Stress state of semi-bounded elastic film (Q2768783)

The authors consider the thermoelasticity problem for a semi-bounded film described by the system of equations NEWLINE\[NEWLINEb_0^2{\partial^2 T\over\partial t^2}+b_1^2{\partial T\over\partial t}+b_2^2 T-{\partial^2 T\over\partial x^2}=f(t,x),{\partial^2 \sigma_1\over\partial x^2}-{1\over c^2}{\partial^2 \sigma_1\over\partial t^2}=(1+\nu)\alpha_{t}\rho{\partial^2 T\over\partial t^2},0\leq t\leq t_1<\infty, x\in (0,\infty),NEWLINE\]NEWLINE with initial conditions \(T|_{t=0}=g_1(x),\;\partial T/\partial t|_{t=0}=g_2(x),\;\sigma_1|_{t=0}=\omega_1(x),\;\partial \sigma_1/\partial t|_{t=0}=\omega_2(x)\), and boundary conditions \((-h_1\partial/\partial x+h_2\partial/\partial t+h_3)T|_{x=0}=\omega_0(t),\;\sigma_1|_{x=0}=\sigma_{10}(t),\;\partial T/\partial x|_{x=\infty}=0,\;\sigma_1|_{x=\infty}=0\). The solution of the problem is obtained by using Laplace transform.