Vibrations of columns in the thermal postbuckling state accounting for temperature effect on material properties

The article is concerned with natural frequencies of thermally buckled columns. The analysis accounts for the effect of temperature on the modulus of elasticity and the coefficient of thermal expansion of the material of the column. The columns are simply supported and two cases of axial boundary conditions include an elastic axial constraint and prescribed axial displacements. It is demonstrated that neglecting the effect of temperature on material properties leads to a significant quantitative mistake at low temperatures and a qualitative mistake at high temperatures. In flexible columns with axially constrained boundaries subject to a prescribed thermal loading the frequencies increase with an increasing temperature, but this trend is reversed at high temperatures due to the sharp drop of the modulus of elasticity. In the contrary, in the columns subject to a prescribed axial displacement in addition to thermal loading, frequencies remain relatively stable and subsequently decrease at high temperatures. It is demonstrated that the frequencies of columns with a low or moderate slenderness ratio are affected by the axial constraint to a much larger degree than those in more flexible columns.