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Steady-State Response to Periodic Excitation in Fractional Vibration System

Published online by Cambridge University Press:  04 January 2016

C. Huang  and
J.-S. Duan
C. Huang
Affiliation:
School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai, China
J.-S. Duan*
Affiliation:
School of Sciences, Shanghai Institute of Technology, Shanghai, China
*
* (duanjs@sit.edu.cn)
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Abstract

The steady-state response to periodic excitation in the linear fractional vibration system was considered by using the fractional derivative operator . First we investigated the response to the harmonic excitation in the form of complex exponential function. The amplitude-frequency relation and phase-frequency relation were derived. The effect of the fractional derivative term on the stiffness and damping was discussed. For the case of periodic excitation, we decompose the periodic excitation into a superposition of harmonic excitations by using the Fourier series, and then utilize the results for harmonic excitations and the principle of superposition, where our adopted tactics avoid appearing a fractional power of negative numbers to overcome the difficulty in fractional case. Finally we demonstrate the proposed method by three numerical examples.

Keywords

Fractional calculusFractional vibrationResponseExcitation.
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 1 , February 2016 , pp. 25 - 33
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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