hollow cylinder

An axially symmetric problem for a hollow cylinder with unloaded bases is considered.  On the inner and outer cylindrical surfaces, the normal and tangential loads are prescribed.  The problem is reduced to a biharmonic equation with corresponding boundary conditions.  Application of the method of variables separation results in a homogeneous boundary value problem for the ordinary differential equation.  Its eigenfunctions have been used to construct an infinite system of homogeneous solutions for the initial biharmonic problem.  Its solution, represented as a series expansion in terms of

The stationary temperature distribution in a three-layer infinitely-long hollow cylinder is modeled and determined under the condition that the internal heat sources are distributed within the second layer in accordance to the parabolic law and the convective-radiative and convective heat exchange with the environment occurs on the inner and outer surfaces, respectively.