Wave packets in a thin cylindrical shell under a non-uniform axial load

Abstract

The propagation of localized families of flexural plane waves in a thin elastic shell under an unsteady axial compression, which is non-uniform with respect to the peripheral coordinate, is considered. The shell can be non-circular and open in the peripheral direction. Conditions of hinged support are specified at the edges, which are optionally plane curves. It is assumed that the initial perturbations of the shell (non-zero initial displacements and velocities) are functions which are localized in the neighbourhood of a certain generatrix. The solution is constructed using the complex WKB-method developed in [1] in the form of a superposition of packets of flexural plane waves propagating in the peripheral direction of the shell. This paper differs from [1] in that in addition to taking account of axial stresses, the solution in the direction of the axis of the shell is assumed to be extremely variable. It is shown that it is possible to use the results obtained to investigate the free vibrations of the shell. The unsteady localized vibrations of a cylindrical shell with an elliptic cross-section under axial forces which increase linearly with time are considered as an example.