HIGH-RESOLUTION ANALYSIS OF THE COMPLEX WAVE SPECTRUM IN A CYLINDRICAL-SHELL CONTAINING A VISCOELASTIC MEDIUM .1. THEORY AND NUMERICAL RESULTS

In this study the relation between frequency and complex wave number o f axisymmetric wave modes in an isotropic, thin-walled, cylindrical sh ell containing a linear viscoelastic medium is derived. Shell wall ben ding 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 t he medium enclosed. A Maxwell model is used for both complex Lame cons tants lambda and mu to describe the constitutive equations of the medi um. By varying the complex moduli, the medium can be modeled as an Inv iscid fluid, an elastic material, or anything between these two extrem es. The interaction of the thin-walled linear elastic shell and the vi scoelastic medium is discussed numerically by calculating the complex dispersion relation. Numerical results are presented for an empty shel l and a shell filled with three types of core material: an inviscid fl uid, a shear dissipative fluid, and a shear elastic fluid. In a compan ion paper [J. Vollmann ef nl., J. Acoust. Sec. Am. 102, 909-920 (1997) ], the experimental setup and the signal processing used to perform th e high-resolution measurement of the dispersion relation are described in detail, Theoretical and experimental results are compared. (C) 199 7 Acoustical Society of America.