Vibration absorption in systems with a nonlinear energy sink: Nonlinear damping

In this work, response regimes are investigated in a system comprising of a linear oscillator (subject to harmonic excitation) and a nonlinear energy sink (NES) with nonlinear damping characteristics. An analytical technique for the treatment of certain class of nonlinear damping functions is developed. Special attention is paid to the case of piecewise-quadratic damping, motivated by possible applications. It is demonstrated that the NES with a properly tuned piecewise-quadratic damping element allows complete elimination of undesirable periodic regimes. In this way, an efficient system of vibration absorption is obtained, and its performance can overcome that of a tuned mass damper (TMD). Numerical results agree satisfactorily with the analytical predictions.