A numerically stable global matrix method for cylindrically layered shells excited by ring forces

Abstract

This paper defines a numerically stable method for modeling cylindrical shells that can have multiple viscoelastic layers and external compliant coatings. The method is numerically stable over a wide range of axial wavenumbers and circumferential orders because it uses a ‘‘global matrix’’ approach with appropriately defined coefficients. The excitations used here are time-harmonic ring forces that can push on the shell in the radial, circumferential, and axial directions. The ring forces can have a linear phase shift around the circumference of the shell, so helical waves can be excited and studied for any circumferential order. Analytically, the order can be complex, although the software is presently implemented for real orders. The method is verified by modeling a thin cylindrical shell surrounded by fluid. To provide a very demanding test of the numerical stability, the drive point response of the shell is computed. This computation demonstrates the numerical stability of the method over a wide range of axial wavenumbers and circumferential orders.