Investigations of Inertia Effects on an Infinite Solid Cylinder Due to Thermal Shock

In this paper the effects of inertia are explored for the case of a thermal excitation applied on the surface of an infinitely long, solid circular cylinder. The linear uncoupled field equations for a homogeneous, isotropic, thermoelastic medium are used to derive the desired field equations of stress and displacement. The solution procedure included, first, the determination of the thermal boundary value problem from the energy equation which is identically satisfied for the uncoupled condition. Secondly, substitution of the strain-displacement relationships and the previously obtained thermal relation into the equilibrium equation containing inertial effects. The equilibrium equation is the only nonidentically satisfied equation. Thirdly, a solution of this equation is then found in the S-domain by Laplace transformation. Finally, the desired displacement equation is transformed into the time-domain as a function of temperature, time and radius of the cylinder by using inverse Laplace transforms and the calculus of residues