Applied Mathematics & Information Sciences

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The dynamic response of a homogeneous transversely isotropic solid bar of cardioidal cross-section immersed in a fluid is studied using the Fourier expansion collocation method (FECM), within the framework of the linearized three-dimensional theory of elasticity. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equations of an inviscid fluid. Three wave potential functions are introduced to uncouple the equations of motion. The frequency equations of longitudinal and flexural (symmetric and antisymmetric) modes are analyzed numerically for a cardioidal cross-sectional transversely isotropic solid bar immersed in a fluid. The computed non-dimensional frequencies are presented in the form of dispersion curves for the material Zinc.

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