竖向基础激励下圆弧拱动内力分析

Dynanic Internal Force Analysis of Circular Arch Under Vertical Base Excitation

文中以竖向基础激励下两端固接圆弧拱为研究对象,运用能量法与哈密顿原理推导了圆弧拱的运动方程,分析了圆弧拱动轴力与动弯矩随圆心角和长细比的变化规律,并用有限元软件建立了数值分析模型,验证了理论解析解的正确性。结果表明,大长细比圆弧拱的动轴力随着圆心角的增加先逐渐增加,然后逐渐减小;对于小长细比的圆弧拱,其无量纲动轴力随着圆心角的增加而增加。大长细比圆弧拱的无量纲动弯矩随圆心角的增加而增加,并在较小的圆心角处达到一个峰值,然后随着圆心角的增加,无量纲动弯矩先减小后增加;对于小长细比的圆弧拱,其无量纲动弯矩随着圆心角的增加而逐渐增加。

This paper takes the fix-ended arch under vertical base excitation as the research object,deduces the motion equation of the arch with the energy method and Hamilton principle,analyzes the variation law of the dynamic axial force and bending moment of the arch with the included angle and rise-span ratio,and establishes a numerical analysis model with finite element software to verify the correctness of the theoretical analytical solution.The results show that the dynamic axial force of the large slenderness ratio of the circular arch first gradually increases with the increase of the central Angle,and then gradually decreases.For an arch with a small slenderness ratio,the dimensionless dynamic axial force increases with the increase of the included angle.The dimensionless dynamic bending moment of an arch with a large slenderness ratio increases with the increase of the included angle,and reaches a peak value at the smaller included angle.For the arch with small slenderness ratio,the dimensionless dynamic bending moment increases gradually with the increase of the included angle.