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摘要
Fractional order derivative is a common expression of damper constitutive model, and it is difficult to obtain analytical solutions to dynamic responses of related structures. Efficient time domain numerical solving has important practical significance. Here, aiming at widely used Riemann-Liouville type fractional order damped structure, firstly, Adams-Moulton algorithm based on multi-step predictor-corrector mechanism was introduced to calculate fractional order derivative, and then an equivalent linear time-invariant dynamic system was constructed at each discrete time instant. Thirdly, combined with Newmark-β numerical integration method, explicit formulas for solving dynamic response at each instant were established to realize direct and rapid solving of dynamic response with high accuracy. Taking a single-DOF vibrator subjected to simple harmonic load/unit pulse as an example, the analytical solution, solutions obtained with two direct numerical solving methods, and the numerical solution obtained with the proposed method were compared to verify the high accuracy and stability of the proposed method. Finally, taking a multi-layer damped structure subjected to earthquake action as an example, the iterative numerical algorithm, the engineering approximation algorithm, and the proposed method were compared to further verify comprehensive advantages of the proposed method in terms of computational accuracy and efficiency, and reveal its potential in engineering applications. ? 2023 Chinese Vibration Engineering Society.
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