Dynamic Stresses and Displacements around Cylindrical Cavities in an Infinite Elastic Medium under Moving Step Loads on the Cavity's Surface

摘要

Potential functions and Fourier series method in the cylindrical coordinate system are employed to solve the problem of moving loads on the surface of a cylindrical bore in an infinite elastic medium. The steady-state dynamic equations of medium are uncoupled into Helmholtz equations, via given potentials. It is used that because of the superseismic nature of the problem, two mach cones are formed and opened toward the rear of the front in the medium. The stresses and displacements are obtained by using integral equations with certain boundary conditions. Finally, the dynamic stresses and displacements for step loads with axisymmetric and nonaxisymmetric cases are obtained and discussed in details via a numerical example. Moreover, effects of Mach numbers and poisson's ratio of medium on the values of stresses are discussed.