Localized families of bending waves in a non-circular cylindrical shell with sloping edges

✍ Scribed by G.I. Mikhasev

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 463 KB
• Volume: 60
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(96)00079-2

✦ Synopsis

The initial-boundary-value problem for the equations of shallow shells describing the motion of a non-circular cylindrical shell is considered. The shell edges are given by not necessarily plane curves. The conditions of a joint support or a rigid damp are considered as boundary conditions. It is assumed that the initial displacements and velocities of the points of the median surface of the shell are functions which decrease rapidly away from some generatrix. In the ease when the shell edges lie in planes perpendicular to the l;eneratrix, the solution of the problem can be constructed as an expansion in beam functions along the generatrix. The expansion enables the original initial boundary-value problem to be reduced to an initial problem, the solution of which can be constructed [11 by Maslov's method . A complex WKB procedure is proposed, which is suitable for non-circular cylimtdcal shells with sloping edges. An asymptotic solution of the equations of motion is constructed by superimposing localized families (wave packets) of flexural waves travelling in a circular direction. A qualitative analysis of the solutions is carried c,ut. As an example wave forms of motion of a cylindrical shell of oblique section are considered.