Non-stationary response of variable-mass Duffing oscillator with mass disturbance modeled as Gaussian white noise

2019 ◽  
Vol 526 ◽  
pp. 121018 ◽  
Author(s):  
Jie Cui ◽  
Wen-An Jiang ◽  
Zhao-Wang Xia ◽  
Li-Qun Chen
Keyword(s):  
White Noise ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Variable Mass ◽  
Stationary Response

Extension of Nonlinear Stochastic Solution to Include Sinusoidal Excitation—Illustrated by Duffing Oscillator

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
R. J. Chang
Keyword(s):  
White Noise ◽  
Correction Factor ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Noise Spectrum ◽  
Linearization Method ◽  
Algebraic Equations ◽  
Stochastic Solution ◽  
Non Gaussian ◽  
Sinusoidal Excitation

A new non-Gaussian linearization method is developed for extending the analysis of Gaussian white-noise excited nonlinear oscillator to incorporate sinusoidal excitation. The non-Gaussian linearization method is developed through introducing a modulated correction factor on the linearization coefficient which is obtained by Gaussian linearization. The time average of cyclostationary response of variance and noise spectrum is analyzed through the correction factor. The validity of the present non-Gaussian approach in predicting the statistical response is supported by utilizing Monte Carlo simulations. The present non-Gaussian analysis, without imposing restrictive analytical conditions, can be obtained by solving nonlinear algebraic equations. The non-Gaussian solution effectively predicts accurate sinusoidal and noise response when the nonlinear system is subjected to both sinusoidal and white-noise excitations.

scholarly journals Stationary Response of Flag-shaped Hysteretic System under Combined Harmonic and White Noise Excitations

2021 ◽  
Author(s):  
L.C. Chen ◽  
Huiying HU ◽  
Shushen Ye
Keyword(s):  
White Noise ◽  
Digital Simulation ◽  
Gaussian White Noise ◽  
Stochastic Averaging ◽  
Harmonic Excitation ◽  
Hysteretic Behavior ◽  
Stationary Response ◽  
Hysteretic System ◽  
Bifurcation Phenomenon ◽  
Stochastic Jump

Abstract The dynamical system containing flag-shaped hysteretic behavior is common in practice. In this paper, the stationary response of flag-shaped hysteretic system excited by harmonic excitation as well as Gaussian white noise is determined with the technique of stochastic averaging. The reliability of the presented approach is demonstrated by relevant digital simulation. The stochastic jump under a certain combination of parameters is found. The stochastic P-bifurcation phenomenon, i.e., the disappearance or appearance of bimodal shape of stationary response, occurs concerning to the variation of system’s parameters. Besides, the response of the system exposed to only harmonic excitation or non-resonance case is also examined for comparison, respectively. The numerical results show that the stationary amplitude response displays typical “soft” system behavior, and the deterministic jump may occur under pure harmonic excitation. Moreover, the non-resonance response is always weaker than that of resonant case.

Probabilistic Solution of Vibro-Impact Systems Under Additive Gaussian White Noise

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
H. T. Zhu
Keyword(s):  
White Noise ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Solution Procedure ◽  
Additive Gaussian White Noise ◽  
Stationary Probability Density Function ◽  
Probabilistic Solution ◽  
Zero Offset ◽  
Polynomial Closure

This paper presents a solution procedure for the stationary probability density function (PDF) of the response of vibro-impact systems under additive Gaussian white noise. The constraint is a unilateral zero-offset barrier. The vibro-impact system is first converted into a system without barriers using the Zhuravlev nonsmooth coordinate transformation. The stationary PDF of the converted system is governed by the Fokker–Planck equation which is solved by the exponential-polynomial closure (EPC) method. A vibro-impact Duffing oscillator with either elastic or lightly inelastic impacts is considered in a numerical analysis. Meanwhile, the level of nonlinearity in displacement is also examined in this study as well as the case of negative linear stiffness. Comparison with the simulated results shows that the EPC method can present a satisfactory PDF for displacement and velocity when the polynomial order is taken as 4 in the investigated cases. The tail of the PDF also works well with the simulated result.

Stationary Solution of Duffing Oscillator Driven by Additive and Multiplicative Colored Noise Excitations

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Siu-Siu Guo ◽  
Qingxuan Shi
Keyword(s):  
White Noise ◽  
Colored Noise ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Approximate Solutions ◽  
Intensity Level ◽  
First Order ◽  
Fpk Equation ◽  
Polynomial Closure ◽  
Mcs Method

A bistable Duffing oscillator subjected to additive and multiplicative Ornstein–Uhlenbeck (OU) colored excitations is examined. It is modeled through a set of four first-order stochastic differential equations by representing the OU excitations as filtered Gaussian white noise excitations. Enlargement in the state-space vector leads to four-dimensional (4D) Fokker–Planck–Kolmogorov (FPK) equation. The exponential-polynomial closure (EPC) method, proposed previously for the case of white noise excitations, is further improved and developed to solve colored noise case, resulting in much more polynomial terms included in the approximate solution. Numerical results show that approximate solutions from the EPC method compare well with the predictions obtained via Monte Carlo simulation (MCS) method. Investigation is also carried out to examine the influence of intensity level on the probability distribution solutions of system responses.

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