Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load
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 \(L_p\), \(1 < p < \infty\).
scientific article; zbMATH DE number 6946031
scientific article