FORTRAN Algorithms for the Three-Dimensional Solution of Two-Layer Solid andHollow Cylinder Dynamic Elasticity Problems With and Without Fluids

摘要

This document contains FORTRAN algorithms for the numerical evaluation of exactclosed form solutions to four fluid/structure interaction mathematical problems that are modeled as cylinders and fluids. The cylinders (infinitely long in the longitudinal x-direction) are modeled as three-dimensional linear viscoelastic solids, and the fluids are treated as inviscid. The outer fluid extends to infinity in the radial r-direction; the inner fluid (contained within the hollow cylinder) is bounded by the inner cylinder at radius r = a. The cylinders are subject to forced harmonic vibration at the solid/fluid interface. The response to both axisymmetric and nonaxisymmetric excitations is calculated, with nonaxisymmetric excitation described in terms of circumferential order number n. The first model is comprised of a single hollow cylinder, filled with an inner fluid and immersed in an outer fluid. The second model consists of a single solid cylinder immersed in an outer fluid. The third model, an extension of the second one, adds a second cylinder in contact with the first cylinder. The fourth model consists of the two-layered cylinder with outer fluid (model three); however, the inner cylinder is now hollow and contains an inner fluid. Structural damping requires that the material properties be represented as complex numbers; therefore, series solutions to the Bessel functions are required. Native algorithms are provided for the Bessel functions, with certain parameter restrictions, and a subroutine is given to allow use of the external FORTRAN Bessel function libraries provided by MathWorks, Inc., without parameter restriction. (AN).