Abstract
Derivations of a differential equation of eight order and boundary conditions of flexural vibrations of a straight rod by accounting for shear strains caused by a transverse load are presented. Unlike existing approaches, use of coefficients of shear and angles of displacements is excluded in all relationships. The article gives the solution of the boundary-value problem on determining the function of plane displacement of sections with transverse shear for a round profile without the traditional introduction and additional determination of the shear function. An exact analytical solution of the boundary-value problem on free flexural vibrations of a cantilever rod by accounting for shears is presented. A numerical example of calculating flexural vibration parameters of a rod with round cross-sectional profile is examined along with evaluation of the effect of shear strain factor on frequency of the principal tone.
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