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Mechanics with Random Forces. / Товстик, Татьяна Михайловна; Товстик, Петр Евгеньевич.

Rational and Applied Mechanics: Volume 2. Special Problems and Applications. ed. / Petr Evgenievich Tovstik. Vol. 2 Springer Nature, 2021. p. 323-351 (Foundations in Engineering Mechanics).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Harvard

Товстик, ТМ & Товстик, ПЕ 2021, Mechanics with Random Forces. in PE Tovstik (ed.), Rational and Applied Mechanics: Volume 2. Special Problems and Applications. vol. 2, Foundations in Engineering Mechanics, Springer Nature, pp. 323-351. https://doi.org/10.1007/978-3-030-64118-4_7

APA

Товстик, Т. М., & Товстик, П. Е. (2021). Mechanics with Random Forces. In P. E. Tovstik (Ed.), Rational and Applied Mechanics: Volume 2. Special Problems and Applications (Vol. 2, pp. 323-351). (Foundations in Engineering Mechanics). Springer Nature. https://doi.org/10.1007/978-3-030-64118-4_7

Vancouver

Товстик ТМ, Товстик ПЕ. Mechanics with Random Forces. In Tovstik PE, editor, Rational and Applied Mechanics: Volume 2. Special Problems and Applications. Vol. 2. Springer Nature. 2021. p. 323-351. (Foundations in Engineering Mechanics). https://doi.org/10.1007/978-3-030-64118-4_7

Author

Товстик, Татьяна Михайловна ; Товстик, Петр Евгеньевич. / Mechanics with Random Forces. Rational and Applied Mechanics: Volume 2. Special Problems and Applications. editor / Petr Evgenievich Tovstik. Vol. 2 Springer Nature, 2021. pp. 323-351 (Foundations in Engineering Mechanics).

BibTeX

@inbook{28c54b79d5344fc3b6f0ffad5fb4c93b,
title = "Mechanics with Random Forces",
abstract = "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.",
author = "Товстик, {Татьяна Михайловна} and Товстик, {Петр Евгеньевич}",
year = "2021",
month = dec,
day = "3",
doi = "10.1007/978-3-030-64118-4_7",
language = "English",
isbn = "978-3-030-64117-7",
volume = "2",
series = "Foundations in Engineering Mechanics",
publisher = "Springer Nature",
pages = "323--351",
editor = "Tovstik, {Petr Evgenievich }",
booktitle = "Rational and Applied Mechanics",
address = "Germany",

}

RIS

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