Nonreciprocity of energy transfer in a nonlinear asymmetric oscillator system with various vibration states

• Published in: Applied mathematics and mechanics Vol. 44; no. 5; pp. 727 - 744
• Main Authors: Chen, Jian’en, Li, Jianling, Yao, Minghui, Liu, Jun, Zhang, Jianhua, Sun, Min
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2023; Springer Nature B.V; Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,School of Mechanical Engineering,Tianjin University of Technology,Tianjin 300384,China; National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology,Tianjin 300384,China%School of Aeronautics and Astronautics,Tiangong University,Tianjin 300387,China%Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,School of Mechanical Engineering,Tianjin University of Technology,Tianjin 300384,China%Agricultural Information Institute of Chinese Academy of Agricultural Sciences,Key Laboratory of Agricultural Big Data,Ministry of Agriculture and Rural Affairs,Beijing 100081,China%School of Science,Tianjin Chengjian University,Tianjin 300384,China
• Edition: English ed.
• Subjects: Amplitudes; Applications of Mathematics; Asymmetry; Classical Mechanics; Energy; Energy distribution; Energy transfer; Exact solutions; Excitation; Flow equations; Fluid- and Aerodynamics; Least squares method; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Oscillators; Partial Differential Equations; Resonant frequencies; Runge-Kutta method; Vibration; nonreciprocity; strong nonlinearity; 74H45; chaotic vibration; energy transfer; higher branch of response; O327
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-023-2987-9

The nonreciprocity of energy transfer is constructed in a nonlinear asymmetric oscillator system that comprises two nonlinear oscillators with different parameters placed between two identical linear oscillators. The slow-flow equation of the system is derived by the complexification-averaging method. The semi-analytical solutions to this equation are obtained by the least squares method, which are compared with the numerical solutions obtained by the Runge-Kutta method. The distribution of the average energy in the system is studied under periodic and chaotic vibration states, and the energy transfer along two opposite directions is compared. The effect of the excitation amplitude on the nonreciprocity of the system producing the periodic responses is analyzed, where a three-stage energy transfer phenomenon is observed. In the first stage, the energy transfer along the two opposite directions is approximately equal, whereas in the second stage, the asymmetric energy transfer is observed. The energy transfer is also asymmetric in the third stage, but the direction is reversed compared with the second stage. Moreover, the excitation amplitude for exciting the bifurcation also shows an asymmetric characteristic. Chaotic vibrations are generated around the resonant frequency, irrespective of which linear oscillator is excited. The excitation threshold of these chaotic vibrations is dependent on the linear oscillator that is being excited. In addition, the difference between the energy transfer in the two opposite directions is used to further analyze the nonreciprocity in the system. The results show that the nonreciprocity significantly depends on the excitation frequency and the excitation amplitude.