The Wave Field of a Layer with a Cylindrical Cavity
The wave field of an infinite elastic layer weakened by a cylindrical cavity is constructed in this paper. The ideal contact conditions are given on the upper and bottom faces of the layer. The normal dynamic tensile load is applied to a cylindrical cavity’s surface at the initial moment of time. The Laplace and finite sin- and cos- Fourier integral transformations are applied successively directly to axisymmetric equations of motion and to the boundary conditions, on the contrary to the traditional approaches, when integral transformations are applied to solutions’ representation through harmonic and biharmonic functions. This operation leads to a one-dimensional vector inhomogeneous boundary value problem with respect to unknown transformations of displacements. The problem is solved using matrix differential calculus. The field of initial displacements is derived after application of inverse integral transformations. The normal stress on the faces of the elastic layer are constructed and investigated depending on the mechanical and dynamic parameters.
KeywordsElastic layer Dynamic load Cylindrical cavity Integral transformation
- 1.Popov, G.Y.: An exact solution of the elasticity theory problem for an infinite layer weakened by a cylindric cavity. Dokladu RUN, 451(5), 1–4 (2013)Google Scholar
- 3.Malitz, P.Y., Privarnikov, A.K.: The application of weber-type transformations to the solution of elasticity problems for layered media with a cylindrical hole. J. Voprosu prochnosty i plastichnossty 56–64 (1971)Google Scholar
- 4.Arutunyan, N.H., Abramyan, B.L.: Some axisymmetric problems for a half-space and an elastic layer with a vertical cylindrical notch. J. Izv. AN Arm. SSR. Mekhanica 22(3), 3–13 (1969)Google Scholar