Mathematics and Statistics Vol. 10(5), pp. 1024 - 1037
DOI: 10.13189/ms.2022.100514
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Mathematical Analysis of Dynamic Models of Suspension Bridges with Delayed Damping

Akbar B. Aliyev ^1,2, Yeter M. Farhadova ^1,*
1 Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan, Azerbaijan
² Azerbaijan State Oil and Industry University, Azerbaijan

ABSTRACT

Suspension bridges are a type of construction in which the deck is suspended under a series of suspension cables that are on vertical hangers. The first modern example of this project began to appear in the early 1800s. Modern suspension bridges are lightweight, aesthetically pleasing and can span longer distances than any other bridge form. Many papers have been devoted to the modelling of suspension bridges, for instance, Lazer and McKenna studied the problem of nonlinear oscillation in a suspension bridge. They introduced a (one-dimensional) mathematical model for the bridge that takes into account of the fact that the coupling provided by the stays connecting the main cable to the deck of the road bed is fundamentally nonlinear, that is, they gave rise to the system of semi linear hyperbolic equation, where the first equation describes the vibration of the road bed in the vertical plain and the second equation describes that of the main cable from which the road bed is suspended by the tie cables. Recently, interest in this field has been increasing at a high rate. In this paper, we investigate some mathematical models of suspension bridges with a strong delay in linear aerodynamic resistance force. We establish the exponential decay of the solution for the corresponding homogeneous system and prove the existence of an absorbing set as well as a bounded attractor.

KEYWORDS
Suspension Bridges, Dynamic Models, Stability, Strong Delay, Absorbing Set

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Akbar B. Aliyev , Yeter M. Farhadova , "Mathematical Analysis of Dynamic Models of Suspension Bridges with Delayed Damping," Mathematics and Statistics, Vol. 10, No. 5, pp. 1024 - 1037, 2022. DOI: 10.13189/ms.2022.100514.

(b). APA Format:
Akbar B. Aliyev , Yeter M. Farhadova (2022). Mathematical Analysis of Dynamic Models of Suspension Bridges with Delayed Damping. Mathematics and Statistics, 10(5), 1024 - 1037. DOI: 10.13189/ms.2022.100514.