New models of explosively accelerated projected shells

The asymptotic basis of models proposed earlier for the effective description of the acceleration of a soft metal shell which is accelerated by an explosion is given. A model of an incompressible liquid-crystal layer possessing linear longitudinal elasticity is considered as the three-dimensional medium. The equations of the shell are derived under assumptions concerning the smoothness or irregularity of the loaded surface of a layer. In the first case, a model of the inertial acceleration of a shell is obtained in the basic approximation and, in the second case, a model of a weakly elastic shell which refines it. The derivations of the asymptotic approach are specifically traced taking the example of a spherical layer. A dispersion relation is presented in the case of the planar problem, which indicates the existence of a finite range of wavelengths of increasing amplitude which can be used to create favourable wave conditions for the development or suppression of instabilities. A solution of problem of three-wave resonance is given.