Out-plane Vibrations of Curved Bars Considering Shear Deformation and Rotatory Inertia

Abstract

In this paper, we show a method for solving the free out-plane vibrations of a uniform curved bar of which the center line is a plane curve considering the effects of the bending, the torsion, the shear deformation and the rotatory inertia of the bar. We solve the equations of vibration exactly by a series solution. As numerical examples, we obtain natural frequencies and mode shapes of symmetric catenary, parabola and cycloid curved bars with clamped ends. The numerical results by the present analysis are compared with the ones by the classical theory and the effects of the shear deformation and the rotatory inertia are clarified.