Determining the Distribution of Values of Stochastic Impulses Acting on a Discrete System in Relation to Their Intensity

• Authors: M. Jabłoński , A. Ozga
• Languages of publication: EN

Abstracts

EN

In our previous works we introduced and applied a mathematical model that allowed us to calculate the approximate distribution of the values of stochastic impulses η_{i} forcing vibrations of an oscillator with damping from the trajectory of its movement. The mathematical model describes correctly the functioning of a physical RLC system if the coefficient of damping is large and the intensity λ of impulses is small. It is so because the inflow of energy is small and behaviour of RLC is stable. In this paper we are going to present some experiments which characterize the behaviour of an oscillator RLC in relation to the intensity parameter λ, precisely to λ E(η). The parameter λ is a constant in the exponential distribution of random variables τ_{i}, where τ_{i} = t_{i} - t_{i - 1}, i = 1, 2, ... are intervals between successive impulses.

Keywords

EN

45.10.-b; 45.30.+s

Discipline

• 45.10.-b: Computational methods in classical mechanics(see also 02.70.-c Computational techniques in mathematical methods in physics)
• 45.30.+s: General linear dynamical systems(for nonlinear dynamical systems, see 05.45.-a)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 1A
• Pages: A-174-A-178

Dates

published

2012-01

Contributors

author

M. Jabłoński

• Faculty of Mathematics and Computer Science, Jagiellonian University, Gołębia 24, 31-007 Cracow, Poland

author

A. Ozga

• AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics Department of Mechanics and Vibroacoustics, al. A. Mickiewicza 30, 30-059 Krakow, Poland

References

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• [2] M. Jabłonski, A. Ozga, Arch. Acoust. 34, 601 (2009)
• [3] M. Jabłoński, A. Ozga, Acta Phys. Pol. A 118, 74 (2010)
• [4] M. Jabłoński, A. Ozga, T. Korbiel, P. Pawlik, Acta Phys. Pol. A 119, 977 (2011)
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• [6] J.B. Roberts, J. Sound Vibrat. 2, 336 (1965)
• [7] J.B. Roberts, J. Sound Vibrat. 2, 375 (1965)
• [8] J.B. Roberts, J. Sound Vibrat. 24, 23 (1972)
• [9] J.B. Roberts, J. Sound Vibrat. 28, 93 (1973)
• [10] J.B. Roberts, P.D. Spanos, Int. J. Non-Linear Mech. 21, 111 (1986)
• [11] L. Takác, Acta Math. Hung. 5, 201 (1954)

Identifiers

DOI

10.12693/APhysPolA.121.A-174