点支式玻璃幕墙索桁架支承体系非线性振动

NONLINEAR VIBRATION OF CABLE TRUSS SUPPORT SYSTEM IN POINT-SUPPORTED GLASS CURTAIN WALL

考虑温度变化及几何非线性影响,采用连续化理论导出点支式玻璃幕墙预应力自平衡索桁架支承体系非线性振动方程。通过Galerkin方法,将偏微分方程转化为常微分方程,并采用Lindstedt-Poincaré(L-P)法对常微分方程进行求解。结合工程实例讨论分析温度变化、振幅、初始张力、矢高等因素对点支式玻璃幕墙预应力自平衡索桁架支承体系非线性振动的影响。算例表明,预应力自平衡索桁架支承体系固有频率随着温度的升高而减小,具有较强的非线性,其自振频率随着振幅发生变化,其非线性振动呈现"硬弹簧"特性,非线性自振频率高于线性振动频率。

Taking the temperature effect and geometric nonlinearity into consideration,the nonlinear vibration equation of prestressed self-balanced cable truss support system in point-supported glass curtain wall was derived by assuming the support system as a continuum membra.By the Galerkin method,the partial differential equation was transformed into ordinary differential equation which was solved with Lindstedt-Poincaré（L-P） method.The effects of temperature,amplitude,initial tension and vector height on the nonlinear vibration were discussed with the engineering example.The result indicates that frequency of self-balanced cable truss support system will decreases,which resulted in the increases of temperature,the vibration of self-balanced cable truss support system belongs to the nonlinear system,which is different from conventional structures,and its frequencies vary with the amplitude of vibration,which shows hard spring characteristic,its nonlinear vibration frequency is higher than linear vibration frequency.