Study on Parametric Vibration and Mode Jumping of Long-span Cable-stayed Spatial Grid Structure Under Wind Load
|School||Harbin Institute of Technology|
|Keywords||cable-stayed spatial grid structure close mode parametric vibration mode jumping perturbation|
Long span cable-stayed spatial grid structure, one of the rigid and flexible structures, has being used widely in the past few decades. However, this type of long span structure, particularly the cable elements in the structure, is usually flexible and can easily oscillate, under environmental and service loads. Dynamic characteristics of the structure also become more complex, this is manifested remarkably in the following ways: the structure vibrates with clear geometrical nonlinearity under the wind load and accompanies with the phenomenon of the parametric vibration of the cable, the parametric vibration would change the effects of the elastic support of the cable to the grid structure. The changes can lead to the happening of the phenomenon of mode jumping. Among the above outstanding problems, the issue of the parametric vibration of the cable has attracted many a researcher to try to address it for a long period of time; those previous studies have more or less limitations. Among the parametric vibration model in those previous researches, most of them are single-cable element models or the coupling model of cable-bridge or pylon-cable only, and most of these studies are carried out by means of analytical and numerical methods. The results are lack of relative experimental verification, especially shortage of experimental research of the coupled model of the parametric vibration. For the characteristic of the time-varying stiffness matrix of the roof structure and the phenomenon of the mode jumping caused by the parametric vibration of the cable, there are still no correlative literatures.Therefore, different from the previous literatures for a single issue with a single method, this paper presents a three-degree-of-freedom (3-DOF) model simplified from long span cable-stayed structure in consideration of interactions between pylons, cables and space structure, in order to investigate the parametric vibration of the inclined cable and the mode jumping in the cable-stayed structure. The numerical analysis, experimental study and finite element simulation are used in this study. The main contents of the study include the following several respects:(1) Research on wind-induced response of the long span cable-stayed spatial grid structureThis paper concerns with the wind-induced response of the long span cable-stayed spatial grid structure primarily, and the primary task is to implement the simulation of the wind velocity. Linear autoregressive model is proposed to simulate the wind velocity. The difficulties and issues of the simulation which affect the accuracy and reliability of the algorithms are focused on remarkably, whose computing programs are implemented in MATLAB. After gaining the wind load, the precise integration method is introduced to solve the nonlinear dynamic response equation.(2) Numerical study on the parametric vibration of the long span cable-stayed spatial grid structureBecause of the vibration forms of the pylon, cable and grid structure influence each other during themselves vibration process, this paper uses the spring elements with a certain mass, stiffness and damping to simulate the vibration of the top of the pylon, uses a cantilever element to stimulate the roof structure, to establish the refined vibration model of the spring cable-stayed cantilever beam structure. The coupling equations of motion are derived for the 3-DOF model. The adaptive Runge-Kutta algorithm is adopted to solve the coupling equations whose computing programs are implemented in MATLAB. Then it focuses on studying influence factors and its various effects on the parametric vibration based on the characteristics of the non-linear dynamic responses. According to the Galerkin Principle, this study defines modal influence coefficient to study the affect of higher order mode shapes to the analysis of the parametric vibration of the cable itself.(3) Model test study on the parametric vibration of the long span cable-stayed spatial grid structureAccording to the refined model mentioned in the second part, a spring-cable- cantilever beam model is designed and constructed to study the possibility of the occurrence and the phenomena of the parametric vibration in the actual physical model. Another aim of the test is to verify the numerical results of the characteristics of the parametric vibration and the rules of the effect of various influence factors. Further studies on the parametric vibration characteristics of multi-cable-stayed cantilever beam structure are carried out to compare with the results of the parametric vibration of single-cable-stayed cantilever beam structure, meanwhile, to validate the happening of the parametric vibration in the actual structure while the roof is stayed by multiple cables simultaneously.(4) Finite element simulation of the parametric vibration of the long span cable-stayed spatial grid structureAs the finite element simulation analysis plays a decisive role in the actual design of engineering structures, especially for the static and dynamic analysis of long span and complex structures. It has the feature of efficiency, repeatability and low cost. Therefore, this part of the paper discusses the related issues during the finite element modeling analysis of long span cable-stayed spatial grid structure. After that, a long span cable-stayed single scallop shell structure is taken as the example to analyze the possibility of occurrence of the parametric vibration emphatically. Finally, the finite element simulation analysis of the parametric vibration phenomena in the model test is carried out to analyze the rules of the influence factors of the parametric vibration.(5) Theoretical investigation into the mode jumping of the long span cable-stayed spatial grid structureAs the parametric vibration of the cable can change the boundary condition and stress condition of the grid structure and will lead to time-varying dynamic characteristics of the grid structure. This effect can also cause the happening of the mode jumping of the structure. Based on traditional matrix perturbation method, this study proposes a simplified perturbation method which can be used to analyze the mechanism of the mode jumping of the close low-frequency structure. The identification criterion of the frequency difference and its standard deviation is presented in this paper to resolve the issue of identification of close modes. The modal projection correlation difference is presented to resolve the issue of identification of modal correlations of close low-frequency structure while the phenomenon of the mode jumping occurred.