Determining the Distribution of Stochastic Impulses Acting on a High Frequency System through an Analysis of Its Vibrations
M. Jabłońskia, A. Ozgab, T. Korbielb and P. Pawlikb
aFaculty of Mathematics and Computer Science, Jagiellonian University, Gołębia 24, 31-007 Cracow, Poland
bDepartment of Mechanics and Vibroacoustics, University of Science and Technology, al. A. Mickiewicza 30, 30-059 Cracow, Poland
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The motion of an oscillator with damping excited by impulses has the form: ξ t = 1/√(a2 - b2) ∑ 0 < ti <t ηi exp(- b(t - ti)) sin(√(a2 - b2)(t - ti)), where ξ t is the deviation of the oscillator from its balanced position and ti is the time of action of an impulse of the value ηi. Under appropriate assumptions regarding random variables {ti + 1 - ti}i = 1 and {ηi}i = 1 ξ t is a process which, in the limit as t tends to infinity, is stationary and ergodic. This fact allows us to derive a linear system of equations determining the approximate distribution of variables ηi whenever the course of the oscillator is known in a sufficiently large interval of time. These equations will be verified in the experiment executed on an electric oscillator RLC of high frequency.
DOI: 10.12693/APhysPolA.119.977
PACS numbers: 45.10.-b, 45.30.+s