Browse > Article

Formulation of a Wittrick-Williams Algorithm for Computing Natural Frequencies of an Active Beam  

김주홍 (인하대학교 산업과학기술연구소)
이우식 (인하대학교 기계공학부)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.15, no.4, 2002 , pp. 579-589 More about this Journal
Abstract
In this paper, a Wittrick-Williams algorithm is developed for the spectral element model of an elastic-piezoelectric two-layer active beam. 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 abrupt sign changes of the determinant of spectral element matrix via infinity instead of via zero. A uniform active beam and a partially patched active beam are considered as the illustrative examples to confirm the present algorithm.
Keywords
Wittrick- William algorithm; spectral element model; active beam; natural frequency;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Leung, A. Y. T. and Zeng, S. P., 'Analytical Formulation of Dynamic Stiffness,' Journal of Sound and Vibration, Vol. 177, No. 4, 1994, pp.555-564   DOI   ScienceOn
2 Leung, A. Y. T., Dynamic Stiffness and Substructures, Springer-Verlag, London, 1993
3 Banerjee, J. R., 'Dynamic Stiffness Formulation for Structural Elements: A General Approach,'Computers & Structures, Vol. 63, No. 1, 1997, pp.101-103   DOI   ScienceOn
4 Lee, U. and Lee, J., 'Spectral-Element Method for Levy-Type Plates Subject to Dynamic Loads,'Journal of Engineering Mechanics, Vol. 125, No. 2, 1999, pp.243-247   DOI   ScienceOn
5 Liao, W. H., Active-Passive Hybrid Structural Control: An Enhanced Active Constrained Layer Damping Treatment with Edge Elements, Ph. D. Thesis, The Pennsylvania State University, PA, 1997
6 Williams, F. W. and Wittrick, W. H., 'Efficient Calculation of Natural Frequencies of Certain Marine Structures,' International Journal of Mechanical Sciences, Vol. 15, No. 10, pp.833-843   DOI   ScienceOn
7 Lee, U., Kim, J. and Leung, A. Y. T., 'Spectral Element Method in Structural Dynamics,' The Shock and Vibration Digest, Vol. 32, No. 6, 2000, pp.451-465   DOI   ScienceOn
8 Williams, F. W. and Wittrick, W. H., 'An Automatic Computational Procedure for Cal- culating Natural Frequencies of Skeletal Structures,' International Journal of Mecha- nical Sciences, Vol. 12, 1970, pp.781-791   DOI   ScienceOn
9 Pearson, D. and Wittrick, W. H., 'An Exact Solution for the Vibration of Helical Springs Using a Bernoulli-Euler Model,' International Journal of Mechanical Sciences, Vol. 28, No. 2, pp.83-96   DOI   ScienceOn
10 Lee, U. and Kim, J., 'Dynamics of Elastic-Piezoelectric Two-Layer Beams Using Spectral Element Method,' International Journal of Solids and Structures, Vol. 37, 2000, pp.4403 -4417   DOI   ScienceOn
11 Doyle, J. F., 'A Spectrally Formulated Finite Element for Longitudinal Wave Propagation,' International Journal of Analytical and Ex- perimental Modal Analysis, Vol. 3, 1988, pp. 1-5
12 Wittrick, W. H. and Williams, F. W., 'A General Algorithm for Computing Natural Frequencies of Elastic Structures,' Quarterly Journal of Mechanics and Applied Mathematics, Vol. 24, Part 3, 1971, pp.263-284   DOI
13 Strang, G., Linear Algebra and Its Applications, Academic Press, New York, 1980
14 Kim, M. C., Jung. H. J., Oh, J. W., and Lee, I. W., 'Solution of Eigenvalue Problems for Nonclassically Damped Systems with Multiple Frequencies,' Journal of the Computational Structural Engineering Institute of Korea, Vol. 11, No. 1, 1998, pp.205-216
15 Doyle, J. F. and Farris, T. N., 'A Spectrally Formulated Finite Element for Wave Propagation in 3-D Frame Structures,' International Journal of Analytical and Experimental Modal Analysis, Vol. 5, 1990, pp.223-237
16 Doyle, J. F., Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, Springer-Verlag, New York, 1997