Non-stationary approximate response of non-linear multi-degree-of-freedom systems subjected to combined periodic and stochastic excitation
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 com...
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Published in | Mechanical systems and signal processing Vol. 166; p. 108420 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Berlin
Elsevier Ltd
01.03.2022
Elsevier BV |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0888-3270 1096-1216 |
DOI: | 10.1016/j.ymssp.2021.108420 |