This paper deals with analyzing free vibrations of the symmetric arch. The boundary conditions of the stress resultants are newly derived, which can be replaced by the conventional boundary conditions of the deflections. All solutions of the natural frequency with the mode shape, using the new boundary conditions, are the same as those of the conventional deflections. The boundary conditions mixed with new and conventional conditions act correctly to calculate natural frequencies. The mode shapes of the stress resultants using the new boundary conditions are reported in two types: symmetric and anti-symmetric modes.

中文翻译：

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对称拱门的自由振动：重新审视应力合力的边界条件

本文涉及分析对称拱的自由振动。新推导了应力合力的边界条件，可以用传统的挠度边界条件代替。所有具有振型的固有频率解，使用新的边界条件，都与常规挠度的解相同。边界条件与新的和常规条件相结合，可以正确计算固有频率。使用新边界条件的应力合成模态以两种类型报告：对称模态和反对称模态。