Abstract:
Dynamics of nonlinear self-excited vibrations for both two degrees of freedom system (2DOFS)
and three degrees of freedom system (3DOFS) using nonlinear springs and dampers is treated as a
boundary value problem (BVP) considering the self-exciting force as a function of displacement,
velocity or combination of both and nonlinear displacement terms. Four different cases have been
considered for this analysis. Each case comprises of four different conditions depending on selfexcited
force function. For different cases, a comparative study is performed varying the values of
parameters to find out whether the system is stable or not. Nonlinearity is also considered for both
springs and dampers to check the effect on the system’s response. A code has been developed to
determine the response of the system. Some parameters for system’s stability have been
determined from the system’s response obtained from the results of the developed code. It has
also been tried to identify some parameters for which the system always tends to be unstable. The
system’s behavior has also been observed by changing the values of self-excited force
coefficients. Numerical analysis using multi-segment integration technique also shows the various
phase planes and limit cycles in case of Van der Pol equation for various values of damping term,
ì. This validates the developed code in analyzing such problems.
