scholarly journals Simultaneous primary and super-harmonic resonance of Duffing oscillator

2021 ◽  
Vol 70 (4) ◽  
pp. 040502-040502
Author(s):  
Li Hang ◽  
◽  
Shen Yong-Jun ◽  
Yang Shao-Pu ◽  
Peng Meng-Fei ◽  
...  
Keyword(s):  
Duffing Oscillator ◽  
Harmonic Resonance ◽  
Super Harmonic Resonance

scholarly journals The modulation of response caused by the fractional derivative in the Duffing system under super-harmonic resonance

2021 ◽  
pp. 126-126
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Qixun Lan ◽  
Yujie Cai ◽  
Huafeng Xu ◽  
...  
Keyword(s):  
Approximate Solution ◽  
Fractional Derivative ◽  
Frequency Response ◽  
Duffing Oscillator ◽  
Time History ◽  
Singularity Theory ◽  
Critical Parameters ◽  
Amplitude Frequency Response ◽  
Harmonic Resonance ◽  
Super Harmonic Resonance

The dynamic characteristics of the 3:1 super-harmonic resonance response of the Duffing oscillator with the fractional derivative are studied. Firstly, the approximate solution of the amplitude-frequency response of the system is obtained by using the periodic characteristic of the response. Secondly, a set of critical parameters for the qualitative change of amplitude-frequency response of the system is derived according to the singularity theory and the two types of the responses are obtained. Finally, the components of the 1X and 3X frequencies of the system?s time history are extracted by the spectrum analysis, and then the correctness of the theoretical analysis is verified by comparing them with the approximate solution. It is found that the amplitude-frequency responses of the system can be changed essentially by changing the order and coefficient of the fractional derivative. The method used in this paper can be used to design a fractional order controller for adjusting the amplitude-frequency response of the fractional dynamical system.

Super-Harmonic Resonance Analysis on Torsional Vibration of Misaligned Rotor Driven by Universal Joint

2010 ◽  
Vol 26-28 ◽  
pp. 1226-1231 ◽  
Author(s):  
Chang Lin Feng ◽  
Yong Yong Zhu ◽  
De Shi Wang
Keyword(s):  
Periodic Solution ◽  
Torsional Vibration ◽  
Stable Region ◽  
Universal Joint ◽  
Weakly Nonlinear ◽  
Resonance Analysis ◽  
Actual Error ◽  
The Stability ◽  
Harmonic Resonance ◽  
Super Harmonic Resonance

The super-harmonic resonance of the nonlinear torsional vibration of misaligned rotor system driven by universal joint was studied considering both natural structure misalignment and actual error misalignment. Utilizing multi-scale method, the periodic solution of weakly nonlinear torsional vibration equation was obtained corresponding to super-harmonic resonance, including amplitude-frequency and phase-frequency characteristic expressions of steady periodic solution. The stability of equilibrium point was investigated using Lyapunov first approximate stability theory, then the stable region and unstable region on the amplitude of the super-harmonic resonance periodic solution, which varied with the detuning parameter. At last, the driving shaft’s steady periodic motion of the first approximation and its calculation simulation were carried out according to the kinetic relation about driven shaft and driving shaft. It is found that jumping phenomenon and dynamic bifurcation occur when the rotating angular velocity of driving shaft is half of the natural frequency of the deriving system. The results above indicate the fundamental characteristic of the nonlinear dynamic on the misaligned rotor, also applying the foundation for advanced bifurcation and singularities analysis.

scholarly journals Super-harmonic resonance of fractional-order van der Pol oscillator

2014 ◽  
Vol 63 (1) ◽  
pp. 010503
Author(s):  
Wei Peng ◽  
Shen Yong-Jun ◽  
Yang Shao-Pu
Keyword(s):  
Fractional Order ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Harmonic Resonance ◽  
Super Harmonic Resonance

Second super-harmonic resonance response of cantilever beam with bolt joint under low pretension

2016 ◽  
Vol 24 (11) ◽  
pp. 2769-2776
Author(s):  
李耀彬 LI Yao-bin ◽  
于化东 YU Hua-dong ◽  
王强龙 WANG Qiang-long ◽  
伞晓刚 SAN Xiao-gang ◽  
刘震宇 LIU Zhen-yu
Keyword(s):  
Cantilever Beam ◽  
Resonance Response ◽  
Harmonic Resonance ◽  
Super Harmonic Resonance

scholarly journals Investigation on Non-Linear Vibration Response of Cantilevered Thin Plates with Crack Using Electronic Speckle Pattern Interferometry

Proceedings ◽  
2018 ◽  
Vol 2 (8) ◽  
pp. 539
Author(s):  
Nan Tao ◽  
Yinhang Ma ◽  
Hanyang Jiang ◽  
Meiling Dai ◽  
Fujun Yang
Keyword(s):  
Mode Shape ◽  
Speckle Pattern ◽  
Experimental Studies ◽  
Forced Response ◽  
Thin Plates ◽  
Mode Shapes ◽  
Electronic Speckle Pattern Interferometry ◽  
Intact Specimen ◽  
Harmonic Resonance ◽  
Super Harmonic Resonance

The time-averaged electronic speckle pattern interferometry (ESPI) is employed to measure the frequencies and mode shapes of thin, cantilevered plates with root-slit. The first 12 order linear resonance frequency and mode shape of an intact cantilevered plate is determined by using FEM calculation. The dynamic response of the intact specimen forced by a PZT actuator is measured and its super-harmonic resonance of forced response is investigated experimentally. The results show that the principal mode shape of super-harmonic vibration is similar to its natural modal. In contrast to linear forcing vibration, the threshold of force for super-harmonic resonance is much higher than that of the former. In addition, linear free response of four cantilevered root-slit plates with variation length of slit are analyzed by applying the FEM calculation, and their responses of forcing vibration were measured by using the ESPI method. The validity and accuracy of the numerical prediction are confirmed through experimental studies. The present work shows that the ESPI technique can provide whole-field and real-time measurement for vibration analysis and can also be employed for validation of the FEM calculation.

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