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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.
Keywords: free vibration of transversely isotropic solid bar; elastic rods loaded with fluid; wave propagation in a cylinders immersed in a fluid; Chebyshev polynomials |
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