Mathematical modelling of torsional vibrations of a truncated conical shell located in an elastic medium

In this article, mathematical modelling of torsional vibrations of a truncated circular conical shell located in an elastic medium is carried out. It is believed that the shell is exposed to external dynamic loads, and its material is homogeneous and isotropic. Based on the exact mathematical formulation of the problem, general equations of nonstationary torsional vibrations of a truncated conical shells have been developed, from which, in particular cases, the equations of vibration of a truncated conical rod, as well as a circular cylindrical shell and a round rod follow. The desired functions found by solving the vibrational equations are used to construct a method for computing the stress-strain state of any point in the system under investigation. As an example.