Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load

被引：27

作者：

Aliyev, Ziyatkhan S. ^{[1
,2
]}

Guliyeva, Sevinc B. ^{[3
]}

机构：

[1] Baku State Univ, AZ-1148 Baku, Azerbaijan

[2] NAS Azerbaijan, Inst Math & Mech, AZ-1141 Baku, Azerbaijan

[3] Ganja State Univ, AZ-2000 Ganja, Azerbaijan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 09期

关键词：

The bending vibrations of a rod; The longitudinal force; Eigenvalue; Eigenfunction; Unconditional basis; STURM-LIOUVILLE PROBLEMS; SPECTRAL PARAMETER; BOUNDARY-CONDITION; OSCILLATION PROPERTIES; EIGENVALUE PARAMETER; ROOT FUNCTIONS; EQUATION; EIGENPARAMETER; BEAM; EIGENFUNCTIONS;

D O I：

10.1016/j.jde.2017.07.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider a spectral problem that describes the bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is fixed and on the right end an inertial mass is concentrated. We give a general characteristic of the location of the eigenvalues on the real axis, we study the structure of root spaces and oscillation properties of eigenfunctions, we investigate the basic properties in the space L-p,1 < p < infinity, of the system of eigenfunctions of this problem. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：5830 / 5845

页数：16

共 5 条

[1] Oscillation and basis properties for the equation of vibrating rod at one end of which an inertial mass is concentrated
Mehrabov, Vuqar A.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (02) : 1585 - 1600
[2] On convergence of spectral expansions for the equation of a vibrating beam, at one end of which an elastically fixed inertial load is concentrated
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[3] Identification of the parameters of a rod with a longitudinal rectangular groove using two spectra of natural frequencies of bending vibrations
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[4] ON THE UNIFORM CONVERGENCE OF FOURIER SERIES EXPANSIONS IN THE SYSTEM OF EIGENFUNCTIONS OF THE EQUATION OF A VIBRATING ROD AT ONE END OF WHICH THE MASS IS CONCENTRATED
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Aliyev, Ziyatkhan S.
Kerimov, Nazim B.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2020, 46 (02): : 226 - 242
[5] Uniqueness of determination of the type of the boundary conditions at one end of a beam from three natural frequencies of its vibrations
Aitbayeva, A. A.
Akhtyamov, A. M.
PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 2016, 80 (03): : 273 - 277

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