About the calculus of the relative frequency shifts for a beam with multiple cracks

Author:

Gillich G R,Nedelcu D,Hamat C O,Wahab M Abdel,Barbinta C I

Abstract

Abstract We propose in this paper a mathematical relationship to calculate the natural frequency shifts of beams due to multiple cracks. The relationship is based on the application of the superposition principle. A crack alters the frequencies for the bending vibration modes in a particular manner, with respect to the crack depth and location. We have shown that the affected beam have the same natural frequencies as a healthy beam with a smaller thickness; this thickness has to be calculated separately for each vibration mode. As a consequence, we can consider the next crack affects healthy beams, one different beam for each considered mode. Subsequent cracks affect a bigger number of beams. For the last crack, we have to calculate the frequencies for a number of beams that is the number of the considered vibration modes to the power equal with the number of cracks. To automate the process of calculating the resulted natural frequencies, we have written a program in Visual Basic for Excel Applications (VBEA), which permits finding the natural frequencies of a beam with up to nine cracks. This application can calculate the natural frequencies for four beam types: with fixed-free, fixed-fixed, simply supported and free-free restraints. The results obtained by calculating the frequencies for several damage scenarios and boundary conditions fit those obtained from simulations by involving the finite element method.

Publisher

IOP Publishing

Subject

General Physics and Astronomy

Reference27 articles.

1. Assessing multiple cracks in beams by a method based on the damage location coefficients;Gillich;Vibroengineering PROCEDIA,2019

2. Vibration-based multi-site damage precise localization via the Functional Model Based Method;Sakaris;Procedia engineering,2017

3. Natural frequencies of damaged beams - a new approach;Gillich;Romanian Journal of Acoustics and Vibration,2012

4. Damage detection and localization in composite beam structures based on vibration analysis;Khatir;Mechanics,2015

5. The influence of transversal crack geometry on the frequency changes of beams;Gillich,2014

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