弹性支撑拱结构的动力特性研究
Study on Dynamic Characteristics of Elastic Supported Arch Structures

以三次B样条函数的线性组合作为拱结构位移振型函数，根据哈密顿原理推导出了弹性支撑拱结构的频率方程，考虑了拱脚处集中质量的附加惯性力等因素的影响，计算分析了竖向弹性支撑和旋转弹性支撑对拱结构动力特性的影响，提出了竖向临界刚度系数的概念。研究结果表明：竖向弹性支撑会使拱结构的基本频率减小，当矢跨比为0.1左右时影响最为显著，同时还会改变拱结构振型序列特点；竖向临界刚度系数是拱结构动力特性的分界点，此时拱结构的基本频率和第二频率几乎相等，若竖向支撑刚度系数小于临界刚度系数，结构的第1阶振型是对称的，而第2阶振型是反对称的，与刚性支撑拱结构的振型序列不同；若竖向支撑刚度系数大于临界刚度系数，结构的第1阶振型是反对称的，而第2阶振型是对称的，与刚性支撑拱结构的振型序列相同；旋转弹性支撑会使拱结构的基本频率减小，但并不改变其振型序列特点。
The displacement mode shape function of the arch free vibration was simulated with a linear combination of cubic B？？spline. The vibration frequency equation of the elastic supported arch structures was derived according to Hamilton principle, in which the additional inertia force of the lumped mass at the arch foot was taken into account. The influences of the vertical and rotational elastic supports on the dynamic characteristics of arch structure were studied. The concept of the vertical critical stiffness coefficient was put forward. The study results show that the vertical elastic supports decrease the natural frequency, and the influence is biggest when the rise？？span ratio is about 0.1. Meanwhile, the vibration mode sequence characteristics change. As the stiffness of the vertical elastic supports is same with the vertical critical stiffness coefficient, the natural frequency and the second frequency is almost equal. If the vertical support stiffness coefficient is less than the critical stiffness coefficient, the first vibration mode of structure is symmetrical, and the second vibration mode is antisymmetric. The vibration mode sequence characteristics are different from those of the arch with rigid supports. If the vertical support stiffness coefficient is greater than the critical stiffness coefficient, the first vibration mode is antisymmetric, while the second vibration mode is symmetrical. The vibration mode sequence characteristics are same with those of the arch with rigid supports. The rotational elastic supports will decrease the natural frequency of the arch structure, but will not change its vibration mode sequence characteristics