Numerical Simulation Of Nonlinear Dynamics In Multi-dimensional Two-time-scale Rigid-flexible Coupling System

Multi-dimens ional nonlinear systems present highly complex dynamic behavior. Time varying and randomization make it even more difficult to analyze the nonlinear behavior of the system. A rigid-flexible coupling system usually contains two-time-scale variables: both fast and slow variables. The wide range motion couples with the elastic deformation, constituting a strongly nonlinear dynamic equation. It may also causes stiff problems, which require a more outstanding numerical method.In this artic le, theoretical analys is and numerical simulation is performed to study a few multi-dimensional two-time-scale rigid-flexible coupling systems. Combining the characteristics of the spring pendulum and the double pendulum, we construct the planar rigid rod and spring pendulum models. Dimensionless dynamical equation is given. A cubic interpolation precise integration method with high precision and efficiency is applied to solve the strongly nonlinear dynamic equation. We employ the maximum Lyapunov exponents and Poincaré sections together with time-history curves and phase plots to analyze the complex nonlinear dynamic behavior of the systems. The path to chaos via quasi-periodic torus breakdown of the fast variable is discovered and controlled parameters range related to the motion state is given. Complex dynamic behavior such as chaos in flexible component is exposed, which is expected to provide references for analys is of systems in engineering both theoretically and numerically.