Plane-strain wave propagation of an impulse-excited fluid-filled functionally graded cylinder containing an internally clamped shell

Abstract

The propagation of stress waves in an impulsive load-excited fluid-filled cylindrical structure containing an internally clamped shell is investigated. The external and internal cylinders are made of functionally graded and homogeneous isotropic materials, respectively. The space between the cylindrical shells is filled with a non-viscous and compressible fluid. The equations of motion for solid media are based on the three-dimensional theory of elasticity. According to the problem definition, for establishing the relationship between the displacement and stress fields, the governing equations are extracted in the form of plane-strain. A laminate model is employed to attain the dynamic equations of the functionally graded cylinder. Next, a transfer matrix is established by considering the continuity conditions of the stress and displacement at the interfaces of the layers. Then, the Laplace transform is utilized to transfer wave equations from the time domain to the Laplace domain. Eventually, a numerical inverse Laplace transform known as the Durbin method is employed to retrieve the solutions obtained into the time domain. An excellent agreement is observed in comparing between results of the present analytical method and previous models. Next, the effects of geometrical and physical properties of the inner shell on the transient response of the functionally graded cylinder are investigated. Also, the von Mises stress as the most effective parameter in the structural design is studied. The results show that the inner shell made of a material with a lower elasticity modulus leads to a reduction in the amount of von Mises stress in the external cylinder. As well as, an inner shell with a greater volume has a more positive effect on the transient response of the functionally graded cylinder.