Out-of-plane Vibrations of Curved Bars with Varying Cross-section

Abstract

In this paper, the out-of-plane free vibrations of a curved bar of which the cross-section varies are analyzed by using the classical theory. The equations of vibration and the boundary conditions are determined from the stationary conditions of the Lagrangian of the bar in a period of vibration. The equations of vibration are solved exactly in a series solution. As numerical examples, the natural frequencies and the mode shapes of symmetric elliptic arc bars with both clamped ends and with both simply supported ends are obtained. And the variations of the natural frequencies and the mode shapes for various cross-sections are investigated.