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首页> 外文会议>International Conference on Vibration Problems >Nonlinear Dynamics of Traveling Continua with low flexural stiffness under Parametric and Internal Resonances
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Nonlinear Dynamics of Traveling Continua with low flexural stiffness under Parametric and Internal Resonances

机译：参数和内部共振下具有低弯曲刚度的连续脉冲的非线性动力学

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This study focuses on the trivial state stability boundary, steady state periodic response and chaotic behavior in the transverse motion of an axially moving viscoelastic continuum subject to parametric excitation and internal resonance. This parametric excitation comes from harmonic fluctuations of the traveling speed. The motion is restricted by viscous damping as well as material damping. The derived nonlinear integro-partial-differential equation of motion is solved through analytic-numerical approach. Direct method of multiple scales is used to solve the nonlinear equation of motion. A continuation algorithm is used to find the steady state response. Furthermore, Runge-Kutta method is applied to find the dynamic behavior of the system. The stable periodic response and the unstable chaotic motions are identified using different tools including the time traces, Phase portraits, Poincare map, fast Fourier transforms. Evolution of maximum Lyapunov exponent is used to locate the range of system parameters for which chaotic behavior exists.
机译：该研究重点介绍了轴向移动的粘弹性连续体的横向运动的阶段稳定性边界，稳态周期性响应和混沌行为，其参数激发和内部共振。该参数激发来自旅行速度的谐波波动。运动受粘性阻尼以及材料阻尼的限制。通过分析 - 数值方法解决了运动的衍生非线性积分部分分型方程。多个尺度的直接方法用于解决运动的非线性方程。继续算法用于找到稳态响应。此外，应用Runge-Kutta方法来找到系统的动态行为。使用不同的工具识别稳定的周期性响应和不稳定的混沌动作，包括时间迹线，相位肖像，庞加拉尔地图，快速傅里叶变换。最大Lyapunov指数的演变用于定位存在混乱行为的系统参数范围。

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