Development of a Wittrick–Williams algorithm for the spectral element model of elastic–piezoelectric two-layer active beams |
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Authors: | Usik Lee Joohong Kim Jinho Shin A Y T Leung |
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Affiliation: | a Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-ku, Inchon 402-751, South Korea b Division of Mechanical Engineering, University of Manchester, Manchester M13 9PL, UK |
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Abstract: | In this paper, a Wittrick–Williams algorithm is developed for the elastic–piezoelectric two-layer active beams. The exact dynamic stiffness matrix (or spectral element matrix) is used for the development. This algorithm may help calculate all the required natural frequencies, which lie below any chosen frequency, without the possibility of missing any due to close grouping or due to the sign change of the determinant of spectral element matrix via infinity instead of via zero. The uniform and partially patched active beams are considered as the illustrative examples to confirm the present algorithm. |
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Keywords: | Wittrick– Williams algorithm Spectral element model Two-layer active beam Natural frequency |
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