Analytical Nonstationary Response of Linear Stochastic MDOF Systems Endowed with Half-Order Fractional Derivative Elements
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 1
Abstract
This paper presents a novel method for obtaining analytical solutions for the nonstationary response of multidegree-of-freedom (MDOF) systems endowed with half fractional derivative elements and subjected to external stochastic excitation. Specifically, first, the proposed technique employs eigenvector expansion of the state-space formulation and Laplace transforms to derive an analytical solution for the impulse/frequency response function (IRF/FRF) of the fractional-order dynamic system. Moreover, by utilizing the Laplace transform method, exact analytical solutions for the second-moment response are obtained in the frequency domain. A comprehensive set of six numerical cases is presented to demonstrate the effectiveness of this novel methodology. These cases include two degenerated scenarios, namely a single-degree-of-freedom (SDOF) system and a two-degree-of-freedom (2-DOF) linear system, both endowed with half-order fractional derivative elements and subjected to stochastic stationary/nonstationary excitations, including white noise, modulated white noise, and modulated colored noise with modified Kanai-Tajimi spectrum. The analytical nonstationary responses derived by the proposed method exhibit exceptional agreement with pertinent Monte Carlo simulations, validating the accuracy and reliability of the proposed approach.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is supported by grants from the National Natural Science Foundation of China (Grant No. 52078399).
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 1 • March 2024
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© 2023 American Society of Civil Engineers.
History
Received: Jun 26, 2023
Accepted: Sep 5, 2023
Published online: Oct 30, 2023
Published in print: Mar 1, 2024
Discussion open until: Mar 30, 2024
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Cited by
- Alberto Di Matteo, Pol D. Spanos, Determination of Nonstationary Stochastic Response of Linear Oscillators With Fractional Derivative Elements of Rational Order, Journal of Applied Mechanics, 10.1115/1.4064143, 91, 4, (2023).