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A continuous vibration theory for beams with a vertical edge crack. (English) Zbl 1197.74062

Summary: In this paper, a continuous model for exural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement eld is a superposition of the classical Euler-Bernoulli beam’s displacement and of a displacement due to the crack. The additional displacement is assumed to be a product between a function of time and an exponential function of space. The unknown functions and parameters are determined based on the zero stress conditions at the crack faces and the concept of \(J\)-integral from fracture mechanics. The governing equation of motion for the beam has been obtained using the Hamilton principle and solved using a modi ed Galerkin method. The results have been compared with nite element results and an excellent agreement is observed.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
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