The method of calculating natural frequencies and forms the transverse vibrations of a rod variable cross-section with elastic securing

Abstract

The paper presents a method of algebraic polynomi-als of the fifth degree to solve the differential equation of the fourth order, describing the bending vibrations of the elastically fixed rod of variable cross-section. To study the accuracy of the considered method, test problems with an accurate analytical solution are considered. The calcula-tions are made for different coefficients of elasticity con-solidate and estimated errors of the numerical calcula-tions. It is shown that with a sufficiently dense grid, the method makes it possible to determine the frequencies and shapes of the natural oscillations of a variable-section rod with an accuracy of five significant digits.