Three-dimensional dispersion analysis of a transversely isotropic solid cylinder of elliptic inner and outer cross-section immersed in a fluid

Introduction In many structural applications requiring high strength-toweight and stiffness-to-weight ratios, the isotropic cylinders are being replaced by the cylinders of composite materials. So the study of frequency equations of wave propagation in anisotropic cylinders must be developed. A through knowledge of various wave propagation characteristics, as a function of material and geometrical parameters is necessary for a wide range of applications, from geophysical prospecting in cased holes, nondestructive evaluation of oil and gas pipelines, to the insulated fiber optic cables for data transmission. The most general form of harmonic waves in a hollow cylinder of circular cross section of infinite length has been analyzed by Gazis (1959). Mirsky (1964) analyzed the wave propagation in transversely isotropic circular cylinders of infinite length and presented the frequency equation in Part I and numerical results in Part II. A method, for solving wave propagation in arbitrary cross-sectionl cylinders and plates and to find out the phase velocities in different modes of vibrations namely longitudinal, torsional and flexural, by constructing frequency equations was devised by Nagaya (1982, 1983, 1984 and 1985) He formulated the Fourier expansion collocation method for this purpose. Following Nagaya, Paul and Venkatesan (1989) studied the wave propagation in an infinite piezoelectric solid cylinder of arbitrary cross section using Fourier expansion collocation method. Guided waves in a transversely isotropic cylinder immersed in a fluid is analyzed by Ahmad (2001). Following Ahmad, Nagay (1995) have studied the longitudinal guided wave propagation in a transversely isotropic rod immersed in fluid, later, Nagy with Nayfeh (1996) discussed the viscosity-induced attenuation of longitudinal guided waves in fluid-loaded rods. Easwaran and Munjal (1995) reported a note on the effect of wall compliance on lowest-order mode propagation in fluidfilled/submerged impedance tubes Sinha et. al. (1992) have discussed the axisymmetric wave propagation in circular cylindrical shell immersed in fluid, in two parts. In Part I, the theoretical analysis of the propagating modes is discussed and in Part II, the axisymmetric modes excluding torsional modes are obtained theoretically and experimentally and are compared. Berlinear and Solecki (1996) have studied the wave propagation in fluid loaded transversely isotropic cylinder. In that paper, Part I consists of the analytical formulation of the frequency equation of the coupled system consisting of the cylinder with inner and outer fluid and Part II gives the numerical results. Venkatesan and Ponnusamy (2002, 2003) have obtained the frequency equation of the free vibration of a solid cylinder of arbitrary cross section immersed in a fluid using Fourier expansion collocation method. The frequency equations are obtained for longitudinal and flexural vibrations and are studied numerically for elliptical and cardioidal cross-sectionl cylinders. In this paper, the wave propagation in a cylinder of elliptic inner and outer cross section immersed in an invicid fluid is analyzed. The frequency equations of longitudinal and flexural modes are analyzed numerically for cylinders with elliptic crosssection using Fourier expansion collocation method. The computed non-dimensional plotted in the form of dispersion curves. Formulation of the problem We consider a homogeneous transversely isotropic infinite cylinder of both inner and outer elliptic cross-section immersed in inviscid fluid. The system is assumed to be linear so that the linearized three-dimensional stress equation of motion is used for both the cylinder and the fluid. The system displacements and stresses are defined by the cylindrical