Vibration of a Cracked Cantilever Beam

[+] Author and Article Information
T. G. Chondros

University of Patras, Greece

A. D. Dimarogonas

Washington University, St, Louis, Missouri

J. Vib. Acoust 120(3), 742-746 (Jul 01, 1998) (5 pages) doi:10.1115/1.2893892 History: Received August 01, 1996; Online February 26, 2008


A continuous cracked bar vibration model is developed for the lateral vibration of a cracked Euler-Bernoulli cantilevered beam with an edge crack. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions for the cracked beam as an one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations of an aluminum cantilever beam with a single-edge crack are presented: the continuous cracked beam vibration model, the lumped crack model vibration analysis, and experimental results. Experimental results fall very close to the values predicted by the continuous crack formulation. Moreover, the continuous cracked beam theory agrees better with the experimental results than the lumped crack flexibility theory.

Copyright © 1998 by The American Society of Mechanical Engineers
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