Parametric Instability of a Non-uniform Beam with Thermal Gradient and Elastic End Support

The dynamic stability of a non-uniform beam with thermal gradient and elastic end support subjected to a pulsating axial load is analysed. An exact analytical approach to the parametric dynamic systems governed by Mathieu equation is presented. The vibration and buckling properties for thermal gradient and end support stiffness are examined. Thereafter, dynamic unstable regions are obtained under various thermal gradient and end support stiffness and compared with the previous solution