Spectral properties for the equation of vibrating beam

Ziyatkhan S. Aliyev^ab, Sevinc B. Guliyeva<sup>c

a</sup> Baku State University
^b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
^c Ganja State University

Abstract: In this paper we study the properties of the natural frequencies and the corresponding harmonics of transverse vibrations of a rod is exposed to tracking and axial forces. It is known that problems of this type leads to a spectral fourth-order problem with spectral parameter in the boundary conditions. We study the general characteristics of the location of the eigenvalues on the real axis and oscillation properties of eigenfunctions of these problems.

MSC: 34B05, 34B09, 34B24

Received: 20.04.2015
Accepted: 04.06.2015

Language: English