Точний розв'язок диференціального рівняння згинних коливань стрижня з урахуванням власної ваги

Abstract

The free transverse oscillations of the rod of uniform cross section taking into account its own weight are considered in this work. The exact solution of the appropriate differential equation of rod’s transverse oscillations, expressed in non-dimensional fundamental functions and initial parameters is attained for the first time. Due to the exact solution, the formulas in an explicit form for dynamic variables of rode state – deflections, angular displacement, bending moment and transverse force – were defined. The analytical form for equation of free oscillation frequency is defined. That has limited the finding of frequency to definition the unknown non-dimensional parameter through frequency equation. As a result, the presence of derivative exact solutions allows to investigate the free oscillations of rod with various types of boundary conditions.