Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk

The dynamics of a circular cylindrical shell carrying a rigid disk on the top and clamped at the base is investigated.The Sanders–Koiter theory is considered to develop a nonlinear analytical model for moderately largeshell vibration. A reduced order dynamical system is obtained using Lagrange equations: radial and in-planedisplacement fields are expanded by using trial functions that respect the geometric boundary conditions.The theoretical model is compared with experiments and with a finite element model developed withcommercial software: comparisons are carried out on linear dynamics.The dynamic stability of the system is studied, when a periodic vertical motion of the base is imposed.Both a perturbation approach and a direct numerical technique are used. The perturbation method allowsto obtain instability boundaries by means of elementary formulae; the numerical approach allows to performa complete analysis of the linear and nonlinear response.