Temperature Effects On Modeling And Vibration Properties Of Cable-stayed Structures

The stiffening girder, the cable system and the cable supported tower are the three important parts of the long-span cable-stayed bridge. On the one hand, the loads on the cable-stayed bridge are very complex, such as: vehicle, earthquake, pedestrian, wind and temperature effects; on the other hand, as the application of the new materials and the development of the construction techniques and mechanics, the span of the cable-stayed bridge is growing constantly, and it is used more and more widely.When the environment temperature changes, every part of the cable-stayed bridge will be contracted or expanded with the increase or decrease of the temperature. There are some mutual constraints between the different parts of the structure, so the expansion and contraction of these structures will be restrained under the temperature effects, more or less, resulting in the generation of the thermal stress. Under the influence of the thermal stress, the dynamics of every part of the structure will be changed accordingly, resulting in the changes of the overall dynamics of the cable-stayed bridge. The results of the previous research show that: the changes in the structure vibration characteristics due to the changes in the temperature may be more apparent than the ones due to the structural damage and the external loads. Therefore, the studies of the effects of the temperature changes on the linear and nonlinear oscillations of the cable-stayed bridge and its basic structures are very important from the quantitative and qualitative analysis.Based on the previous studies on the topic, the main works in this dissertation are as follows:(1) The homotopy analysis method is introduced to solve the nonlinear vibration equations of the suspended cable, and the method is independent of the small parameter assumption and the convergence of the solutions is ensured by introducing an auxiliary parameter. Taking the suspended cable as an example, this section compared and analyzed the differences in the results of the free vibration and primary resonances of the suspended cable which are obtained by the Lindstedt-Poincare method, Multiple scales method and Homotopy analysis method, and some relevant results lay the foundation for solving the nonlinear equations in the next few chapters. The results show that no matter the sag-to-span ratio and the vibration amplitude are large or small, the vibration characteristics of the system could be described very well by the low order solutions of the homotopy analysis method. Different displacement fields curves and the axial tension force curves might be obtained by different analytical methods;(2) By introducing the thermally stressed equilibrium state of the suspended cable, the temperature effects on the static mechanics are investigated and the nonlinear vibration equations of the cable which take the temperature effects into consideration are derived. Then, the homotopy analysis method is introduced to solve the relevant equations, and the temperature effects on the linear and nonlinear dynamics of the suspended cable are illustrated by the numerical solutions. The results show that: the temperature effects affect the linear and nonlinear vibration properties of the suspended cable, and the effects of the warming and cooling on the linear and nonlinear vibration properties of the suspended cable which have the same absolute value are not symmetric;(3) By using the direct force method, the temperature effects on the static mechanics of the stayed-cable are investigated, and the nonlinear vibration equations of the stayed cable under the excitation of the moving end are derived. By using the mathematical software, the fourth-order discretized equations are solved, and the temperature effects on the nonlinear vibration equations of the cable are illustrated by using the amplitude frequency response curves. Moreover, the relevant conclusions are also obtained by the finite element soltuions. The research shows that: the temperature effects would affect the resonance response and energy transfer process of the system;(4) By introducing the temperature changes in the stress-strain relationship, the nonlinear vibration equations of the beam which based on the Hamilton’s variation principle under the axial force are derived. Three types of boundary conditions are also considered, and the linear equations are analyzed. Moreover, the relevant conclusions are verified by the finite element software. Then, the nonlinear equations are solved by the Galerkin discretization, and the homotopy analysis method is applied to analyze and discuss the temperature effects on the nonlinear vibrations properties of the beam. It shows that the temperature effects have significant influence on the vibration properties of the beam, and the influence is related with the boundary conditions. Moreover, the effects of the warming and cooling on the vibration properties of the beam which have the same absolute value are not symmetric;(5) Using the Hamilton’s variation principle, introducing the effects of the static configuration of the system and combing the coupling connection conditions and boundary conditions, the model of cable-stayed beam is re-established. Considering the temperature effects and conclusions on the cable and beam in the previous chapters, the previous obtained equations of the cable-stayed beam are updated by considering the temperature effects. Then, the numerical results show the temperature effects on the mode frequencies and shapes of the cable-stayed beam. The results show that the effects of the temperature changes on the vibration frequencies of the cable-stayed beam are related with the stiffness ratio between the beam and cable and the order of the frequency.