scholarly journals DYNAMIC BEHAVIOR OF TWO ELASTICALLY CONNECTED NANOBEAMS UNDER A WHITE NOISE PROCESS

2020 ◽  
Vol 18 (2) ◽  
pp. 219
Author(s):  
Ivan R. Pavlović ◽  
Ratko Pavlović ◽  
Goran Janevski ◽  
Nikola Despenić ◽  
Vladimir Pajković
Keyword(s):  
Lyapunov Exponent ◽  
White Noise ◽  
Axial Loading ◽  
Regular Perturbation ◽  
White Noise Process ◽  
Noise Process ◽  
Asymptotic Expressions ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Moment Stability

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.

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.

scholarly journals MOMENT LYAPUNOV EXPONENTS AND STOCHASTIC STABILITY OF A THIN-WALLED BEAM SUBJECTED TO AXIAL LOADS AND END MOMENTS

2021 ◽  
Vol 19 (2) ◽  
pp. 209
Author(s):  
Goran Janevski ◽  
Predrag Kozić ◽  
Ratko Pavlović ◽  
Strain Posavljak
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Degrees Of Freedom ◽  
Simulation Method ◽  
Stochastic Dynamic ◽  
Regular Perturbation ◽  
Thin Walled ◽  
The Moment ◽  
Moment Stability ◽  
Moment Lyapunov Exponents

In this paper, the Lyapunov exponent and moment Lyapunov exponents of two degrees-of-freedom linear systems subjected to white noise parametric excitation are investigated. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining both the almost-sure and the moment stability of a stochastic dynamic system. As an example, we study the almost-sure and moment stability of a thin-walled beam subjected to stochastic axial load and stochastically fluctuating end moments.  The validity of the approximate results for moment Lyapunov exponents is checked by numerical Monte Carlo simulation method for this stochastic system.

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.

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

2000 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Dimensional System ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Regular Perturbation ◽  
Weak Noise ◽  
Two Dimensional System ◽  
The Moment ◽  
Moment Lyapunov Exponents

Abstract The moment Lyapunov exponents of a two-dimensional system under bounded noise parametric excitation are studied in this paper. 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.

scholarly journals A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning

2017 ◽  
Author(s):  
Henrik T. Sykora ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
White Noise ◽  
Time Evolution ◽  
Material Properties ◽  
Discretization Method ◽  
Chatter Detection ◽  
Turning Process ◽  
Stochastic Parameters ◽  
Stability Chart ◽  
The Moment ◽  
Moment Stability

In this work the effect of the inhomogeneous material properties are investigated in regenerative turning processes by introducing white noise in the cutting coefficient. The model is a one degree of freedom linear delayed oscillator with stochastic parameters. A full discretization method is used to calculate the time evolution of the second moment to determine the moment stability of the turning process. The resultant stability chart is compared with the deterministic turning model.

scholarly journals Empirical White Noise Processes and the Subjective Probabilistic Approaches

2019 ◽  
Vol 48 (1) ◽  
pp. 19-30
Author(s):  
András Rövid ◽  
László Palkovics ◽  
Péter Várlaki
Keyword(s):  
White Noise ◽  
Random Number ◽  
White Noise Process ◽  
Random Number Generators ◽  
Noise Process ◽  
Complementary Approach ◽  
Fuzzy Random

The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis.

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