Stability of Slender Non-Conservative Columns Made of Thermo-Active Gradient Materials

The paper is concerned with stability analysis of slender thin-walled cantilever beam subjected to axial distributed follower load, modelled as Leipholz columns and made of functionally gradient materials. Both transverse and longitudinal material gradients are studied as a result of different phase mixture with inclusion of thermo-active shape memory alloy (SMA). Attention is focused on the effect of phase transformation in SMA caused by increase of temperature and resulting in considerable changes of the local visco-elastic material properties which in turn affect system stability. Equivalent homogeneous beam stiffness and internal Kelvin-Voigt loss factor are determined using Kirchhoff's hypothesis and the visco-elastic principle. Partial equation of transverse column vibration is transformed to ordinary equations by means of two-mode Galerkin's discretisation based on the cantilever beam functions. Eigen-value behaviour and critical follower force are studied for various material gradient configurations. A concept of intelligent column is proposed utilizing longitudinal material functionality induced by non-uniform temperature distribution.