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.

Bifurcation Induced by Mass Variation in Piecewise Linear System

2012 ◽  
Vol 226-228 ◽  
pp. 531-535
Author(s):  
Yue Hua Li ◽  
Shi Dong Chen
Keyword(s):  
Linear System ◽  
Frequency Response ◽  
Averaging Method ◽  
Piecewise Linear ◽  
Singularity Theory ◽  
Excitation Amplitude ◽  
Mass Variation ◽  
Piecewise Linear System ◽  
Amplitude Frequency Response ◽  
Two Parameters

This paper investigates the bifurcations of the periodic solutions in the piecewise linear systems. Firstly the equation about amplitude-frequency response is deduced by the averaging method. Then the bifurcation classification is conducted by applying the singularity theory. The effects of the two parameters, the mass and the excitation amplitude, are discussed. The balance position will be changed when the quality changed, So the system is divided into two kinds of state. The results show that the parameter plane is divided into thirteen regions where bifurcation types are different. At last, discussing the amplitude- frequency response of different regions. this paper provides some theoretical guidance for system of considering load variation, and it is significant to help research the change in amplitude-frequency characteristic of piecewise linear system.

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

Vibration Analysis of Diesel’s Undercarriage by Virtual Measure and Actual Measure

2011 ◽  
Vol 228-229 ◽  
pp. 621-626
Author(s):  
Peng Liu ◽  
Ying Yun Huang ◽  
Hao Peng Gao ◽  
Da Sheng Ou
Keyword(s):  
Frequency Response ◽  
Time Domain ◽  
Vibration Analysis ◽  
Response Characteristics ◽  
Amplitude Frequency Response ◽  
Actual Measure ◽  
Frequency Response Characteristics ◽  
The Difference

This paper proposes to verify and test the vibration of diesel’s undercarriage got by virtual measure and actual measure through the analysis of time domain characteristics and amplitude frequency response characteristics of three-orientation vibrant speed of diesel’s undercarriage, represents the difference in time domain characteristics and amplitude frequency response characteristics got by virtual measure and actual measure, expounds the reasons of difference and puts forward a method to diminution the difference. It proves that virtual measure can replace actual measure in a way, though there are some difference in existence, we can erase these difference to the best of ours’ abilities through enough analysis.

DESIGN OF -1/2n ORDER ANALOG FRACTANCE APPROXIMATION CIRCUIT USING CONTINUED FRACTIONS DECOMPOSITION

2012 ◽  
Vol 21 (04) ◽  
pp. 1250035 ◽  
Author(s):  
YAN LIU ◽  
YI-FEI PU ◽  
JI-LIU ZHOU ◽  
XIAO-DONG SHEN
Keyword(s):  
Fractional Calculus ◽  
Frequency Response ◽  
Experimental Evidence ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Analog Circuit ◽  
Synthesis Method ◽  
Network Synthesis ◽  
Network Function ◽  
Amplitude Frequency Response

In order to solve the most important problem of the fractional calculus (FC) application, the realization of analog circuit of fractance, continued fraction theory is applied to design the -1/2n order analog fractance approximation circuit. The author presents a network function of ideal fractance and decomposes it in continued fractions (CFs) form to obtain the corresponding analog fractance approximation circuit. The new circuit consists of ordinary passive RC component through network synthesis method. Simulations are performed for the verification of the new circuit. Experimental evidence has proved that the performance of novel -1/2n order analog fractance approximation circuit is good in both amplitude-frequency response and phase-frequency response.

Two types of scale effects on the nonlinear forced vibration of axially moving nanobeams

2020 ◽  
Vol 34 (10) ◽  
pp. 2050095
Author(s):  
Jing Wang ◽  
Jianqiang Sun
Keyword(s):  
Mechanical Properties ◽  
Frequency Response ◽  
Continuum Mechanics ◽  
Forced Vibration ◽  
Characteristic Length ◽  
Scale Effects ◽  
Material Characteristic ◽  
Main Resonance ◽  
Amplitude Frequency Response ◽  
Axially Moving

Various non-classical continuum mechanics models appearing in previous studies cannot perfectly explain the mechanical properties of micro- and nanomaterials. Establishing a reasonable continuum mechanics model that comprehensively reflects the scale effect on material deformation is of great practical significance for objectively explaining the variation law of mechanical properties of micro- and nanomaterials under the combined action of different scale effects. Based on nonlocal strain gradient theory, a new scale-dependent model is proposed for axially moving nanobeams. In this study, an asymptotic expansion is performed using the multiscale time method to obtain the amplitude-frequency response curve of the equilibrium solutions for the forced vibration problem. Afterwards, the effects of various system parameters, especially the scale parameters, on the resonance curve are examined. Finally, the effects of nonlocal parameters and material characteristic length parameters on the amplitude-frequency response curves are investigated through typical numerical examples. The numerical results show that the nonlocal parameters promote the emergence of the main resonance, whereas the material characteristic length parameters suppress the emergence of the main resonance. Moreover, these parameters also affect the response amplitude and the skewness and jumping point of the amplitude-frequency characteristic curve.

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