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.
