Frequencies and modes of vibration of a cylindrical shell with attached rigid body

We consider a mechanical system consisting of a circular cylindrical shell and perfectly rigid body attached to one of the shell ends. Starting from the principle of virtual works, we construct a mathematical model of the equilibrium state of our system subjected to stresses of general form. A boundary eigenvalue problem describes free vibrations of the “body – shell” system, and its approximate solution is determined. We construct the exact solution of the above problem by replacing the shell with an equivalent Timoshenko beam. The effect of the rigid body on the system vibrations is estimated, and the accuracy of the beam approximation to shell bending vibrations is studied.