THERMAL EFFECTS IN VISCOELASTIC WAVE PROPAGATION.
STANFORD UNIV CA DIV OF ENGINEERING MECHANICS
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This paper mainly deals with dynamic problems in linear viscoelastic solids when the effect of thermomechanical coupling is considered, that is, the interaction between the stress field and the temperature field. Throughout the analysis a thermorheologically simple material is studied. According to Schaperys theory of thermomechanical phenomena for linear viscoelasticity, the energy equation is derived but with a modified form of the operational specific that which gives additional expressfions in the strain components. The linearity of the displacement vector in the equations of motion and the boundary condition makes it possible to separate the problem into two parts one due to thermal expansion with the other due to boundary traction. For sinusoidal boundary traction, the system of equations associated with boundary stress assumes a similar form to that in elasticity with the elastic constants depending on the position vector. For the case of axial symmetry the solution is found by the method of internal reflection which was initiated by H. Bremmer for the solution of the one-dimensional inhomogeneous wave equation. By the use of this solution numerical values of the temperature profile and stress field are found. Author