This paper presents a technique to obtain the transition curves of fractional periodic time-delayed (FPTD) systems based on a proposed explicit harmonic balance (EHB) method. This method gives the analytical Hill matrix of FPTD systems explicitly with a symbolic computation-free algorithm. Furthermore, all linear operations on Fourier basis vectors including fractional order derivative operators and time-delayed operators for a linear FPTD system are obtained. This technique is illustrated with parametrically excited simple and double pendulum systems, with both time-delayed states and fractional damping.
Transition Curve Analysis of Linear Fractional Periodic Time-Delayed Systems Via Explicit Harmonic Balance Method
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 28, 2015; final manuscript received August 28, 2015; published online November 13, 2015. Assoc. Editor: Gabor Stepan.
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Butcher, E. A., Dabiri, A., and Nazari, M. (November 13, 2015). "Transition Curve Analysis of Linear Fractional Periodic Time-Delayed Systems Via Explicit Harmonic Balance Method." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041005. https://doi.org/10.1115/1.4031840
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