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Statistical analysis of linear oscillators with fractional derivative damping subjected to stationary and nonstationary stochastic excitations

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  • Sun, Wenkai
  • Kong, Xianren

Abstract

The statistical analysis of dynamic response of linear oscillators with rational and irrational fractional-order damping under stationary/nonstationary stochastic excitation is performed based on the Karhunen–Loève (K–L) expansion method. The K–L expansion method is utilized to decompose the autocovariance function of stochastic excitation into a set of independent identically distributed (iid) random variables and deterministic sub-excitations. For each deterministic sub-excitation, the dynamic response of the fractional order system is obtained by numerical method, and the statistical properties of the stochastic response of original system are obtained. Numerical cases include a single-degree-freedom (SDOF) linear system endowed with rational order and irrational order fractional derivative damping and subjected to stochastic stationary/nonstationary excitations represented by autocovariance function of four types, including exponential, squared exponential, Wiener process and nonstationary exponentially modulated autocovariance. The stochastic response derived by the K–L expansion method in time-domain exhibits satisfactory agreement with the results of frequency-domain solution or Monte Carlo (MC) simulations, validating the accuracy and reliability of the K–L expansion method.

Suggested Citation

  • Sun, Wenkai & Kong, Xianren, 2026. "Statistical analysis of linear oscillators with fractional derivative damping subjected to stationary and nonstationary stochastic excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 681(C).
    • Handle: RePEc:eee:phsmap:v:681:y:2026:i:c:s0378437125007447
    DOI: 10.1016/j.physa.2025.131092
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    References listed on IDEAS

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