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Equivalent Nonlinearization Technique for Random Analysis of Nonlinear System With Fractional Derivative Damping
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Equivalent Nonlinearization Technique for Random Analysis of Nonlinear System With Fractional Derivative Damping
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Journal Article
Equivalent Nonlinearization Technique for Random Analysis of Nonlinear System With Fractional Derivative Damping
2025
Overview
Solving nonlinear systems with fractional derivative damping is often challenging, particularly in cases of strong damping and excitation. To derive solutions for such strong nonlinear systems more concisely, this manuscript presents an approximate method for analyzing the random responses of nonlinear systems with fractional derivative damping. By representing the system responses as generalized harmonic functions, the impact of fractional derivative damping is effectively transformed into a quasilinear damping and quasilinear stiffness with amplitude‐dependent coefficients. Consequently, the nonlinear system with fractional derivative damping is approximately replaced by a modified nonlinear system that excludes the fractional derivative term. The equivalent nonlinear system of this modified nonlinear system is established through a careful selection of the equivalent system family and by minimizing the discrepancies between them. This process leads to an iterative determination of the equivalent nonlinear system, allowing the statistical properties of the original system with fractional derivative damping to be approximated using those of the equivalent system. The consistency of the proposed results with those obtained from Monte Carlo simulations demonstrates the method’s effectiveness, while its simplicity highlights its advantages over conventional stochastic averaging techniques. Furthermore, the proposed approach can be extended to strong nonlinear damping systems, such as hysteresis systems and viscoelastic systems subjected to Gaussian white noise.
Publisher
John Wiley & Sons, Inc,Wiley
