ERVIS GEGA , FOTION MITRUSHI, JURGEN SHANO ,RAMADAN FIRANJ
KEYWORDS : Numerical method, differential equation, phase space, time series, Lyapunov exponents.
ABSTRACT :
Numerical methods of integration of differential equations give us a clearer and simpler picture of the dynamics and progress of the system, especially in cases where the system is unbalanced and jumps from one type of stability to another with the change of one of the parameters. The QZS vibration isolator is a simple case where numerical methods for solving ODE equations are quite favourable and efficient. In this study, a simplified Vibration Isolator model has been considered and the dynamics equations have been solved by means of numerical integration for different values of frequency and other parameters that affect the performance of the system assuming an inappropriate mass placed in system. Phase spaces, time series, and Poincare maps for the entire parameter space are presented. The chaoticity of the system has been studied by means of Lyapunov exponents and it has been concluded that the system is not chaos by considering different values of the control parameter. The presence of “periodic windows” in the bifurcation diagram, which was simulated with a simple but special method, through Poincare maps, was also ascertained. Examining the system dynamics for a wide range of control parameters gives us a clear picture of the system performance.