The perturbation method in problems of the dynamics of inhomogeneous elastic rods
type: Item
instance of: scholarly article
title: The perturbation method in problems of the dynamics of inhomogeneous elastic rods
zbMATH Open document ID: 0787.73040
DOI: 10.1016/0021-8928(92)90028-7
author: L. D. Akulenko
author: Georgy V. Kostin
published in: Journal of Applied Mathematics and Mechanics
publication date: 1994-03-03T00:00:00Z
review text: The regular perturbation method (the small-parameter method) is developed in order to investigate the dynamics of weakly inhomogeneous rods with arbitrary distributed loads and boundary conditions of various types leading to self-conjugate boundary value problems. The approach rests on the introduction of a perturbed argument, namely, the Euler variable, and a suitable representation of the eigenfunctions. It enables one to carry uniform constructions of the basis and the eigenvalues, as well as the frequencies with any required accuracy in terms of the small parameter using quadratures of known functions.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 500909
zbMATH Keywords: small-parameter method
zbMATH Keywords: self-conjugate boundary value problems
zbMATH Keywords: Euler variable
zbMATH Keywords: eigenfunctions
MaRDI profile type: Publication
full work available at URL: 0021-8928(92)90028-7
OpenAlex ID: W2009740573
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description: scientific article; zbMATH DE number 500909