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目前用能量法求拱的自振频率一般采用了轴向不伸长的假定,忽视了拱的变形的一个方面,并只限于求一个自振频率。本文根据能量原理,在同时考虑弯曲变形和轴向变形的情况下建立了求解平面拱有限个自振频率的公式,介绍了求解方法,并讨论了用能量法求解拱的自振频率时位移函数选择的原则。通过对反对称第一振型频率计算和分析,对目前拱的频率近似计算中存在的问题进行了讨论和评述。
At present, the frequency of self-vibration using energy method generally adopts the assumption of non-elongation in the axial direction, ignoring one aspect of the deformation of the arch and is limited to finding a natural frequency. In this paper, based on the energy principle, the formulas for solving the finite natural frequencies of planar arch are established considering both the bending deformation and the axial deformation. The solving method is introduced and the displacement function when the natural frequency of the arch is solved by energy method The principle of choice. Through the calculation and analysis of the first symmetrical anti-symmetric frequency, the problems existing in the approximate calculation of the frequency of the arch are discussed and discussed.