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title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Propagation of one-dimensional elastic waves in media with random parameters
Creators: name: Ð¡Ð¼Ð¸ÑÐ½Ð¾Ð², Ð¡ÐµÑÐ³ÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð£Ð¿ÑÑÐ³Ð¸Ðµ Ð²Ð¾Ð»Ð½Ñ
Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ
ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½Ð¾Ðµ ÑÐ°Ð·Ð»Ð¾Ð¶ÐµÐ½Ð¸Ðµ
ÐºÐ¾ÑÑÐµÐ»ÑÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·
Ð¼Ð°ÑÐºÐ¾Ð²ÑÐºÐ¸Ðµ Ð¿ÑÐ¾ÑÐµÑÑÑ
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¤Ð¾ÐºÐºÐµÑÐ°-ÐÐ»Ð°Ð½ÐºÐ°-ÐÐ¾Ð»Ð¼Ð¾Ð³Ð¾ÑÐ¾Ð²Ð°
wave equation
spectral decomposition
correlation analysis
Markov process
Fokker-Plank-Kolmogorov equation

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description: The subject of the graduate qualification work is âPropagation of one-dimensional elastic waves in media with random parametersâ. The given work is devoted to the study of the propagation of one-dimensional waves in media with random elastic-mass characteristics. Young's modulus and mass density are taken as random parameters of the medium. The relevance of this problem is that this formulation can be used to study of propagation of seismic waves. The paper considers two approaches to the analytical study of this problem. In the work, using the method of integral spectral decomposition and using the Fokker-Planck-Kolmogorov equation, dependences for the expected value of the wave amplitude and for its variance are obtained. The paper considers the case in which the randomness in the Young's modulus and mass density are completely correlated. Also the caseÂ  when only the density of the medium is a random function, and the Young's modulus is assumed to be deterministic is considered. The Dirichlet boundary conditions are considered in this paper. It was found that with an increase in the spatial coordinate, reliable information about the wave amplitude decreases and tends to zero. To verify the analytical results, numerical simulation of random waves propagation in a medium with a deterministic Young's modulus and a random density was carried out. It was found that the analytical results coincide satisfactorily with the numerical simulation.