Free Vibrations of L-Bar : Both Ends Built-in

Abstract

The free vibrations of a bar bent to L-type (both ends built-in) are discussed. The method used is to minimize Lagrangian which is expressed in terms of the unknown functions and the known and unknown boundary values which describe the vibrations. In the case when there are lateral, twisting and longitudinal vibrations at the same time, the vibratory functions are obtained in general forms, and Lagrangian is expressed in terms of the boundary values. Using the known boundary conditions and the conditions of continuity, Lagrangian is expressed in terms of unknown constants. Then, Lagrangian is again minimized about the unknown constants and these constants and the frequency equations are obtained. In the case of an L-bar, the frequency equations of both vibrations in the plane of L-bar and perpendicular to that plane are obtained and the numerical calculations are carried out, and the comparison with the contents of papers already published is made.