Thermal viscoelastic state of piecewise unbounded cylinder-anisotropic plate with circular hole under random in time temperature field (Q2703292)

Let us consider the plate \(\Pi_{n}=\{r: r\in (R_{0},R_{1})\cup (R_{1},R_{2})\cup\ldots\cup(R_{n},\infty)\); \(R_{0}>0\}\) with zero temperature at \(t\leq 0\). The authors find the correlation matrix of the nonstationary stochastic temperature field \(T\). \(T\) is a bounded in region \(D_{n}=\{(t,r): t\in(0,\infty)\); \(r\in\Pi_{n}\}\) solution of the system of heat equations \({1\over a_{j}^{2}}{\partial \over\partial t}T_{j}+ \chi_{j}^{2}T_{j}-({\partial^{2}\over\partial r^{2}} +{1\over r}{\partial \over\partial r})T_{j}=f_{j}(t,r)\), \(j=1,\dots, n+1\) with zero initial conditions, with boundary conditions \((\alpha_{11}^{0}{\partial\over\partial r}+\beta_{11}^{0})T_{1} |_{r=R_{0}}=g_{n+2}(t)\); \(\lim_{r\to\infty}{\partial\over\partial r}T_{n+1}=0\); and conditions of imperfect thermal contacts \([(b_{j}{\partial\over\partial r}T_{j}+T_{j})- T_{j+1}]|_{r=R_{j}}=0\), \([{\partial\over\partial r}T_{j}- \nu_{j}{\partial\over\partial r}T_{j+1}] |_{r=R_{j}}=0\), \(j=1,\dots, n\). Here \(g_{n+2}(t)\) is a stationary (in the wide sense) stochastic function; \(f_{j}(t,r)=\psi_{j}(r)g_{j}(t), j=1,\dots, n+1\), where \(\psi_{j}(r)\) are nonstochastic functions, \(g_{j}(t)\) are stationary (in the wide sense) stochastic functions.