LOCALIZED FAMILIES OF BENDING WAVES IN A NONCIRCULAR CYLINDRICAL-SHELL WITH SLOPING EDGES

The initial-boundary-value problem for the equations of shallow shells describing the motion of a non-circular cylindric;tl shell is conside red. The shell edges are given by not necessarily plane curves. The co nditions of a joint support or a rigid clamp are considered as boundar y conditions. It is assumed that the initial displacements and velocit ies of the points of the median surface of the shell are functions whi ch decrease rapidly away from some generatrix. In the case when the sh ell. edges lie in planes perpendicular to the generatrix, the solution of the problem can be constructed as an expansion in beam functions a long the generatrix. The expansion enables the original initial bounda ry-value problem to be reduced to an initial problem the solution of w hich can be constructed [1] by Maslov's method [2]. A complex WKB proc edure is proposed, which is suitable for non-circular cylindrical shel ls with sloping edges. An asymptotic solution of the equations of moti on is constructed by superimposing localized families (wave packets) o f flexural waves travelling in a circular direction. A qualitative ana lysis of the solutions is carried out. As an example wave forms of mot ion of a cylindrical shell of oblique section are considered. Copyrigh t (C) 1996 Elsevier Science Ltd.