scholarly journals Moment Lyapunov exponents and stochastic stability of a double-beam system under compressive axial loading

2010 ◽  
Vol 47 (10) ◽  
pp. 1435-1442 ◽  
Author(s):  
Predrag Kozić ◽  
Goran Janevski ◽  
Ratko Pavlović
Keyword(s):  
Lyapunov Exponents ◽  
Stochastic Stability ◽  
Axial Loading ◽  
Beam System ◽  
Double Beam ◽  
Moment Lyapunov Exponents

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.

Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading

2011 ◽  
Vol 81 (12) ◽  
pp. 1993-2005 ◽  
Author(s):  
Vladimir Stojanović ◽  
Predrag Kozić ◽  
Ratko Pavlović ◽  
Goran Janevski
Keyword(s):  
Axial Loading ◽  
Rotary Inertia ◽  
Beam System ◽  
Double Beam

Vibration and buckling of a double-beam system under compressive axial loading

2008 ◽  
Vol 318 (1-2) ◽  
pp. 341-352 ◽  
Author(s):  
Y.Q. Zhang ◽  
Y. Lu ◽  
S.L. Wang ◽  
X. Liu
Keyword(s):  
Axial Loading ◽  
Beam System ◽  
Double Beam

Almost sure stochastic stability of a viscoelastic double-beam system

2013 ◽  
Vol 83 (11) ◽  
pp. 1591-1605 ◽  
Author(s):  
Ivan Pavlović ◽  
Ratko Pavlović ◽  
Predrag Kozić ◽  
Goran Janevski
Keyword(s):  
Stochastic Stability ◽  
Beam System ◽  
Double Beam

Moment Lyapunov Exponents and Stochastic Stability of a Three-Dimensional System on Elastic Foundation Using a Perturbation Approach

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Vladimir Stojanović ◽  
Marko Petković
Keyword(s):  
Lyapunov Exponents ◽  
Elastic Foundation ◽  
Stochastic Stability ◽  
Coupled Oscillators ◽  
Complex Structure ◽  
Perturbation Approach ◽  
Dimensional System ◽  
Regular Perturbation ◽  
Moment Stability ◽  
Moment Lyapunov Exponents

In this paper, the stochastic stability of the three elastically connected Euler beams on elastic foundation is studied. The model is given as three coupled oscillators. Stochastic stability conditions are expressed by the Lyapunov exponent and moment Lyapunov exponents. It is determined that the new set of transformation for getting Ito∧ differential equations can be applied for any system of three coupled oscillators. The method of regular perturbation is used to determine the asymptotic expressions for these exponents in the presence of small intensity noises. Analytical results are presented for the almost sure and moment stability of a stochastic dynamical system. The results are applied to study the moment stability of the complex structure with influence of the white noise excitation due to the axial compressive stochastic load.

Moment Lyapunov exponents and stochastic stability of moving narrow bands

2010 ◽  
Vol 17 (7) ◽  
pp. 988-999 ◽  
Author(s):  
Predrag Kozić ◽  
Ratko Pavlović ◽  
Goran Janevski ◽  
Vladimir Stojanović
Keyword(s):  
Lyapunov Exponents ◽  
Stochastic Stability ◽  
Narrow Bands ◽  
Moment Lyapunov Exponents

Moment Lyapunov Exponents of a Two-Dimensional Viscoelastic System Under Bounded Noise Excitation

2002 ◽  
Vol 69 (3) ◽  
pp. 346-357 ◽  
Author(s):  
W.-C. Xie
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Regular Perturbation ◽  
Stochastic Fluctuation ◽  
Viscoelastic System ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Moment Lyapunov Exponents

The moment Lyapunov exponents of a two-dimensional viscoelastic system under bounded noise excitation are studied in this paper. An example of this system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The stochastic parametric excitation is modeled as a bounded noise process, which is a realistic model of stochastic fluctuation in engineering applications. The moment Lyapunov exponent of the system is given by the eigenvalue of an eigenvalue problem. The method of regular perturbation is applied to obtain weak noise expansions of the moment Lyapunov exponent, Lyapunov exponent, and stability index in terms of the small fluctuation parameter. The results obtained are compared with those for which the effect of viscoelasticity is not considered.

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