Extensional Waves in a Transversely Isotropic Solid Bar Immersed in an Inviscid Fluid Calculated Using Chebyshev Polynomials

The extensional vibration in a homogeneous transversely isotropic solid bar immersed in an inviscid fluid is studied using the linearized, three-dimensional theory of elasticity. The equations of motion of solid bar and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equations of an inviscid fluid. The solution of the frequency equations are obtained by Chebyshev polynomial series using the geometric boundary conditions. The computed non-dimensional frequencies are presented in the form of dispersion curves for the material Zinc. To compare the model with exiting literature, the longitudinal vibration of cylindrical bar without fluid are obtained and they show good agreement.