Free Vibration of Stepped Beams

The beams having steppedly varying cross section along the axis are practically used as structres and members of structures, and the behaviour of the continuously varying cross sectional beams can be known by analyzing the equivalent multistepped beams. From these viewpoints, the simple analysis for stepped beams must be established. In this paper, the free vibration of stepped beams is analyzed on the usual assumption of the continuity of forces at the stepped sections. The differential equation of free vibration of stepped beam is expressed by using the unit step function, so that we can easily obtain the general differential equation of stepped beam regardless of the number of the steps. Moreover, the frequency equations and mode equations of stepped beams are obtained generally regardless of the number of the steps and the boundary conditions, similarly to the uniforml beams