Own torsive vibrations of a prism cemented bar with a hole in the center of the section

A solution to the problem of determining the lowest natural vibration frequencies of a bar of rectangular cross section with a hole in the center of the section with a cemented surface layer is provided. Presence of carbon in the cemented layer allows to consider the bar as a body of a heterogeneous structure characterized by heterogeneity with a variable modulus of elasticity in the surface layer. The solution is based on the distributed mass discretization method and the finite element method in the torsion problem.