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Computation of lower bound eigenvalues using the Wittrick-Williams algorithm
Howson, William Paul, Watson, A.
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A general adaptive finite element eigen-algorithm stemming from Wittrick-Williams algorithm
Thin-Walled Structures, 2021Abstract Stemming from Wittrick-Williams algorithm for transcendental eigenproblems, a general adaptive finite element (FE) procedure is proposed for general linear eigenproblems. The pivot of the proposed procedure is the counting method based on Sturm sequences, a simplified version of the Wittrick-Williams algorithm for linear matrix eigenproblems,
Si Yuan, Haohan Sun
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Thin-Walled Structures, 2021
Abstract In this study, the dynamic stiffness method is applied to a cracked beam that incorporates Rayleigh bar theory and Timoshenko beam theory, and the Wittrick-Williams algorithm is used to pinpoint natural frequencies. The influence of a crack on the two components of the Wittrick-Williams algorithm, namely, the number of negative leading ...
Xutao Sun
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Abstract In this study, the dynamic stiffness method is applied to a cracked beam that incorporates Rayleigh bar theory and Timoshenko beam theory, and the Wittrick-Williams algorithm is used to pinpoint natural frequencies. The influence of a crack on the two components of the Wittrick-Williams algorithm, namely, the number of negative leading ...
Xutao Sun
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Materials Today: Proceedings, 2021
Abstract The Wittrick–Williams algorithm is used as the solution technique in the dynamic stiffness matrix to compute the natural frequencies of the orthotropic plate for different boundary conditions, aspect ratios, thickness ratios and modulus ratios.
Suraj Yadav
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Abstract The Wittrick–Williams algorithm is used as the solution technique in the dynamic stiffness matrix to compute the natural frequencies of the orthotropic plate for different boundary conditions, aspect ratios, thickness ratios and modulus ratios.
Suraj Yadav
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An improved Wittrick-Williams algorithm for beam-type structures
Composite Structures, 2018Abstract With the help of the dynamic stiffness method, the problem of dynamic characteristics analysis of an engineering structure can be transformed into the problem of solving the transcendental frequency equation. The Wittrick-Williams algorithm can provide the upper and lower bounds of any given modal frequency, so that the numerical solution ...
Danhui Dan
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International Journal of Mechanical Sciences, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Usik Lee, A Y T Leung
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Usik Lee, A Y T Leung
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Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems
Journal of Vibration and Acoustics, Transactions of the ASME, 1997A precise integration algorithm has recently been proposed by Zhong (1994) for dynamic stiffness matrix computations, but he did not give a corresponding eigenvalue count method. The Wittrick-Williams algorithm gives an eigenvalue count method for pure displacement formulations, but the precise integration method uses a mixed variable formulation ...
Zhong Wanxie +2 more
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007
Since 1970, the Wittrick–Williams algorithm has been applied with increasing sophistication in structural mechanics to guarantee that eigenvalues cannot be missed and are calculated accurately. The underlying theorem enables its application to any discipline requiring eigenvalues of self-adjoint systems of differential equations. Its value
Andrew Watson, Antonia J Jones
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Since 1970, the Wittrick–Williams algorithm has been applied with increasing sophistication in structural mechanics to guarantee that eigenvalues cannot be missed and are calculated accurately. The underlying theorem enables its application to any discipline requiring eigenvalues of self-adjoint systems of differential equations. Its value
Andrew Watson, Antonia J Jones
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On the Wittrick-Williams algorithm for modes of flexible structures
Optimization Methods and Software, 1993We present a new proof of the oft-used Wittrick-Williams algorithm for finding modes of flexible structures, generalizing it at the same time a little, and noting the relation to positive-real transfer functions and electrical circuit theory.
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