Design of dynamic absorber for two DOF system by fixed points theory (2nd report: case of the system with different mass and stiffness, and excited secondary mass)

Abstract

The fixed points theory is applied for the dynamic absorber attached to two degree of freedom system with different mass and stiffness. In this study, the case that the dynamic absorber is connected to the excited mass which is far from the base is considered. The frequencies of fixed points and the ratio of natural frequencies to equalize the amplitudes at fixed points are analytically derived, in case that the responses at fixed points are in phase. The damping coefficients which make fixed points extremal value are also obtained. It is found that some ratios of mass and stiffness have no fixed points with same amplitude in the frequency response curve of unexcited mass. But the fixed points always exist in the frequency response curve of excited mass. Furthermore, mass and stiffness ratios which equalize the amplitudes of all fixed points are obtained. For the frequency response curve of unexcited mass, the stiffness ratio that equalizes the amplitudes of all fixed points is uniquely determined for arbitrary chosen mass ratio. But for the frequency response curve of excited mass, the mass ratio changes the number of the stiffness ratio that equalizes the amplitudes of all fixed points into two or zero.