Non-stationary approximate response of non-linear multi-degree-of-freedom systems subjected to combined periodic and stochastic excitation

• Published in: Mechanical systems and signal processing Vol. 166; p. 108420
• Main Authors: Kong, Fan, Han, Renjie, Li, Shujin, He, Wei
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.03.2022; Elsevier BV
• Subjects: Algorithms; Approximation; Combined excitation; Degrees of freedom; Differential equations; Equations of motion; Equivalence; Excitation; Linear equations; Mathematical analysis; Monte Carlo simulation; Multi-degree-of-freedom; Non-stationary; Nonlinear response; Nonlinear systems; Runge–Kutta methods; Stationary response; Statistical linearization; Non-stationary; Multi-degree-of-freedom; Runge–Kutta methods; Statistical linearization; Combined excitation
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2021.108420

An approximate method is presented for determining the non-stationary response of multi-degree-of-freedom non-linear systems subjected to combined periodic and stochastic excitation. Specifically, first, decomposing the system response as a combination of a periodic and of a zero-mean stochastic component, transfers the equation of motion into two sets of equivalent coupled differential sub-equations, governing the deterministic and the stochastic component, respectively. Next, the derived stochastic sub-equations under non-stationary stochastic excitation are cast into equivalent linear equations by resorting to the non-stationary statistical linearization method. Further, the related Lyapunov differential equations governing the second moment of the linear stochastic response, and the deterministic sub-equations governing the periodic response, are solved simultaneously using standard numerical algorithms. Pertinent Monte Carlo simulation demonstrates the applicability and accuracy of the proposed semi-analytical method. •Decomposing the total response gives coupled stochastic/deterministic sub-systems.•Applying statistical linearization to stochastic sub-system yields Lyapunov equation.•Considering simultaneously the derived two sub-systems yields the total response.