单层平面索网结构非线性频率简化计算方法研究

单层平面索网玻璃幕墙结构是广泛应用于大型公共建筑中的一种新型结构形式,由于其挠度较大,结构具有较高的几何非线性,其动力特点不同于传统的线性结构。采用连续化薄膜理论建立了单索幕墙的非线性振动方程,并采用谐波平衡法求解了结构非线性频率的解析表达式,为校核解析公式的正确性,将其计算结果同精确的有限元非线性时程方法的计算结果进行了比较,吻合很好,该解析公式具有相当高的精度。同时指出结构位移为3/2结构振幅位置处的刚度即为单索幕墙结构的等效线性刚度,采用该等效线性刚度即可得到上述非线性频率的解析表达式。此外得到的结构非线性振动方程和非线性频率为结构在动力荷载下响应的求解提供了基础。

STUDY ON SIMPLIFIED CALCULATION METHOD OF NONLINEAR FREQUENCY OF SINGLE-LAYER CABLE NET

Glass curtain wall construction with single-layer cable net is widely adopted structural form in nowadays Chinese public great buildings. Because of its large deflection and high nonlinearity, the dynamic performance of cable net is greatly different from that of the conventional linear structures. The continuous membrane theory was used to formulate the nonlinear vibration differential equation of cable net, and harmonic balance method was used to solve the analytic formula of the nonlinear frequency. In order to verify the above analytic formula, its analytical results were compared with those of the precise nonlinear FEM time-history method. The comparison tells us that the two sorts of results have good accordance. It implies that the analytic formula has high precision. At the same time, it is pointed out that when the structural displacement is 3 /2of the amplitude of vibration, the stiffness of cable net is the equivalent linearized stiffness based on the equivalent energy, and the above nonlinear frequency analytic formula can be obtained by equivalent linearized stiffness. Furthermore, the nonlinear vibration differential equation and nonlinear frequency gained by the study is the basement of the response analysis of cable net under dynamic load.