Wave Propagation in a Fluid-Loaded Homogeneous, Transversely Isotropic, ElasticCylinder of Arbitrary Thickness

摘要

The problem of wave propagation in an infinite, fluid-loaded, homogeneous,transversely isotropic cylinder is studied within the framework of the linearized, three-dimensional theory of elasticity. The equations of motion of the cylinder are formulated using the constitutive equations of a transversely isotropic material with a preferred material direction collinear with the longitudinal axis of the cylinder. The equations of motion of the internal and external fluids are formulated using the constitutive equations of an inviscid fluid. Displacement potentials are used to solve the equations of motion of the cylinder and the fluids. The frequency equation of the coupled system, consisting of the cylinder and the internal and external fluids, is developed under the assumption of perfect-slip boundary conditions at the fluid-solid interfaces. This frequency equation is general in axial wavenumber k, circumferential wavenumber n, cylinder wall thickness h, and radial frequency. Cut-off frequencies and frequency spectra are computed for the n=1 modes in hollow cylinders, hypothetical fluid columns, fluid-filled cylinders, and cylinders that are fluid filled and immersed in fluid. Numerical results are obtained for two isotropic cylinders composed of steel and soft (linear) and for a highly anisotropic, fiber-reinforced cylinder. (AN).