杆系结构在周期荷载下的自参数共振机制研究

The skeletal structures are often subjected to periodic loads (that are produced by water flows). When the frequency of periodic force has a certain coupled relation with the natural frequency of the skeletal structure or the sub-structure, a parametric (or auto-parametric) resonance of the structure will be aroused. This dynamic instability will bring a serious risk to the structure. Auto-parametric resonance of the skeletal structures has been seldom investigated, and the mechanism is not clear now. In this project, the equations of parametric vibration will be established for the general skeletal structures under the multi-points excitations. The unstable domains of auto-parametric vibration are investigated for the skeletal structures under multi-points excitations. The auto-parametric internal resonance and the corresponding instability regions are studied for these structures. The combined parametric resonance is investigated for these structures. Considering the effects of geometric nonlinearity, the nonlinear motion equations for parametric vibration of skeletal structures will also be established to numerically analyze the characteristics of steady-state parametric responses of the structure. The experimental approaches will be applied to investigate the instability mechanism of the skeletal structures under multi-excitations and to verify the theoretical predictions. The experimental methods will alos be applied to study the internal resonance and the response characteristics of parametric resonance. An analog approach is used to investigate the similarity between the parametric sloshing of fluid and the parametric vibration of structure, and thus the mechanism of parametric vibration of structures is indirectly revealed through the liquid parametric sloshing. The studies of this project will reveal the mechanism of auto-parametric resonances of the skeletal structures under periodic loads.

杆系结构常常受到（由于水流引起的）周期性荷载作用，当周期荷载的频率与杆系结构或局部子结构频率形成某种耦合关系时，可能诱发杆系结构的（自）参数共振，这种动力失稳将对结构安全构成严重威胁，目前关于杆系结构的自参数共振问题的研究还很不充分，其共振机制还不清楚。本项目将建立一般杆系在多点周期激励下的结构参数振动方程，分析多点激励下杆系结构的自参数不稳定区域；研究结构自参数内共振现象以及不稳定区域；研究杆系结构的组合参数共振问题；建立考虑几何非线性的杆系结构参数振动方程，分析杆系结构非线性稳态参数共振的响应特征；采用实验方法研究杆系结构在多点激励下的自参数振动失稳机制并验证理论结果；采用实验方法研究杆系结构的内共振现象以及参数共振的响应特征；采用比拟方法研究液体参数晃动与结构参数振动的相似性，通过液体的参数晃动来间接揭示结构的参数振动机制。本项目的研究拟揭示杆系结构在周期荷载作用下的自参数共振机制。

杆系结构常常受到（由于水流引起的）周期性荷载作用，当周期荷载的频率与杆系结构或局部子结构频率形成某种耦合关系时，可能诱发杆系结构的（自）参数共振，这种动力失稳将对结构安全构成严重威胁，目前关于杆系结构的自参数共振问题的研究还很不充分，其共振机制还不清楚。本项目建立了一般杆系结构（线性）参数振动方程，采用数值与试验方法研究了结构自参数内共振现象以及不稳定区域，揭示了结构自参数内共振的机制及潜在的危害； 采用理论与实验方法研究了杆系结构在多点激励下的自参数振动失稳机制，揭示了两点激励相位差对稳定边界的影响；首次提出了框架结构动态轴力传递系数的概念，基于动态轴力传递系数，提出了框架结构参数共振稳定性分析的简化计算方法，适合于复杂杆系结构的动力稳定分析；对三维空间结构自参数内共振的稳定性进行了数值模拟和试验研究，首次发现了结构的扭转动力失稳现象；采用向量结构力学的方法，首先建立考虑几何非线性的杆系结构参数振动方程及相应的数值计算格式，分析了杆系结构非线性稳态参数共振的响应特征，采用模型试验验证了数值理论结果，为杆系结构参数共振的大幅非线性分析提供了一个有力的分析工具；首次在波流水槽内研究了流激（涡振与尾流激振）自参数共振问题，试验揭示了流激参数共振的一些新现象。本项目研究从多角度、多层次揭示了杆系结构在周期荷载作用下的自参数共振机制。