Spectral properties for the equation of vibrating beam

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.