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Fourier Analysis of Mode Shapes of Damaged Beams

Kanchi Venkatesulu Reddy1, Ranjan Ganguli2

Graduate Student, Dept. of Aerospace Engg., Indian Institute of Science, Bangalore 560012, India.
Asst. Professor (, corresponding author, Dept. of Aerospace Engg., Indian Institute of Science, Bangalore 560012, India.

Computers, Materials & Continua 2007, 5(2), 79-98.


This paper investigates the effect of damage on beams with fixed boundary conditions using Fourier analysis of the mode shapes in spatial domain. A finite element model is used to obtain the mode shapes of a damaged fixed-fixed beam. Then the damaged beams are studied using a spatial Fourier analysis. This approach contrasts with the typical time domain application of Fourier analysis for vibration problems. It is found that damage causes considerable change in the Fourier coefficients of the mode shapes. The Fourier coefficients, especially the higher harmonics, are found to be sensitive to both damage size and location and amplify the changes in the mode shape due to the damage. Therefore, we formulate a damage index in the form of a vector of Fourier coefficients which is robust and unique for a given damage size and damage location. The effect of noise in the mode shape data is considered and it is found that Fourier coefficients provide a useful indication of damage even in the presence of noise. Various damage levels are considered and it is found that higher modes are needed to detect small amount of damage.


Cite This Article

K. V. . Reddy and R. . Ganguli, "Fourier analysis of mode shapes of damaged beams," Computers, Materials & Continua, vol. 5, no.2, pp. 79–98, 2007.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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