固接抛物线浅拱的平面内稳定性分析

In-plane stability of shallow fixed parabolic arches

对固接抛物线浅拱的静力及动力稳定性问题进行了研究.基于哈密尔顿原理推导出抛物线浅拱的动力学控制方程,并推得非线性静力平衡方程及静力跃越和分岔屈曲的解析方程;利用体系不稳定平衡时的能量守恒原理确立了发生动力屈曲的临界条件并得到动力屈曲相对荷载上限及下限值.分析结果表明:浅拱的修正长细比及结构已存在荷载是影响浅拱屈曲的重要参数,阶跃荷载作用下浅拱的静力及动力屈曲相对荷载随着长细比的增加而增加,而动力屈曲荷载随结构已存在荷载的增大而减小;当稳定平衡时系统势能大于零,浅拱的动力屈曲荷载将显著提高.

In-plane static and dynamic buckling of fixed parabolic arches is concerned. The equa- tions of motion are derived from Hamilton＇s principle, and the nonlinear equilibrium equations and static buckling equilibrium equations are deduced for shallow parabolic arches. The law of conserva- tion of energy is used along the unstable equilibrium paths to establish the criterion for dynamic buck- ling of shallow arches, and analytical solutions for the lower and upper dimensionless dynamic buck- ling loads of arches under the step load are obtained. It is found that modified slenderness ratio and the pre-applied static load are important parameters affecting the buckling of shallow arches, and that the static and dimensionless dynamic buckling loads increase with an increase of modified slenderness ratio. It is also shown that dynamic buckling loads are reduced by raising pre-applied static loads. The dynamic buckling loads will be significantly improved when the system potential energy along the stable equilibrium path are positive.