On the estimation of linear viscous damping in the duffing oscillator

Abstract

This paper introduces simple analytical expressions for the damping ratio and the non-linearity in the hardening Duffing oscillator. The damping ratio and the non-linearity are estimated using the jump-up and the jump-down frequencies from the displacement response of the system. The jump-up and the jump-down frequencies are obtained analytically using the frequency-amplitude relationship of the system, which is solved using the Harmonic Balance method (HBM). Both the force- and the base-excited systems are investigated in this paper. Experimental results for the base-excited system are included to demonstrate the accuracy of the estimation.