State-space approach to thermoelastic interactions in generalized thermoelasticity type III

The present work is attempted to formulate the state-space approach to the problems of thermoelastic interactions with energy dissipation on the basis of the theory of generalized thermoelasticity type-III, recently developed by Green and Naghdi. The formulation is then applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected to two different types of boundary conditions: (1) sudden increase in temperature and zero stress and (2) sudden increase in load and zero temperature change. Integral transform method is applied to obtain the solution of the problem. The short time approximated solutions for the field variables have been constructed analytically for both the cases. The problem is illustrated with the help of different graphs of numerical values of the field variables.