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Finite element method for the vibration of cracked beams with varying cross section
Author(s) -
Haskul Mehmet,
Kısa Murat
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510055
Subject(s) - structural engineering , finite element method , vibration , spring (device) , beam (structure) , stiffness , stiffness matrix , normal mode , cross section (physics) , flexibility method , massless particle , strain energy release rate , fracture mechanics , inverse , matrix (chemical analysis) , section (typography) , strain energy , natural frequency , materials science , physics , mathematics , engineering , geometry , acoustics , composite material , computer science , particle physics , quantum mechanics , operating system
Vibration analysis of cracked beams having linearly varying cross‐sections both in thickness and width was investigated. A computer program using the finite element method has been written to find the dynamical characteristics (natural frequencies and mode shapes) of the cracked beam. The cracked section in the beam has been modeled by a massless spring whose flexibility depens on the local flexibility induced by the crack. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expression. Some examples have been given to explain the proposed method and investigate the effects of the depth and location of cracks on the natural frequencies and mode shapes. The results of current study and those in the literature are compared and good agreements have been found. Consequently it is showed that proposed method is reliable and simple. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)