Transient solutions for longitudinally impacted inhomogeneous conical shells

Here we study transient elastic wave propagation in inhomogeneous conical shells. The uniaxial theory is employed and two separate techniques are used for extracting information about the stress field for impact problems. Firstly the formal Karal-Keller method is used enabling us to directly determine asymptotic wavefront expansions for the stress field. A transform technique, based on Eason's 1], is then used to obtain conditions on the physical parameters of the medium which give solutions to the governing equation in terms of Bessel functions and some particular problems are discussed. Previously unknown simple closed-form solutions are obtained. Our results have application to the propagation of waves in filamentary cones of constant wall thickness or in homogeneous cones having an axial temperature gradient.