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根据弹性体系动力稳定理论,采用能量法和Hamilton原理,分别建立了高温(火灾)环境中缀条式和缀板式格构柱在轴向周期荷载作用下的动力偏微分方程。利用Galerkin方法将其转化为二阶常微分Mathieu型参数振动方程,求得周期解所包围的动力不稳定区域。通过分析长细比、恒载、温度等参数对轴心受压格构柱动力不稳定区域的影响,探讨了两种格构柱发生参数振动的动力稳定性问题,为高温环境下结构工程动力分析与设计提供参考依据。
According to the theory of dynamic stability of elastic system, the dynamic partial differential equations under the action of axial periodic load are established respectively by energy method and Hamilton principle, under the environment of high temperature (fire). The Galerkin method was used to convert it into the second-order differential equation of ordinary differential equations with Mathieu-type parameters. The dynamic instability region surrounded by periodic solutions was obtained. By analyzing the effects of slenderness ratio, dead load, temperature and other parameters on the dynamic instability region of the lattice columns subjected to axial compression, the dynamic stability of parametric vibration of two kinds of lattice columns is discussed. Analysis and design provide a reference.