An Analytical Model for a Clamped Isotropic Beam Under Thermal Effects

Abstract

Structures and industrial equipment often operate in environments where temperature variations take place. Although thermal effects may be negligible in some cases, they have caused the unexpected failure of mechanical systems many times. Whether or not temperature has significant effects on the dynamical behavior of such machines and structures depends upon several aspects, amongst which are geometry, material properties and boundary conditions. In this paper we investigate the dynamical behavior of a clamped beam under the influence of a uniform, quasi-statically varying temperature field. An analytical model was used, based on Euler-Bernoulli’s beam theory with the introduction of the proper boundary conditions. Temperature effects are included in terms of an axial force that shows up when the beam tends to thermally expand, but this expansion is restrained by the clamping. Preliminary results do not agree with experimental data, since perfect clamping is difficult to achieve in practice. Finally the model is updated with the inclusion of axial and torsional springs connecting the beam to the support. The spring constants were calculated through optimization procedure to minimize the differences between the natural frequencies obtained from the analytical model and the corresponding experimental ones. Agreement with experimental results is reasonable up to the 4th mode of the beam. In the future, this analytical model is to be used for design and simulation of an active controller that accounts for temperature changes in the structure.