To accurately simulate the dynamics of a pulsed reactor, it is necessary to know the shape of the fuel rod at the moment of the next power pulse. Since the numerical methods for solving this dynamic problem of thermoelasticity require too much computation time, an analytical method was applied. The problem of finding the natural frequencies and eigenfunctions of an inhomogeneous rod is solved. Analytical expressions for eigenfunctions are obtained; they give a good match with calculations using the Galerkin method and the ANSYS calculations.

The results of the numerical-analytical solution of the equation of motion of an inhomogeneous fuel rod are compared with the solution by the finite element method (ANSYS). The prospects for using the method in studying the dynamics of the NEPTUN reactor are considered.