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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 434868, 12 pages
Research Article

Dynamic Stability of Euler Beams under Axial Unsteady Wind Force

1Engineering Technology Research and Development Center for Structural Safety and Health Monitoring, Guangzhou University, Guangzhou, Guangdong 510006, China
2State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China

Received 19 October 2013; Revised 12 February 2014; Accepted 12 February 2014; Published 23 March 2014

Academic Editor: Masoud Hajarian

Copyright © 2014 You-Qin Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Dynamic instability of beams in complex structures caused by unsteady wind load has occurred more frequently. However, studies on the parametric resonance of beams are generally limited to harmonic loads, while arbitrary dynamic load is rarely involved. The critical frequency equation for simply supported Euler beams with uniform section under arbitrary axial dynamic forces is firstly derived in this paper based on the Mathieu-Hill equation. Dynamic instability regions with high precision are then calculated by a presented eigenvalue method. Further, the dynamically unstable state of beams under the wind force with any mean or fluctuating component is determined by load normalization, and the wind-induced parametric resonant response is computed by the Runge-Kutta approach. Finally, a measured wind load time-history is input into the dynamic system to indicate that the proposed methods are effective. This study presents a new method to determine the wind-induced dynamic stability of Euler beams. The beam would become dynamically unstable provided that the parametric point, denoting the relation between load properties and structural frequency, is located in the instability region, no matter whether the wind load component is large or not.