Natural modes of Bernoulli-Euler beams with a single-edge crack

Mo How H. Shen, Christophe Pierre

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations

Abstract

The equation of motion and associated boundary conditions are derived for a uniform Bernoulli-Euler beam containing one single-edge crack. The main idea is to use a generalized variational principle that allows for modified stress, strain, and displacement fields that enable one to satisfy the compatibility requirements in the vicinity of the crack. The concentration in stress is represented by introducing a crack function into the beam's compatibility relations. A displacement function is also introduced to modify the in-plane displacement and its slope near the crack. Both functions are chosen to have their maximum value at the cracked section and to decay exponentially along the beam's longitudinal direction. The rate of exponential decay is evaluated from finite element calculations. The resulting equation of motion is solved for simply supported and cantilevered beams with single-edge cracks by a Galerkin and a local Ritz procedure, respectively. These theoretical natural frequencies and mode shapes are confirmed by comparisons with experimental and finite element results, and in both cases a close match is obtained. The possibility of determining the cracked beams' damage properties from the changes of its dynamic behavior is discussed.

Original languageEnglish
Pages (from-to)2079-2093
Number of pages15
JournalCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
Issue numberpt 4
StatePublished - 1990
Event31st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Part 3 (of 4): Structural Dynamics I - Long Beach, CA, USA
Duration: 2 Apr 19904 Apr 1990

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