low-energy frequency.