Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › Рецензирование
Mechanics with Random Forces. / Товстик, Татьяна Михайловна; Товстик, Петр Евгеньевич.
Rational and Applied Mechanics: Volume 2. Special Problems and Applications. ред. / Petr Evgenievich Tovstik. Том 2 Springer Nature, 2021. стр. 323-351 (Foundations in Engineering Mechanics).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › Рецензирование
}
TY - CHAP
T1 - Mechanics with Random Forces
AU - Товстик, Татьяна Михайловна
AU - Товстик, Петр Евгеньевич
PY - 2021/12/3
Y1 - 2021/12/3
N2 - The present chapter gives a brief account on the methods of determination of probabilistic characteristics of motion of mechanical systems subject to random forces. In the introductory sections we give the required definitions of random variables and processes. In the definition of the probabilistic characteristics, we shall be mostly concerned with the correlation level when the expectations and correlation function are determined under the condition that these characteristics are given for the exterior forces. For the stationary processes, the Fourier transform is used and the spectral densities are defined. For statistically linear systems it proves possible to find an exact solution. However, nonlinear systems can be treated only by approximate methods (the methods of statistical linearization and statistical modeling). The method of the solution of the Fokker-Planck-Kolmogorov equation, mentioned at the end of this chapter.
AB - The present chapter gives a brief account on the methods of determination of probabilistic characteristics of motion of mechanical systems subject to random forces. In the introductory sections we give the required definitions of random variables and processes. In the definition of the probabilistic characteristics, we shall be mostly concerned with the correlation level when the expectations and correlation function are determined under the condition that these characteristics are given for the exterior forces. For the stationary processes, the Fourier transform is used and the spectral densities are defined. For statistically linear systems it proves possible to find an exact solution. However, nonlinear systems can be treated only by approximate methods (the methods of statistical linearization and statistical modeling). The method of the solution of the Fokker-Planck-Kolmogorov equation, mentioned at the end of this chapter.
UR - http://www.scopus.com/inward/record.url?scp=85120881211&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-64118-4_7
DO - 10.1007/978-3-030-64118-4_7
M3 - Chapter
SN - 978-3-030-64117-7
VL - 2
T3 - Foundations in Engineering Mechanics
SP - 323
EP - 351
BT - Rational and Applied Mechanics
A2 - Tovstik, Petr Evgenievich
PB - Springer Nature
ER -
ID: 89339619