Free Vibrations of Symmetric Arch: Boundary Conditions of Stress Resultants Revisited

Abstract

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.