Vibrations or a Connecting System of Curved Bar : Out-of-plane

Abstract

In this paper, we express the Lagrangian of out-of-plane vibrations of a uniform curved bar of which the center line is a plane curve by unknown boundary values, that is, displacements and slopes at boundary. And by using the Lagrangian, we show a method for analyzing rigorously out-of-plane vibrations of a system connecting uniform curved bars. As examples, we analyze the vibrations of a symmetric U-bar with built-in ends composed of an elliptic arc bar and straight bars and those of a catenary curved bar and straight bars and we obtain the natural frequencies and the mode shapes.