单层索网体系非线性自振特性研究

刚性结构通常采用“Rayleigh法”的线性化方法近似计算结构的基频，但是单层索网体系属于非线性预应力体系，其自振频率会随着振幅发生变化。通过分析结果表明，当节点质量较大时，用假定惯性荷载的方法计算的误差较大；“Rayleigh法”计算索网频率是基于微幅振动的假定，不能反映其振幅较大时的自振特性。本文采用连续化理论，推导了单层索网体系第一、二阶非线性自振频率近似公式，并将计算结果和瞬态分析结果进行对比，两者吻合较好。非线性自振特性的研究对于单层索网体系在风荷载作用下的响应分析具有十分重要的意义。

Analysis on nonlinear natural frequencies of cable net

Cable net system for supporting glass facade is gaining more and more popularity in recent years, because of the merits of excellent transparency, light weight, etc, while the research on its vibration characteristic is essential at present. The fundamental frequency of an ordinary structure is conventionally calculated by Rayleigh method which is actually a linear approximate one. However monolayer cable net belongs to the system of a nonlinear prestressed structure, which is different from conventional structures, and its frequencies vary with the amplitude of vibration. It is shown that the Rayleigh approach by using inertial loads leads to relatively large deviation for the cable nets of lumped-mass systems with heavy nodal mass. On the other hand, this method is based on the assumption of a small vibration amplitude, which can not reflect the characteristic of large amplitude. The explicit formulas for the first two nonlinear frequencies of cable net are derived by assuming the net as a continuum membrane. The comparison of the results through the formulas and those from nonlinear transient analysis demonstrates a good consistency. The research on nonlinear vibration property is of vital importance for further investigation on the wind-induced responses of cable net for supporting glass facade.