Moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and Gaussian white noise excitation

2017 ◽  
Vol 89 (1) ◽  
pp. 539-552 ◽  
Author(s):  
D. L. Hu ◽  
X. B. Liu ◽  
W. Chen
Keyword(s):  
Lyapunov Exponent ◽  
White Noise ◽  
Stochastic Stability ◽  
Gaussian White Noise ◽  
White Noise Excitation ◽  
Moment Lyapunov Exponent

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.

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

scholarly journals Steady-State Dynamical Response of a Strongly Nonlinear System with Impact and Coulomb Friction Subjected to Gaussian White Noise Excitation

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Guidong Yang ◽  
Dongmei Huang ◽  
Wei Li ◽  
Meng Su ◽  
Francesco Pellicano
Keyword(s):  
Steady State ◽  
White Noise ◽  
Coulomb Friction ◽  
Gaussian White Noise ◽  
Original System ◽  
Probability Density Functions ◽  
Dynamical Response ◽  
Strongly Nonlinear ◽  
White Noise Excitation ◽  
Strongly Nonlinear System

The paper is devoted to the steady-state dynamical response analysis of a strongly nonlinear system with impact and Coulomb friction subjected to Gaussian white noise excitation. The Zhuravlev nonsmooth transformation of the state variables combined with the Dirac delta function is utilized to simplify the original system to one without velocity jump. Then, the steady-state probability density functions of the transformed system are derived in terms of the stochastic averaging method of energy envelope. The effectiveness of the presented analytical procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different restitution coefficients, amplitudes of friction, and noise intensities on the steady-state dynamical responses are investigated in detail. Results show different intensities of Gaussian white noise can affect the peaks value of the probability density functions, whereas the variations of restitution coefficients and amplitudes of friction can induce the occurrence of stochastic P-bifurcation.

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