High-resolution analysis of the complex wave spectrum in a cylindrical shell containing a viscoelastic medium. Part I. Theory and numerical results

Abstract

In this study the relation between frequency and complex wave number of axisymmetric wave modes in an isotropic, thin-walled, cylindrical shell containing a linear viscoelastic medium is derived. Shell wall bending and longitudinal motion are coupled in an empty cylindrical shell. When a viscoelastic medium is enclosed, the shell motion is affected by the complex bulk and shear modulus, as well as by the density of the medium enclosed. A Maxwell model is used for both complex Lamé constants λ and μ to describe the constitutive equations of the medium. By varying the complex moduli, the medium can be modeled as an inviscid fluid, an elastic material, or anything between these two extremes. The interaction of the thin-walled linear elastic shell and the viscoelastic medium is discussed numerically by calculating the complex dispersion relation. Numerical results are presented for an empty shell and a shell filled with three types of core material: an inviscid fluid, a shear dissipative fluid, and a shear elastic fluid. In a companion paper [J. Vollmann et al., J. Acoust. Soc. Am. 102, 909–920 (1997)], the experimental setup and the signal processing used to perform the high-resolution measurement of the dispersion relation are described in detail. Theoretical and experimental results are compared.