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A semi-analytical method for non-stationary response determination of nonlinear systems subjected to combined excitation
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Fan KONG1, 2, Hai-jun LIAO1, Ren-jie HAN1, 3, Yi ZHANG4, Xu HONG2
Journal of Vibration Engineering | 2024, 37(8) : 1339 - 1348
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Journal of Vibration Engineering | 2024, 37(8): 1339-1348
A semi-analytical method for non-stationary response determination of nonlinear systems subjected to combined excitation
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Fan KONG1, 2, Hai-jun LIAO1, Ren-jie HAN1, 3, Yi ZHANG4, Xu HONG2
Affiliations
  • 1School of Civil Engineering & Architecture, Wuhan University of Technology, Wuhan 430070, China
  • 2College of Civil Engineering, Hefei University of Technology, Hefei 230009, China
  • 3College of Civil Engineering, Tongji University, Shanghai 200092, China
  • 4China Construction Third Bureau First Engineering Co., Ltd., Wuhan 430040, China
Published: 2024-08-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.08.008
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The nonlinear dynamic systems exhibit particular behaviors when subjected to combined deterministic and stochastic excitation. A semi-analytical method for calculating the nonstationary response of a fractional nonlinear oscillator subjected to combined excitation is proposed. Representing the system response as a sum of a deterministic component and zero-mean stochastic component leads to two equivalent sub-equations for the differential equation of motion. The time-varying harmonic balance method is used for the nonstationary solution of the deterministic differential sub-equation，while the statistical linearization method is utilized for obtaining an equivalent linear substitution for the stochastic sub-equation. A semi-analytical solution of the equivalent linear equation is obtained by the Prony-SS and Laplace transform technique. The unknown deterministic/stochastic response components are obtained by solving the derived nonlinear algebraic equations simultaneously. Monte Carlo simulations demonstrate the applicability and accuracy of this method.

statistical linearization  /  time-varying harmonic balance  /  fractional derivative  /  nonlinear system  /  Prony-SS algorithm
Fan KONG, Hai-jun LIAO, Ren-jie HAN, Yi ZHANG, Xu HONG. A semi-analytical method for non-stationary response determination of nonlinear systems subjected to combined excitation[J]. Journal of Vibration Engineering, 2024 , 37 (8) : 1339 -1348 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.08.008
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Year 2024 volume 37 Issue 8
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Article Info
doi: 10.16385/j.cnki.issn.1004-4523.2024.08.008
  • Receive Date：2022-10-05
  • Online Date：2026-02-12
  • Published：2024-08-28
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History
  • Received：2022-10-05
  • Revised：2022-12-27
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Affiliations
    1School of Civil Engineering & Architecture, Wuhan University of Technology, Wuhan 430070, China
    2College of Civil Engineering, Hefei University of Technology, Hefei 230009, China
    3College of Civil Engineering, Tongji University, Shanghai 200092, China
    4China Construction Third Bureau First Engineering Co., Ltd., Wuhan 430040, China
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