Moment Lyapunov exponents of the stochastic parametrical Hill’s equation

Kozić, Predrag; Pavlović, Ratko; Janevski, Goran

doi:10.1016/j.ijsolstr.2008.07.015

Cited by 8 publications

(7 citation statements)

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“…Following the results from the authors' previous works [9][10][11], where the regular perturbation method is performed, the analytical expression for the moment Lyapunov exponent is…”

Section: Lyapunov Exponents and Stability Conditionsmentioning

confidence: 99%

“…The results from this study were further used for the study of the almost-sure and moment stability of a double-beam system under stochastic compressive axial loading. Similarly, the moment Lyapunov exponents of the stochastic parametrical Hill's equation were investigated by the same authors in [10]. Pavlović et al [11] used this method to compare the analytically obtained results of the moment Lyapunov exponent for a simple nanobeam numerically determined for the same system.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Behavior of Two Elastically Connected Nanobeams Under a White Noise Process

Pavlović

Janevski

et al. 2020

FU Mech Eng

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This paper investigates the almost-sure and moment stability of a double nanobeam system under stochastic compressive axial loading. By means of the Lyapunov exponent and the moment Lyapunov exponent method the stochastic stability of the nano system is analyzed for different system parameters under an axial load modeled as a wideband white noise process. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises.

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“…Following the results from the authors' previous works [9][10][11], where the regular perturbation method is performed, the analytical expression for the moment Lyapunov exponent is…”

Section: Lyapunov Exponents and Stability Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Behavior of Two Elastically Connected Nanobeams Under a White Noise Process

Pavlović

Janevski

et al. 2020

FU Mech Eng

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“…Therefore, numerical approaches have to be employed to evaluate the moment Lyapunov exponents. The numerical approach is based on expanding the exact solution of the system of Itô stochastic differential equations, (33), in powers of the time increment h and the small parameter ε, as proposed in [Milstein and Tret'yakov 1997]. The state vector of the system (4) is to be rewritten as a system of Itô stochastic differential equations with low noise in the form…”

Section: Numerical Determination Of the P-th Moment Lyapunov Exponent And Conclusionmentioning

confidence: 99%

Moment Lyapunov exponents and stochastic stability for two coupled oscillators

Kozi

Janevski

2010

JOMMS

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The Lyapunov exponent and moment Lyapunov exponent of two degree-of-freedom linear systems subjected to white noise parametric excitation are investigated. Through a perturbation method we obtain the explicit asymptotic expressions for these exponents in the presence of low intensity noise. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining the almostsure and moment stability of a stochastic dynamical system. As an example, we study the almost-sure and moment stability of the flexural-torsion stability of a thin elastic beam subjected to a stochastically fluctuating follower force. The validity of the approximate results for moment Lyapunov exponents is checked by a numerical Monte Carlo simulation for these stochastic systems.

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“…A total of N samples of the solutions of (33) are generated. The weak Runge-Kutta scheme of the s-th realization of (33) at the (k + 1)-th iteration with t (k+1) − t (k) = h, where h is the time step of integration, is given by [Milstein and Tret'yakov 1997]:…”

Section: Numerical Determination Of the P-th Moment Lyapunov Exponentmentioning

confidence: 99%

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2009

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $600 a year (print and electronic); $460 a year (electronic only). Subscriptions, requests for back issues, and changes of address should be sent toThis paper investigates the singular integral equation method for examining the stress intensity factor and the T-stress in the asymptotic solution of a kinked crack with an infinitesimal kink length. A numerical technique for the branch crack problem is introduced, which depends upon distribution of dislocation along the crack face. The technique reduces the branch crack problem to the solution of a singular integral equation. The kinked cracked problem can be considered as a particular case of the branch crack, and this problem can be solved by using the suggested technique. It is found from the computed results that the available asymptotic solution can give qualitatively correct results for stress intensity factors and the T-stress. In addition, the available asymptotic solution can only give sufficiently accurate results in a narrow range of the length of the kinked portion and the inclined kink angle.Numerical procedures are developed for the homogenization and evaluation of the stress field in a composite as a consequence of the presence of embedded SMA (shape-memory alloy) wires. In particular, the elastic field developed at the end of the SMA wire self-strain process is studied, knowledge of which is necessary to evaluate the feasibility of such a hybrid composite.First, the numerical procedures are applied to the study of both a representative volume element (RVE) included in a theoretically infinite periodic medium and a RVE located near the medium free boundary, in order to evaluate the tangential stress field generated at the end of the fiber; then they are applied to the study of a plate able to bend after the effect of self-strain of the SMA wire.Observations are reported about the obtained results and about the similarities and the differences between the two problems.The Lyapunov exponent and moment Lyapunov exponent of two degree-of-freedom linear systems subjected to white noise parametric excitation are investigated. Through a perturbation method we obtain the explicit asymptotic expressions for these exponents in the presence of low intensity noise. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining the almostsure and moment stability of a stochastic dynamical system. As an example, we study the almost-sure and moment stability of the flexural-torsion stability of a thin elastic beam subjected to a stochastically fluctuating follower force. The validity of the approximate results for moment Lyapunov exponents is checked by a numerical Monte Carlo simulation for these stochastic systems.A method was devised to evaluate the adhesion between a film and a substrate. A front-end coated bullet is accelerated by a gas gun and hits the substrate of the specimen under test. The impact generates a compressive stre...

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Moment Lyapunov exponents of the stochastic parametrical Hill’s equation

Cited by 8 publications

References 10 publications

Dynamic Behavior of Two Elastically Connected Nanobeams Under a White Noise Process

Dynamic Behavior of Two Elastically Connected Nanobeams Under a White Noise Process

Moment Lyapunov exponents and stochastic stability for two coupled oscillators

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