An Exact Analysis of the Transient Interaction of Acoustic Plane Waves With a Cylindrical Elastic Shell

Abstract

The governing system of differential equations for the linear problem of the transient interaction of plane acoustic waves and a submerged elastic cylindrical shell is transformed into a system of Volterra integral equations of the second kind. The integral equations are solved by a step-by-step integration scheme and numerical results to the problem are obtained exactly within the limit of series solution imposed by the Gibb’s phenomenon and within the limit of numerical truncation and roundoff errors. Detailed features of the transient response of the shell were revealed.

Modeling and Simulation of Underwater Shock Problems Using a Coupled Lagrangian—Eulerian Analysis Approach

“…10 with the 8-term finite series analytical solution found by Huang (1970). Again, very good agreement between the finite element and analytical solutions is seen.…”

“…These analyses examined the elastic response of a spherical shell and an infinite cylinder to loading from a plane acoustic step wave propagating through an acoustic fluid media. Huang (1969Huang ( , 1970) solved these problems analytically, using a direct inverse Laplace transform of a finite number of terms of the infinite series expansion of the equations for the respective shells. For our finite element analyses, the same material properties, parameters, and nondimen- Spherical Shell Subjected to a Plane Acoustic Step Wave Figure 3 shows the geometry of the spherical shell subjected to a plane acoustic step wave problem.…”

Transient Response of Two Fluid-Coupled Cylindrical Elastic Shells to an Incident Pressure Pulse

“…(21) and (22) give the late time shell deflections long after the incident wave has engulfed the outer shell and they can also be This procedure has been demonstrated to be quite effective in previous studies of the single cylindrical shell problem [ 4,5].…”

“…[4] and plotted in solid lines for the case wherein the outer shell is absent. (22) and (24) respectively.…”

“…in order to juxtapose solutions to those for a single shell previously obtained in Ref. [4], the version of shell equations of motion used therein is also used here . In the Laplace transform domain , they are…”