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Only recently the mode shape has been considered [10 14].
Mode shape has been widely applied in damage identification and localization for plate-like structures.
The location of the coupling with respect to the bending mode shape has a strong influence on the vibrations.
Hence, wavelet-transformed rotation mode shape has the potential to identify damages at any locations, which would not be possible by using only rotation mode shape alone.
It was found that the rotation of mode shape has the characteristic of localization at the damaged region even though the displacement modes are not localized.
The numerical results clarify that the rotation of mode shape has the characteristic of localization at the damaged region even though the displacement modes are not localized.
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To utilize the mode shape information in real systems, many measurement-based methods for estimating the mode shape have been proposed.
Eigenfrequency with mode shapes has shown to have significant influence on transmitting-receiving characteristics of pMUT.
A normalization scheme for complex mode shapes has also been developed.
For the satellite system considered here, the orthogonality calculation is highly sensitive to experimental errors, so a set of noisy mode shapes has a small probability of passing the orthogonality criteria for some of the TAMs.
First, the problem of natural frequencies and mode shapes has been approached by considering the Helmholtz equation in an elliptical domain, the solution of which can be expressed by means of Mathieu functions.
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