Wave propagation and transient response of a fluid-filled FGM cylinder with rigid core using the inverse Laplace transform

This paper studies the wave propagation and transient response of a fluid-filled functionally graded material (FGM) cylinder with rigid core using the Laplace transform. The mechanical properties of the FGM are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the structure according to a specific grading pattern. The FGM cylinder is approximated by a laminate model, for which the solution is expected to gradually approach the exact one as the number of layers' increases. For each layer of the cylinder, equations of motion are extracted based on elasticity theory. The equations of motion are derived in the form of plane strain according to the problem definition. Then, transfer matrix method, which includes a global transfer matrix that composed as the product of the local transfer matrices by applying continuity of the displacement and stress components at the interfaces of neighboring layers, is employed. This problem is solved in the Laplace domain and the Durbin's numerical Laplace transform inversion is employed to convert the obtained results into the time domain. Finally, the effects of various radius of rigid core on hydrodynamic field of fluid and transient response of the FGM cylinder subjected to impulsive loads are examined in detail. The numerical results show that von-misses stress considerably decreased by increasing the radius of rigid core.