Moment Lyapunov exponent and stochastic stability for a binary airfoil driven by an ergodic real noise

2013 ◽  
Vol 73 (3) ◽  
pp. 1601-1614 ◽  
Author(s):  
X. Li ◽  
X. B. Liu
Keyword(s):  
Lyapunov Exponent ◽  
Stochastic Stability ◽  
Real Noise ◽  
Moment Lyapunov Exponent

scholarly journals Stochastic Stability of Coupled Viscoelastic Systems Excited by Real Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jian Deng
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Stochastic Stability ◽  
Random Fluctuation ◽  
Largest Lyapunov Exponent ◽  
Real Noise ◽  
The Largest Lyapunov Exponent ◽  
The Stability ◽  
The Moment ◽  
Moment Lyapunov Exponents

The moment stochastic stability and almost-sure stochastic stability of two-degree-of-freedom coupled viscoelastic systems, under the parametric excitation of a real noise, are investigated through the moment Lyapunov exponents and the largest Lyapunov exponent, respectively. The real noise is also called the Ornstein-Uhlenbeck stochastic process. For small damping and weak random fluctuation, the moment Lyapunov exponents are determined approximately by using the method of stochastic averaging and a formulated eigenvalue problem. The largest Lyapunov exponent is calculated through its relation with moment Lyapunov exponents. The stability index, the stability boundaries, and the critical excitation are obtained analytically. The effects of various parameters on the stochastic stability of the system are then discussed in detail. Monte Carlo simulation is carried out to verify the approximate results of moment Lyapunov exponents. As an application example, the stochastic stability of a flexural-torsional viscoelastic beam is studied.

Moment Lyapunov Exponent and Stochastic Stability of Two Coupled Oscillators Driven by Real Noise

2001 ◽  
Vol 68 (6) ◽  
pp. 903-914 ◽  
Author(s):  
N. Sri Namachchivaya ◽  
H. J. Van Roessel
Keyword(s):  
Lyapunov Exponent ◽  
Asymptotic Approximation ◽  
Coupled Oscillators ◽  
Stability Index ◽  
Stationary Solutions ◽  
Real Noise ◽  
Moment Lyapunov Exponent ◽  
The Stability ◽  
The Moment

In a recent paper an asymptotic approximation for the moment Lyapunov exponent, gp, of two coupled oscillators driven by a small intensity real noise was obtained. The utility of that result is limited by the fact that it was obtained under the assumption that the moment p is small, a limitation which precludes, for example, the determination of the stability index. In this paper that limitation is removed and an asymptotic approximation valid for arbitrary p is obtained. The results are applied to study the moment stability of the stationary solutions of structural and mechanical systems subjected to stochastic excitation.

Moment Lyapunov Exponent for Two Coupled Oscillators Driven by Real Noise

1996 ◽  
Vol 56 (5) ◽  
pp. 1400-1423 ◽  
Author(s):  
N. Sri Namachchivaya ◽  
H. J. Van Rossel ◽  
M. M. Doyle
Keyword(s):  
Lyapunov Exponent ◽  
Coupled Oscillators ◽  
Real Noise ◽  
Moment Lyapunov Exponent

scholarly journals Stochastic Stability of a Fractional Viscoelastic Plate Driven by Non-Gaussian Colored Noise

2021 ◽  
Author(s):  
Dongliang Hu ◽  
Yong Huang
Keyword(s):  
Lyapunov Exponent ◽  
Stochastic Stability ◽  
Colored Noise ◽  
Viscoelastic Plate ◽  
Dynamic Equations ◽  
Stochastic Dynamic ◽  
Gaussian Colored Noise ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Non Gaussian

Abstract In this paper, the moment Lyapunov exponent and stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise is investigated. Firstly, the stochastic dynamic equations with two degrees of freedom are established by piston theory and Galerkin approximate method. The fractional Kelvin–Voigt constitutive relation is used to describe the material properties of the viscoelastic plate, which leads to that the fractional derivation term is introduced into the stochastic dynamic equations. And the noise is simplified into an Ornstein-Uhlenbeck process by utilizing the path-integral method. Then, via the singular perturbation method, the approximate expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulations. Finally, the effects of the noise, viscoelastic parameters and system parameters on the stochastic dynamics of the viscoelastic plate are discussed.

Moment Lyapunov Exponent and Stochastic Stability of Binary Airfoil under Combined Harmonic and Non-Gaussian Colored Noise Excitations

2018 ◽  
Vol 17 (02) ◽  
pp. 1850010 ◽  
Author(s):  
D. L. Hu ◽  
X. B. Liu
Keyword(s):  
Lyapunov Exponent ◽  
Stochastic Stability ◽  
Colored Noise ◽  
Singular Perturbation Method ◽  
Random Forces ◽  
Gaussian Colored Noise ◽  
Moment Lyapunov Exponent ◽  
Path Integral Method ◽  
The Moment ◽  
Non Gaussian

Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non–Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.

Stochastic Stability of Linear Gyroscopic Systems: Application to Pipes Conveying Fluid

2002 ◽  
Author(s):  
Lalit Vedula ◽  
N. Sri Namachchivaya
Keyword(s):  
Lyapunov Exponent ◽  
Stochastic Stability ◽  
Perturbation Approach ◽  
Almost Sure Stability ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Gyroscopic Systems ◽  
Two Degree Of Freedom ◽  
Pulsating Fluid ◽  
Moment Stability

In this paper we obtain asymptotic approximations for the moment Lyapunov exponent, g(p), and the Lyapunov exponent,λ, for a two-degree-of-freedom gyroscopic system close to a double zero resonance and subjected to small damping and noisy disturbances. Using a perturbation approach, we show analytically that the moment and the top Lyapunov exponent grow in proportion to ε1/3 when the damping and noise respectively are of O(ε) and O(ε). These results, pertaining to pth moment stability and almost-sure stability of the trivial solution, are applied to study the stochastic stability of a pipe conveying pulsating fluid.

scholarly journals Stochastic Stability Analysis of Coupled Viscoelastic Systems with Nonviscously Damping Driven by White Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Di Liu ◽  
Yanru Wu ◽  
Xiufeng Xie
Keyword(s):  
Lyapunov Exponent ◽  
White Noise ◽  
Lyapunov Exponents ◽  
Stochastic Stability ◽  
Time History ◽  
Kernel Functions ◽  
Direct Monte Carlo Simulation ◽  
Viscoelastic System ◽  
Moment Lyapunov Exponent ◽  
The Moment

Nonviscously damped structural system has been raised in many engineering fields, in which the damping forces depend on the past time history of velocities via convolution integrals over some kernel functions. This paper investigates stochastic stability of coupled viscoelastic system with nonviscously damping driven by white noise through moment Lyapunov exponents and Lyapunov exponents. Using the coordinate transformation, the coupled Itô stochastic differential equations of the norm of the response and angles process are obtained. Then the problem of the moment Lyapunov exponent is transformed to the eigenvalue problem, and then the second-perturbation method is used to derive the moment Lyapunov exponent of coupled stochastic system. Lyapunov exponent also can be obtained according to the relationship between moment Lyapunov exponent and Lyapunov exponent. Finally, the effects of various physical quantities of stochastic coupled system on the stochastic stability are discussed in detail. These results are validated by the direct Monte Carlo simulation technique.

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