Lowest Symmetrical and Antisymmetrical Natural Frequency Equations of Shallow Arches on Elastic Foundations

탄성지반 위에 놓인 낮은 아치의 최저차 대칭 및 역대칭 고유진동수 방정식(구조 및 재료 \circled1)

This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations are assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Sinusoidal arches with hinged-hinged and clamped-clamped end constraints are considered in analysis. The frequency equations (lowest symmetical and antisymmetrical natural frequency equations) are obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated.