Abstract
Based on the fractional variational theory and Hamilton principle, this paper extends a semi-analytic solution and further develops a fractional-order dynamical model of pipe flow. This model facilitates the dynamical coupling of hydraulic and mechanical systems, and ensures easily have the solution for both the physical characteristics by state space equation or the damped vibration characteristics by fractional Bagley–Torvik equation. Subsequent application in an actual hydropower system reveals the potential periodic vibration of pipe flow and the effect of fractional order memory on the dashpot time constant. The comparison of these findings with the smaller alignment index (SALI) detection results reaffirms the soundness of this study.
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