Wyznaczanie Częstości Drgań Własnych i Amplitud Układu o Skończonej Liczbie Stopni Swobody
To determine the natural frequencies and amplitudes of a system with a finite number of degrees of freedom (and in many numerical problems of mechanics and physics) it is necessary to find the eigenvalues and eigenvectors of a matrix. The present paper proposes a method for determining the coefficie...
| Published in: | Engineering Transactions |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Fundamental Technological Research Polish Academy of Sciences
1967-06-01
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| Online Access: | https://et.ippt.pan.pl/index.php/et/article/view/2684 |
| Summary: | To determine the natural frequencies and amplitudes of a system with a finite number of degrees of freedom (and in many numerical problems of mechanics and physics) it is necessary to find the eigenvalues and eigenvectors of a matrix. The present paper proposes a method for determining the coefficients of the characteristic (secular) equation of matrix based on certain properties of almost triangular matrices. After determining the roots of the characteristic equation (the eigen-values) the eigenvectors of the matrix can be determined by this method in a simple manner. The method is characterized by a simple computation scheme and the fact that a smaller number of multiplications and divisions must be done than in the well-known methods of Krylov, Danilevsky and Le Verrier. |
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| ISSN: | 0867-888X 2450-8071 |