On the Dispersion of Axisymmetric Waves Propagating in a Two-layer Hollow Cylinder Containing an Inviscid Liquid (Lucite + water case)

This work deals with the investigation of axisymmetric longitudinal waves propagating in a two-layer hollow cylinder with inviscid fluid.The corresponding problem is formulated in the framework of the piecewise homogeneous body model, using the exact equations and relations of elastodynamics to describe the motion of the cylinder and the linearized Euler equations to describe the flow of the fluid.By solving the corresponding eigenvalue problem, analytical expressions for the unknown functions are obtained and with these expressions and the corresponding boundary, contact and compatibility conditions, the dispersion equation is obtained.The roots of this equation are found numerically and thus the dispersion curves for the zeroth, first and second mod are constructed.Concrete numerical results are obtained for the case where the material of the inner layer is Lucite, but the material of the outer layer is assumed to be a hypothetical material whose Poisson's ratio and density (Young's modulus) are the same as those of the material of the inner layer, but the Young's modulus (density) of the outer layer is different from that of the inner layer.Water is chosen as the fluid in the cylinder.