Details
| Original language | English |
|---|---|
| Article number | 104192 |
| Journal | International Journal of Non-Linear Mechanics |
| Volume | 147 |
| Early online date | 23 Aug 2022 |
| Publication status | Published - Dec 2022 |
Abstract
A semi-analytical method is proposed for determining the response of a lightly damped single-degree-of-freedom nonlinear system subjected to combined deterministic and non-stationary stochastic excitations. This is attained by combining the stochastic averaging and statistical linearization methodologies. Specifically, first, the system response is decomposed into two components, namely the deterministic and the stochastic parts. This leads to a set of coupled differential sub-equations governing, respectively, the deterministic and the stochastic component of the response. Next, aiming at solving the set of differential sub-equations, an additional expression is derived by applying the statistical linearization methodology, followed by the application of a stochastic averaging step to the stochastic sub-equations. Therefore, an equivalent time-varying linear system is defined for the original nonlinear system. The stochastic averaging method is then applied to the linearized system for reducing its order, and thus, its complexity from a solution perspective. In this regard, an additional equation is derived, which connects the deterministic and stochastic components of the response. The latter and the deterministic differential sub-equations are solved simultaneously for determining the system response. A single-degree-of-freedom nonlinear system exhibiting quadratic and cubic nonlinear stiffness is considered for assessing the reliability of the proposed technique. The obtained results are compared with pertinent Monte-Carlo simulation estimates.
Keywords
- Combined excitation, Evolutionary stochastic process, Nonlinear system, Statistical linearization, Stochastic averaging
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal of Non-Linear Mechanics, Vol. 147, 104192, 12.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Non-stationary response determination of nonlinear systems subjected to combined deterministic and evolutionary stochastic excitations
AU - Han, Renjie
AU - Fragkoulis, Vasileios C.
AU - Kong, Fan
AU - Beer, Michael
AU - Peng, Yongbo
N1 - Funding Information: The authors gratefully acknowledge the support from the German Research Foundation (Grant No. FR 4442/2-1 ) and from the National Natural Science Foundation of China (Grant no. 52078399 ).
PY - 2022/12
Y1 - 2022/12
N2 - A semi-analytical method is proposed for determining the response of a lightly damped single-degree-of-freedom nonlinear system subjected to combined deterministic and non-stationary stochastic excitations. This is attained by combining the stochastic averaging and statistical linearization methodologies. Specifically, first, the system response is decomposed into two components, namely the deterministic and the stochastic parts. This leads to a set of coupled differential sub-equations governing, respectively, the deterministic and the stochastic component of the response. Next, aiming at solving the set of differential sub-equations, an additional expression is derived by applying the statistical linearization methodology, followed by the application of a stochastic averaging step to the stochastic sub-equations. Therefore, an equivalent time-varying linear system is defined for the original nonlinear system. The stochastic averaging method is then applied to the linearized system for reducing its order, and thus, its complexity from a solution perspective. In this regard, an additional equation is derived, which connects the deterministic and stochastic components of the response. The latter and the deterministic differential sub-equations are solved simultaneously for determining the system response. A single-degree-of-freedom nonlinear system exhibiting quadratic and cubic nonlinear stiffness is considered for assessing the reliability of the proposed technique. The obtained results are compared with pertinent Monte-Carlo simulation estimates.
AB - A semi-analytical method is proposed for determining the response of a lightly damped single-degree-of-freedom nonlinear system subjected to combined deterministic and non-stationary stochastic excitations. This is attained by combining the stochastic averaging and statistical linearization methodologies. Specifically, first, the system response is decomposed into two components, namely the deterministic and the stochastic parts. This leads to a set of coupled differential sub-equations governing, respectively, the deterministic and the stochastic component of the response. Next, aiming at solving the set of differential sub-equations, an additional expression is derived by applying the statistical linearization methodology, followed by the application of a stochastic averaging step to the stochastic sub-equations. Therefore, an equivalent time-varying linear system is defined for the original nonlinear system. The stochastic averaging method is then applied to the linearized system for reducing its order, and thus, its complexity from a solution perspective. In this regard, an additional equation is derived, which connects the deterministic and stochastic components of the response. The latter and the deterministic differential sub-equations are solved simultaneously for determining the system response. A single-degree-of-freedom nonlinear system exhibiting quadratic and cubic nonlinear stiffness is considered for assessing the reliability of the proposed technique. The obtained results are compared with pertinent Monte-Carlo simulation estimates.
KW - Combined excitation
KW - Evolutionary stochastic process
KW - Nonlinear system
KW - Statistical linearization
KW - Stochastic averaging
UR - http://www.scopus.com/inward/record.url?scp=85137066877&partnerID=8YFLogxK
U2 - 10.1016/j.ijnonlinmec.2022.104192
DO - 10.1016/j.ijnonlinmec.2022.104192
M3 - Article
AN - SCOPUS:85137066877
VL - 147
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
SN - 0020-7462
M1 - 104192
ER -