The modulation of response caused by the fractional derivative in the Duffing system under 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.

Nonlinear Vibrations of Innovative One-Way Clutch in Vehicle Alternator

One-way clutches have been proposed for vehicle alternators. The clutch can play an important role in reducing vibrations of the vehicle engine accessory system, but the severe vibrations of the clutch subsystem limit its stability and durability. This paper investigates the nonlinear vibrations of a one-way clutch between the accessory pulley and the alternator shaft. The one-way clutch is modelled as a discontinuous stiffness system, and the simplified model is analyzed using discontinuous transform to determine the periodic, primary resonance and the sub and super harmonic resonance solutions. The typical system model is numerically solved and the spectrum and phase plots are characterized. The results give a big picture of and insights into the nonlinear vibration features of one-way clutch system. A relevant US patent is pending.

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

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.