Dynamic Modeling Theory Of Arch Bridge And Cable-Stayed Beam And Research On The In-Plan Free Vibration

Arch structure and cable structure are widely used in the bridge engineering to enlarge the span capacity of the bridges. Arch structure is mainly used in hybrid arch bridges, and the hybrid arch bridges studied in this paper are composed of arch rib, hangers or upright columns and main girder, including through arch bridge, half-through arch bridge and deck arch bridge. Cable structure is mainly used in cable-stayed bridge, whose basic component unit is cable-stayed beam structure. In order to investigate the in-plan free vibration characteristics of the hybrid arch bridges and the cable-stayed beam structure, this paper establishes the refined dynamic modeling theories of hybrid arch bridges and cable-stayed beam according to their boundary conditions and continuity conditions, the transfer matrix method is utilized to solve the eigenvalue problems, and then the parametric analyses are conducted to explore the in-plan free vibration characteristics. The main works of this thesis in detail are as followings:(1) According to the characteristics of the through arch bridge and without considering the mass of the hanger, the through arch bridge mechanical model is simplified as the arch-spring-beam combination system. Based on the boundary conditions, the governing differential equations of in-plan free vibration of the arch-spring-beam combination system are established by Hamilton principle, where transfer matrix method is utilized to solve the eigenvalue problem. At the same time, a finite element model is modeled by the finite element software ANSYS to verify the validity of the proposed theory and method. Finally, the parametric analyses of the through arch bridge’s in-plan free vibration characteristics are conducted by the proposed theory and method.(2) Applying the above simplified arch-spring-beam dynamic model, study theory and method into the investigation of the half-through arch bridge and deck arch bridge’s in-plan free vibration characteristics, the finite element software ANSYS is utilized to verify the applicability. Finally, parametric analyses are also made to study the half-through arch bridge and deck arch bridge’s in-plan free vibration characteristics, and the in-plan free vibration characteristics of the three kinds of arch bridges are analyzed contrastively.(3) The model theories of in-plan free vibration of the cable-stayed beam with CFRP cable are established from both aspects of considering the cable sag or not. When the cable sag is considered, starting from the dynamic equilibrium conditions of the infinitesimal element, the governing differential equations of in-plan free vibration of the cable-stayed beam are established, and based on the boundary conditions and continuity conditions, the eigen-equation of the cable-stayed beam with sagged cable is obtained. When the cable sag is not considered, the vibration theories of taut string and Euler beam are used to described the vibrations of cable and beam of the cable-stayed beam respectively, based on the boundary conditions and the dynamic equilibrium conditions at the joint of cable and beam, the transfer matrix method is utilized to obtain the eigen-equation of the cable-stayed beam with taut cable. Dimensionless processing is made in both of the methods, and the finite element software ANSYS is also used to verify the validity. Finally, parametric analyses are conducted to explore the in-plan free vibration characteristics of the cable-stayed beam.This paper first proposed not only the universal dynamical model and modeling theory for studying the in-plan vibration characteristics of full deck arch bridge, half-through arch bridge and through arch bridge, but also the modeling theory of cable-stayed beam by utilizing the simple vibration theories of taut string and Euler beam and considering the boundary conditions and continuity conditions. The two research methods not only simplify the complicated engineering problems, but also reflect the in-plan free vibration characteristics which the three kinds of arch bridges and cable-stayed beam should have in real project. The finally parametric analyses can provide some references for the constructions of the three kinds of arch bridges and cable-stayed beam.