Green's-Function Technique in the Dynamics of a Finite Cylindrical Shell

Abstract

The Reissner linearized equations of motion, including hysteretic- and viscous-damping terms, are adopted in the study of the dynamics of a finite, thin, elastic cylindrical shell of circular cross section. The integral representation of the radial displacement solution is obtained for an arbitrary, time-dependent pressure field over the shell surface and the associated Green's-function solution is calculated. In particular, the shell response to a moving shock wave (step-function discontinuity), impinging upon the shell at an arbitrary angle of incidence, is calculated. In the special case of axial symmetry, two additional waveforms are considered, that of a moving exponentially decaying shock wave and of a ramp/step-function wave. Typical numerical results are given in the form of displacement-time curves and the effects of the pressure-wave parameters (decay and rise time) are examined. The dynamic behavior of a prepressurized shell is also considered. It is shown that the Green's-function solution remains form-invariant under the introduction of an internal static pressure P0; this, in turn, leads to a simple rule for deducing the response to a given external pressure field when P0≠0 from known solutions corresponding to the case of P0 = 0.