On the development of the Timoshenko theory of transversal oscillations of elastic rods

Abstract

The key stages of the development of generalized dynamic theories of bending oscillations of rods, plates, and shells, based on the shear model proposed in 1921 by S.P. Timoshenko, an outstanding Ukrainian scientist, are considered. The mathematical construction of equations of the theory of plates obtained as hyperbolic approximations of the elastodynamics problem for a layer are presented and the analytical expression for the shear coefficient is derived. Some relevant current studies are mentioned. The propagation of waves along an elastically fixed strip is studied as an example.