Stochastic averaging on a nonlinear oscillator with coordinate-dependent mass excited by Gaussian white noises

2021 ◽  
Vol 143 ◽  
pp. 110609
Author(s):  
Gen Ge ◽  
Jie Liu
Keyword(s):  
Nonlinear Oscillator ◽  
Stochastic Averaging ◽  
Dependent Mass ◽  
White Noises

First-Crossing Problem of Weakly Coupled Strongly Nonlinear Oscillators Subject to a Weak Harmonic Excitation and Gaussian White Noises

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Y. J. Wu ◽  
H. Y. Wang
Keyword(s):  
Harmonic Function ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Digital Simulation ◽  
Stochastic Averaging ◽  
Harmonic Excitation ◽  
Van Der Pol Oscillator ◽  
Strongly Nonlinear ◽  
Set Up ◽  
White Noises

We study first-crossing problem of two-degrees-of-freedom (2DOF) strongly nonlinear mechanical oscillators analytically. The excitation is the combination of a deterministic harmonic function and Gaussian white noises (GWNs). The generalized harmonic function is used to approximate the solutions of the original equations. Four cases are studied in terms of the types of resonance (internal or external or both). For each case, the method of stochastic averaging is used and the stochastically averaged Itô equations are obtained. A backward Kolmogorov (BK) equation is set up to yield the failure probability and a Pontryagin equation is set up to yield average first-crossing time (AFCT). A 2DOF Duffing-van der Pol oscillator is chosen as an illustrative example to demonstrate the effectiveness of the analytical method. Numerically analytical solutions are obtained and validated by digital simulation. It is shown that the proposed method has high efficiency while still maintaining satisfactory accuracy.

On certain properties of nonlinear oscillator with coordinate-dependent mass

2017 ◽  
Vol 381 (39) ◽  
pp. 3417-3423 ◽  
Author(s):  
B.I. Lev ◽  
V.B. Tymchyshyn ◽  
A.G. Zagorodny
Keyword(s):  
Nonlinear Oscillator ◽  
Dependent Mass

scholarly journals Stochastic Bifurcations of a Fractional-Order Vibro-Impact System Driven by Additive and Multiplicative Gaussian White Noises

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yong-Ge Yang ◽  
Ya-Hui Sun ◽  
Wei Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Stochastic Systems ◽  
Original System ◽  
Stochastic Averaging ◽  
Impact Factors ◽  
Stochastic Bifurcation ◽  
Fractional Order Systems ◽  
Impact System ◽  
White Noises

Stochastic fractional-order systems or stochastic vibro-impact systems can present rich dynamical behaviors, and lots of studies dealing with stochastic fractional-order systems or stochastic vibro-impact systems are available now, while the discussion on the stochastic systems with both vibro-impact factors and fractional derivative element is rare. This paper is concerned with the stochastic bifurcation of a fractional-order vibro-impact system driven by additive and multiplicative Gaussian white noises. Firstly, we can remove the discontinuity of the original system with the help of nonsmooth transformation and obtain the equivalent stochastic system. Then, we adopt the stochastic averaging method to get the approximately analytical solutions. At last, an example is discussed in detail to assess the reliability of the developed approach. We also find that the coefficient of restitution factor, fractional derivative coefficient, and fractional derivative order can induce the stochastic bifurcation.

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