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Response of a Single‐mass Vibroimpact System to White‐noise Random Excitation
Author(s) -
Dimentberg M. F.,
Menyailov A. I.
Publication year - 1979
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19790591205
Subject(s) - white noise , mathematics , gaussian , excitation , fokker–planck equation , mathematical analysis , parametric statistics , piecewise , piecewise linear function , random variable , additive white gaussian noise , physics , statistical physics , quantum mechanics , differential equation , statistics
A simple linear single‐mass oscillator with one or two rigid barriers is considered for the cases of external or parametric white‐noise random excitation. This problem is treated by using a certain piecewise‐differentiable transform of the dependent variable. For the special case of external and elastic impact the solution of the corresponding Fokker‐Planck‐Kolmogorov equation is straightforward, leading to Gaussian and truncated Gaussian stationary distributions of the velocity and displacement respectively. The general case is treated in “quasiconservative” approximation by averaging energy. This leads to a first‐oder stochastic equation for the energy and to a closed‐form solution for the stationary probability density p(E). In the case of parametric excitation necessary and sufficient conditions for the existence of p(E) are obtained.