Ndjomatchoua Frank T, Djomo Thierry L M, Kemwoue Florent F, Gninzanlong Carlos L, Kepnang Maxime P, Siewe Martin S, Tchawoua Clément, Pedro Sansao A, Kofane Timoleon C
Spatial Transformation of Landscapes, Sustainable Impact through Rice-Based Systems, International Rice Research Institute (IRRI), DAPO Box 7777-1301, Metro Manila, Philippines.
Department of Civil Engineering, National Higher Polytechnic Institute, University of Bamenda, P.O. BOX 39, Bambili, Bamenda, Cameroon.
Chaos. 2022 Aug;32(8):083144. doi: 10.1063/5.0082235.
The present study considers the nonlinear dynamics of a Duffing oscillator under a symmetric potential subjected to a pulse-type excitation with a deformable shape. Our attention is focused on the effects of the external excitation shape parameter r and its period. The frequency response of the system is derived by using a semi-analytical approach. Interestingly, the frequency-response curve displays a large number of resonance peaks and anti-resonance peaks as well. Surprisingly, a resonance phenomenon termed here as shape-induced-resonance is noticed as it occurs solely due to the change in the shape parameter of the external periodic force. The system exhibits amplitude jumps and hysteresis depending on r. The critical driving magnitude for the chaos occurrence is investigated through Melnikov's method. Numerical analysis based on bifurcation diagrams and Lyapunov exponent is used to show how chaos occurs in the system. It is shown that the threshold amplitude of the excitation to observe chaotic dynamics decreases/increases for small/large values of r. In general, the theoretical estimates match with numerical simulations and electronic simulations as well.
本研究考虑了在对称势作用下受具有可变形形状的脉冲型激励的达芬振子的非线性动力学。我们的注意力集中在外部激励形状参数r及其周期的影响上。采用半解析方法推导了系统的频率响应。有趣的是，频率响应曲线还显示出大量的共振峰和反共振峰。令人惊讶的是，这里注意到一种仅由于外部周期力形状参数的变化而出现的共振现象，称为形状诱导共振。系统根据r表现出振幅跳跃和滞后现象。通过梅尔尼科夫方法研究了混沌发生的临界驱动幅度。基于分岔图和李雅普诺夫指数的数值分析用于展示系统中混沌是如何发生的。结果表明，对于r的小/大值，观察到混沌动力学的激励阈值幅度减小/增大。一般来说，理论估计与数值模拟以及电子模拟也相匹配。
