Rayleigh's quotient for multiple cracked beam and application

Nguyen Tien Khiem, Tran Thanh Hai
Author affiliations

Authors

  • Nguyen Tien Khiem Institute of Mechanics, VAST
  • Tran Thanh Hai Institute of Mechanics, VAST

DOI:

https://doi.org/10.15625/0866-7136/33/1/34

Keywords:

natural frequencies, multiple cracked beam, Rayleigh's quotient

Abstract

Rayleigh's quotient for Euler-Bernoulli multiple cracked beam with different boundary conditions has been derived from the governed equation of free vibration. An appropriate choosing of approximate shape function in terms of mode shape of uncracked beam and specific functions satisfying conditions at cracks and boundaries leads to an explicit expression of natural frequencies through crack parameters that can simplify not only the analysis of natural frequencies of cracked beam but also the crack detection problem. Numerical analysis of natural frequencies of the cracked beam by using the obtained expression in comparison with the well-known methods such as the characteristic equation and finite element method shows their good agreement. The analytical expression of natural frequencies applied to the crack detection problem allows the result of detection to be improved.

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Published

30-03-2011

Issue

Section

Research Article