On the general theory of thermo-elastic friction

Summary A theory of the thermo-elastic dissipation in vibrating bodies is developed, starting from the three-dimensional thermo-elastic equations. After a discussion of the basic thermodynamical foundations, some general considerations on the problem of the conversion of mechanical energy into heat are given. The solution of the coupled thermo-elastic equations is found in the form of series expansions in terms of normalised orthogonal eigenfunctions. For the coefficients an infinite system of algebraic equations with constants, which are complicated field integrals, is derived. An approximate solution of the infinite system is given. In some cases the coupling-constants can be calculated exactly, in other cases they have to be determined on the base of approximate theories.