Symmetric and asymmetric periodic motions of a nonlinear oscillator with a tuned mass damper inerter

In this paper, periodic responses in a nonlinear oscillator with electromagnetic resonant shunt tuned mass damper inerter (ERS-TMDI) are studied. Symmetric and asymmetric periodic motions of such a system are obtained through an implicit mapping method. The stability and bifurcation analysis of periodic motions are completed through eigenvalue analysis. Frequency–amplitude characteristics of periodic motions are presented by the finite Fourier series analysis for a better understanding of nonlinear responses of the nonlinear oscillator with electromagnetic resonant shunt tuned mass damper inerter. Numerical simulations of the stable periodic motions are presented to verify the semi-analytical predictions of symmetric and asymmetric periodic motions. The asymmetric periodic motions cannot be obtained easily by the traditional methods. The frequency–amplitude characteristics of symmetric and asymmetric periodic motions are very good for design of ERS-TMDI. The results presented herein are also applicable for wind-induced vibration, earthquake building vibration reduction and energy harvesting.