Vibration of a U-Bar in Its Plane

Abstract

The vibration of a U-bar which occurs in its plane is studied. The U-bar consists of a circular are bar and two straight bars or of three straight bars. The ends of U-bar are built in and the material and the sectional dimensions of two legs are homogeneous and uniform respectively. The frequency equations and the boundary values are obtained by minimizing the Lagrangian. The frequencies of U-bar are calculated and shown graphically. The experiments are carried out and their results are compared with the theoretical ones.