A SPATIAL DECAY ESTIMATE FOR TRANSIENT THERMOELASTIC PROCESS IN A COMPOSITE SEMISPACE
Józef Ignaczak · Journal of Thermal Stresses · 2000
A Saint-Venant's principle associated with a one-dimensional dynamic coupled ther moelastic effective modulus theory for a microperiodic layered semispace is presented. In such a theory, the displacement u=u(x,t) and the temperature theta=theta(x,t) (x>=0,t>=0) are approximated by u(x,t)=U(x,t)+h(x)V(x,t) and theta(x,t)=THETA(x,t)+ h(x)PHI(x,t), where U(x,t) and PHI(x,t) represent a macrodisplacement and a macrotemperature, respectively; V(x,t) and PHI(x,t)denote a displacement corrector and a temperature corrector, respectively; h=h(x) is a prescribed periodic microshape function; and the pairs (U,THETA) and (V,PHI) are found by solving an initial boundary value problem described by a system of linear partial differential equations with effective thermoelastic moduli subject to suitable initial and boundary conditions. It is shown that the thermoelastic energy associated with a solution to the problem and stored in the semi-space lying beyond a distance x from the loaded boundary x=0 over the time interval [0,t] decays exponentially as x to infinity and its decay length L depends on the time t, an effective velocity of thermoelastic wave (c*l), an effective time (T*), and an effective thermoelastic coupling parameter (epsilon*). In particular, it is shown that for small (large) times the function L reveals behavior of the decay length for a pure thermal (elastic) energy of a semispace.