On Axially Symmetric Elastic Wave Propagation in a Fluid-Filled Cylindrical Shell

摘要

The early stages of propagation of a water hammer disturbance are investigated, water hammer constituting a special case of axially symmetric elastic wave propagation in a fluid-filled cylindrical shell. Many of the objectionable features of the elementary (Joukowsky) water hammer theory are removed, and particular emphasis is placed upon consideration of the effects of radial inertia of the fluid and of the shell. The formulation is appropriate for consideration of any axially symmetric acoustics disturbance which originates in the fluid and any of the usual engineering boundary conditions which describe constraints on motion of the end, or ends, of the shell. Motion of the shell is described by a thin-shell theory, and motion of the fluid is described by the axially symmetric wave equation, nonhomogeneous boundary conditions providing coupling of the fluid and shell motions. Application of a finite Hankel transform to the axially symmetric wave equation yields an infinite system of one-dimensional wave equations representing motion of the fluid. Integration of a finite set of these wave equations in conjunction with equations governing motion of the shell is accomplished numerically after a straight-forward application of the method of characteristics. (Author)