Lateral Vibrations of L-bar : Built-in-Free

Abstract

The author has studied the lateral vibration of an L-bar with one end built-in and the other free. Two kinds of vibration can be considered, viz., the vibration perpendicular to the plane of the L-bar (including a twisting vibration), and the vibration in the plane (including a longitudinal one). To find the frequency equations, we give some unknown constants to the boundary values, and determine such vibration function and unknown constants as to minimize the Lagrangian. The results are given by the nondimensional frequencies in the table and diagrams. Further, in this paper, the author compared these experimental data with the Rayleigh method and strict solutions, and explained the combined vibrations caused by the inter-relation of some ratios and angles between the legs of the L-bar.