Thermally induced vibration of a cantilever beam with periodically varying intensity of a heat source

In this paper an exact solution to the problem of the thermally induced vibration of a cantilever beam is presented. It is assumed that on a part of the beam the surface acts as a periodically time-varying heat source. The changing of the beam temperature produces thermal stresses, which cause displacements of the beam. The vibration of the beam is governed by the Bernoulli-Euler equation which includes the variable thermal moment. The heat equation and the vibration problem are solved by using the Green’s function method. The symbolic software Mathematica has been used to obtain the solution of the problem in an analytical form.