Non-linear stochastic response distributions by local statistical linearization

2001 ◽  
Vol 36 (7) ◽  
pp. 1135-1151 ◽  
Author(s):  
H.J. Pradlwarter
Keyword(s):  
Statistical Linearization ◽  
Stochastic Response ◽  
Non Linear

scholarly journals Approximate Stochastic Response of Hysteretic System With Fractional Element and Subjected to Combined Stochastic and Periodic Excitation

2021 ◽  
Author(s):  
Fan Kong ◽  
Renjie Han ◽  
Yuanjin Zhang
Keyword(s):  
Fractional Order ◽  
Harmonic Balance Method ◽  
System Response ◽  
Statistical Linearization ◽  
Algebraic Equations ◽  
Stochastic Response ◽  
Hysteretic System ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Linear Differential

Abstract A method based on statistical linearization is proposed, for determining response of the single-degree-of-freedom (SDOF) hysteretic system endowed with fractional derivatives and subjected to combined periodic and white/colored excitation. The method is developed by decomposing the system response into a combination of a periodic and of a zero-mean stochastic components. In this regard, first, the equation of motion is cast into two sets of coupled fractional-order non-linear differential equations with unknown deterministic and stochastic response components. Next, the harmonic balance method and the statistical linearization for the fractional-order deterministic and stochastic subsystems are used, to obtain the Fourier coefficients of the deterministic component and the variance of the stochastic component, respectively. This yields two sets of coupled non-linear algebraic equations which can be solved by appropriate standared numerical method. Pertinent numerical examples, including both softening and hardening Bouc-Wen hysteretic system endowed with different fractional-orders, are used to demonstrate the applicability and accuracy of the proposed method.

Non-linear stochastic response of a shallow cable

2006 ◽  
Vol 41 (3) ◽  
pp. 327-344 ◽  
Author(s):  
J.W. Larsen ◽  
S.R.K. Nielsen
Keyword(s):  
Stochastic Response ◽  
Non Linear

Stochastic Response of Hysteresis System Under Combined Periodic and Stochastic Excitation Via the Statistical Linearization Method

2021 ◽  
Vol 88 (5) ◽  
Author(s):  
Fan Kong ◽  
Pol D. Spanos
Keyword(s):  
Harmonic Balance Method ◽  
Linearization Method ◽  
System Response ◽  
Statistical Linearization ◽  
Algebraic Equations ◽  
Stochastic Response ◽  
Single Degree Of Freedom ◽  
Stochastic Component ◽  
Linear Differential

Abstract A statistical linearization approach is proposed for determining the response of the single-degree-of-freedom of the classical Bouc–Wen hysteretic system subjected to excitation both with harmonic and stochastic components. The method is based on representing the system response as a combination of a harmonic and of a zero-mean stochastic component. Specifically, first, the equation of motion is decomposed into a set of two coupled non-linear differential equations in terms of the unknown deterministic and stochastic response components. Next, the harmonic balance method and the statistical linearization method are used for the determination of the Fourier coefficients of the deterministic component, and the variance of the stochastic component, respectively. This yields a set of coupled algebraic equations which can be solved by any of the standard apropos algorithms. Pertinent numerical examples demonstrate the applicability, and reliability of the proposed method.

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