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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
Affiliation:
School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai, China
J.-S. Duan*
Affiliation:
School of Sciences, Shanghai Institute of Technology, Shanghai, China
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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.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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