Double-layered cylinders are widely used in engineering. In order to predict its elastic dynamic responses which are crucial to establish design method, its radial displacement considering the effect of axial strain is divided into two parts: a quasi-static part meeting inhomogeneous stress boundary conditions and a dynamic part complying with homogeneous stress boundary conditions. The quasi-static part is determined by homogeneous linearity method, and the dynamic part is worked out by the separation of variables method and orthogonal expansion technique. In the expression of displacement there still exists two unknown variables, i.e., the axial strain and the radial stress at the interface between the inner shell and outer shell of the double-layered cylinder. By using axial force balance and radial displacement continuity, a set of Volterra integral equations of the second kind are derived, which can be solved successfully by an interpolation method. Numerical results are presented and discussed for comparison dynamic responses between a monobloc cylinder and a comparable double-layered cylinder.

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