The Solution of a Spectral Task on Variable Section Compressed Beams Vibrations by Numerical Methods

Abstract

Free flexural free vibrations of variable section are considered. The vibrations mathematical model represents the boundary value problem consisting of the hyperbolic type and boundary conditions main equation. By means of separation method of variables the task at the beginning comes to homogeneous differential equation of the fourth order for fundamental function with the corresponding boundary conditions. The grid area of an argument change and fundamental function in it are applied. That leads to an algebraic problem of eigenvalues. Multimodal non-negative function which null values match its eigenvalues is designed. The finite differences methods and coordinate descent in combination with the specified function sections graphic visualization at a small amount of descents with an adequate accuracy for eigenvalues practice are given. The known ways to define fundamental functions are applied.