自然弯曲梁结构的动力分析

A Dynamic Analysis of the Natural Curved Slender Beams

应用拉氏乘子法，建立了一端固定、一端自由的自然弯曲细长梁动力分析的广义泛函。由泛函驻值条件导出曲梁关于位移的动力学方程、固定边界上的位移边界条件和自由边界上力的边界。上述方法还可推广到完全约束边界及其它各种不完全约束边界的情况。对于非保守体系和地下拱形结构的情况也作了考虑。

The Lagrange's multiplier method is applied in this paper to set up a generalized function of dynamic analysis of the natural curved slender beams which have one built-in end and one free end. Through this functional stationary value condition, the dynamic equations about of the curved beams and the displacement boundary conditions in the built-in end as well as the force conditions in the free end can be obtained. The above-mentioned method can also be generalized to complete constrained boundary and other various incomplete constrained boundaries. Lastly, attention has also been paid to the non-conservative system and underground arched structures.