Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load
type: Item
instance of: scholarly article
title: Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load
zbMATH Open document ID: 1412.34079
author: Ziyatkhan S. Aliyev
author: Sevinc B. Guliyeva
published in: Journal of Differential Equations
publication date: 2018-10-02T00:00:00Z
review text: This article is devoted to the study of the spectral properties of the eigenvalue problem for ordinary differential equations of fourth order with eigenvalue parameter in the boundary conditions. This problem arises when variables are separated in the dynamical boundary value problem describing small vibrations of a homogeneous rod whose left end is fixed rigidly and on the right end an inertial mass is concentrated. The authors study the location of the eigenvalues on the real axis, the structure of the root subspaces and the oscillation properties of eigenfunctions of this problem and their derivatives. Moreover, there are obtained sufficient conditions for the system of eigenfunctions of the considered problem with two remote functions to form a basis in the space \(L_p\), \(1 < p < \infty\).
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 6946031
zbMATH Keywords: bending vibrations of a rod
zbMATH Keywords: longitudinal force
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenfunction
zbMATH Keywords: unconditional basis
MaRDI profile type: Publication
full work available at URL: j.jde.2017.07.002
OpenAlex ID: W2734736679
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DOI: 10.1016/J.JDE.2017.07.002
description: scientific article; zbMATH DE number 6946031