Stability analysis of vibration absorbers

Abstract

Nonlinear dynamics of a two degrees-of-freedom (DOF) tuned and damped (untuned) vibration absorber systems using nonlinear springs and dampers are stndied as a boundary value problem. As far as tuned absorber is concerned, five different combinations of linear and nonlinear springs have been comprehensively analyzed. For the different cases, a comparative study is made varying the forcing frequency. Another comparison is for response versus time for different spring types at three important forcing frequencies: the tuned frequency and two resonant frequencies. Analysis shows that the response of the system is changed because of the spring nonlinearity; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. Similar investigation is made on untuned vibration absorbers, for 16 different cases varying the spring and damper characteristics. Analysis shows that higher nonlinearity terms make the system more unstable. Change in response is more evident near the frequency ratio of unity. Numerical simulation shows that the systems exhibit quasi periodic motion and instability as system's amplitude increases with time in prescribed boundary conditions. After analyzing 2 DOF system analysis is then made for a linear 3 DOF system.