In this paper, the author investigated the phenomenon of flutter, which may be the cause of instability of construction structure when it is affected by aerodynamics. By analyzing the effect of aerodynamic on the structure via mathematical analysis, the author has established a mathematical model to study the stability of the structure in the aerodynamic flux that moves supersonically. | VNU Journal of Science: Mathematics – Physics, Vol. 33, No. 2 (2017) 88-95 Mathematical Model in Studying the Stability of Dynamic Systems Le Hong Lan* Department of Basic Science, Transport and Communications University, , Cau Giay, Hanoi, Vietnam Received 25 April 2017 Revised 30 May 2017; Accepted 05 June 2017 Abstract: In this paper, the author investigated the phenomenon of flutter, which may be the cause of instability of construction structure when it is affected by aerodynamics. By analyzing the effect of aerodynamic on the structure via mathematical analysis, the author has established a mathematical model to study the stability of the structure in the aerodynamic flux that moves supersonically. Keywords: Aerodynamics, flutter, stability. 1. Introduction Aerodynamic load is a significant element when calculating physical structure of large constructions, such as skyscrapers, antenna towers, suspension bridges, etc. This is especially important for flying equipments. Aerodynamic that affects on the structures in both the same direction as well as the perpendicular one of gas flow, depends on magnitudes, characteristics of the gas flow and the movements of the structures. Aerodynamic stability of technical systems is the most important consideration when calculating structures under aerodynamic load. The study of static and dynamic nonlinear patterns of flutter and the aerodynamic stability has a significant impact in practical problems. Although there are many works dealt with the stability of sheet structures which have composite materials, however, almost the previous publications, the authors have mainly applied finite element methods [1-8]. The main content of this paper is a dynamic analysis of sheet structure that has functionally graded materials under aerodynamic load. One of the unstable situations is flutter, which might cause the instability of structure under aerodynamic load. In the sheet structure the energy from gas flow was generated
