Non-linear Analysis of Rotational Inertial Double-Tuned Mass Damper by Harmonic Balance Method

Abstract

A theoretical non-linear analysis of rotational inertia double-tuned mass damper (RIDTMD) is carried out to suppress vibration of a single degree of freedom (SDOF) non-linear spring, mass system, which undergoes external harmonic force excitation. An approximate solution to the governing equation of motions system is obtained by using harmonic balance method (HBM) for the primary resonance condition and verified with that of fourth-order Runge–Kutta method. It is shown that with the addition of cubic non-linear stiffness in the RIDTMD, vibration suppression SDOF primary system is more than only linear stiffness at resonating frequency of operation. This work is an extended work of Garrido et al. (Eng Struct 56:2149–2153, 2013), where only linear analysis has been carried out.