Dynamic stability analysis of frame systems by application of the finite element method

Dynamic instability occurs when a structural system's displacements increase unboundedly with time. In this research, dynamic stability of frame systems subjected to multiple axial periodic forces is investigated. Under action of such loads, a frame system may experience lateral dynamic instability with application of additional minor lateral disturbances. Instability occurs when the frequency of the exciting force is equal to approximately twice the natural frequency of the system. Investigation of this condition involves determining regions of applied load-frequency pairs for which a frame responds in a dynamically unstable fashion. In this paper, the Finite Element Method is used to locate these regions. Direct numerical integration is performed to calculate dynamic responses of a frame system for both cases of dynamic stable and unstable conditions using the Newmark-β method along with the Hilber-Hughes-Taylor modification.; Numerical examples are used to compare results obtained by the methods of this study with theoretical solutions. Comparisons indicate that the techniques used give satisfactorily accurate results. Examples of dynamic stability analysis included are for a simply supported column, portal frame and multistory frame all under periodic axial loads, with different lateral disturbances such as imposed displacement, dynamic lateral force, and ground movement. Results indicate that dynamic axial loads have a strong influence on dynamic response of a frame system when compared with the respective system without dynamic axial loads.