Analysis of Non-linear Self-excited Vibrations for Multiple Degrees of Freedom Systems

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.