THE APPLICATION OF THE EIGENFUNCTION TECHNIQUE TO THE SOLUTION OF DYNAMIC PROBLEMS FOR CURVED THERMOELASTIC BODIES

摘要

The problem of thermoelasticity in the general formulation can be decomposed into three more simple problems. In the first problem, the trial method is utilized to find the boundary functions which must satisfy only the boundary conditions. The second problem with homogeneous boundary and the inhomogeneous initial conditions is reduced to the eigenfunction- eigenvalue (EFV) problem by means of the introduction of specific ^-variables and the separation of time. For solving this problem, a system of linear algebraic equations is obtained as a result of the satisfaction of the boundary conditions at the points of division of the curvilinear boundary of the body into small parts. When the eigenfunctions and eigenvalues are found, the solution of the third problem with homogeneous boundary and initial conditions is determined using the spectral decomposition of the desired functions and the nonhomogeneous terms in a coupled system of differential equations. The thermoelastic model is used in the calculations of the units of engines of different type, mechanisms, and in other cases. Even the linear version of the model is fairly complicated. This is especially the case for the derivation of the solution of the boundary-value and initial-boundary value problems for bodies with complex curved shape.