Stability of elastic systems under a stochastic parametric excitation |
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Authors: | V D Potapov |
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Institution: | (1) Moscow State University of Means Communication, Obraztsov str., 15, 127994 Moscow, Russia;(2) Sadovaya Kudrinskaya str. 28/30, Apt. 36, 123001 Moscow, Russia |
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Abstract: | An efficient method to investigate the stability of elastic systems subjected to the parametric force in the form of a random
stationary colored noise is suggested. The method is based on the simulation of stochastic processes, numerical solution of
differential equations, describing the perturbed motion of the system, and the calculation of top Liapunov exponents. The
method results in the estimation of the almost sure stability and the stability with respect to statistical moments of different
orders. Since the closed system of equations for moments of desired quantities y
j
(t) cannot be obtained, the statistical data processing is applied. The estimation of moments at the instant t
n
is obtained by statistical average of derived from the solution of equations for the large number of realizations. This approach allows us to evaluate the influence
of different characteristics of random stationary loads on top Liapunov exponents and on the stability of system. The important
point is that results found for filtered processes, are principally different from those corresponding to stochastic processes
in the form of Gaussian white noises. |
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Keywords: | Stability Stochastic equations Numerical method |
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