稳定型悬索桥的非线性力学特性研究

The stable type suspension bridge is a new structure that is especially suitable for using in mountainous westward. And the research group， where the applicant is located， has investigated the stable type suspension bridge using finite element analysis and model experiment since twenty years ago. This project is confined to research the static and dynamic mechanical behavior of the structure by a mathematical model. In this project, the new equation of bending vibration is obtained by the Hamilton principle with constraint multiplier; the static bending of the structure is researched using the improved two-step perturbation method; and the partial differential equation is reduced by the direct multi-scale method; afterwards the nonlinear oscillations are investigated through the bifurcation theory of the ordinary differential equations; finally, the experiment research are performed by a 1:15 model of 120m span stable type suspension bridge. The following objectives are approached. (1) The partial differential equations for the structure transverse bending vibration are derived. (2) The static mechanical properties and dynamics are researched by the approximate analytical solutions and bifurcation theory, in order that clarify the inverse-tensional cables influence on the structure. (3) The mathematical model is checked by model experiment. (4) The simple design formulas of the static and dynamic analysis are proposed that may be available at plan design phase for the medium and small stable type suspension bridge (span of less than 300 meters).

稳定型悬索桥是特别适合西部山区使用的新型结构。申请人所在课题组使用有限元和模型实验对稳定型悬索桥进行了二十多年的研究。本项目将通过数学模型来研究该结构的静力及动力学行为。申请人拟通过带约束乘子的Hamilton原理建立稳定型悬索桥弯曲振动的数学模型；改进二次摄动法来研究结构的静力学特性；应用直接多尺度方法对偏微分方程进行降维，之后用常微分方程的分岔理论来研究结构的非线性动力学行为；并以120米跨的1:15模型进行实验研究。拟达成如下研究目标：（1）建立稳定型悬索桥弯曲振动数学模型；（2）通过非线性方程的近似解析解和分岔理论研究结构的静力和非线性振动行为，弄清反张索对结构力学行为的影响。（3）通过模型实验来检验理论研究的主要结论；（4）提出中小型稳定型悬索桥（跨度小于300米）方案设计时进行静力及动力计算的简化公式。

经过四年工作，项目团队完成了立项时预期的绝大多数研究内容，取得了良好的成果。项目主要获得三方面成果：（1）建立了稳定型悬索桥的弯曲振动方程，并通过实验和理论系统的研究该结构的力学性质。研究表明，稳定型悬索桥不但在小型桥梁中比普通悬索桥更具有稳定性优势，而且在大型桥梁中同样具有稳定性优势；（2）发现教科书中经典的悬索桥弯曲运动模型的缺陷，并对该模型进行了改进；（3）澄清了轻型悬索桥，刚度扰动对结构气动不稳定影响的机制。项目执行期间共计发表期刊论文9篇，其中SCI论文三篇（包括国际著名SCI一区期刊Nonlinear Dynamics论文1篇）。项目资助培养硕士研究生14名，其中4名已经毕业。