Thermal buckling and natural vibration of the beam with an axial stick-slip-stop boundary

As a first attempt to study the dynamics of a heated structure with complicated boundaries, this paper deals with the thermal buckling and the natural vibration of a simply supported slender beam, which is subject to a uniformly distributed heating and has a frictional sliding end within a clearance. This sliding end is initially at a stick status under the friction force, but may be slightly slipping due to the thermal expansion of the beam until the sliding end contacts a stop, i.e., the bound of the clearance. The material properties of the beam are temperature-independent for low temperature, but temperature-dependent for high temperature. For each case, the analytic solutions for the critical buckling temperature and the natural frequencies of the heated beam are derived first. Then, discussions are made to reveal the effects of beam parameters, such as the ratio of beam length to beam thickness, the ratio of clearance to beam length and the temperature-dependent material properties, on the critical buckling temperature and the fundamental natural frequency of the heated beam. The study shows that both friction force and clearance have significant influences on the critical buckling temperature and the fundamental natural frequency of the beam. When the friction force is not very large, the clearance can greatly increase the critical buckling temperature. These conclusions enable one to properly design the stick-slip-stop boundary so as to improve the mechanical performance of the beam in thermal environments.