Frequency response characteristics of two DOF Duffing system with mass proportional damping

Abstract

In our previous study, stiffness proportional damping is used, and the nonlinear characteristics appears only near the first resonance frequency. To investigate nonlinear property of higher order mode, mass proportional damping is considered because the modal damping coefficients decrease as mode order increases. In this paper, we use two combinations of the stiffnesses. These combinations of the stiffnesses have same natural frequencies, but differ in the localization of linear modal vectors. Frequency response curves are calculated by harmonic balance method. Numerical results show that the nonlinear characteristics appears only near the second resonance frequency in both combinations of stiffnesses. But there is difference in the ratios of the peak values of amplitudes of first and second resonance for two combinations of stiffnesses. The system with localized modal vectors has larger ratio of peak values of amplitudes than the system with un-localized ones. In addition, modal coordinates are calculated by multiplying the displacements by linear modal vectors. Although the modal vectors are calculated for the corresponding linear system, the modal coordinates can mostly decouple first and second modes. Frequency response curves of the modal coordinate for two combinations of stiffness system become almost same.