On the prediction of damping and vibratory behaviour of free-free multilayered conical shells

An analysis is presented for the prediction of resonance frequencies (omega) and the associated system loss factors (eta(s)) for all families of modes of vibrations in free-free multilayered conical shells, which are frequently used in aircraft, missiles and other allied systems. Because of the spin of a high order, missiles and gun-launched shells are subjected to torsional vibrations (axisymmetric). The governing equations of motion for the axisymmetric vibrations of a general multilayered conical shell have been derived using Hamilton's vibrational principle. The solution is obtained by utilising simple trignometric series modal assumptions in Galerkin's procedure. The correspondence principle of linear viscoelasticity for harmonic motions is used for evaluating the damping effectiveness of shells with elastic and viscoelastic layers. The resonance frequencies and the associated system loss factors for three-, five- and seven-layered conical shells with free edges are evaluated and their variations with geometric parameters are investigated. An increase in the number of layers (N) increases maximum obtainable eta(s) for most of the modes with proper selection of geometric parameters, but increasing N beyond 5 yields only marginal increase in eta(s). Uniformly high values of eta(s) are obtained for all modes of vibration for high values of thickness ratio parameter. For thick shells, more layers are advisable for relatively high values of eta(s) for all modes.