Methode de Lanczos par bloc appliquee aux problemes de vibration des structures amorties
Keywords:
Lanczos method, eigen frequencies and modes, damped structuresAbstract
The block Lanczos method for finding eigenvalues and eigenvectors and its application to the computation of the complex frequencies and modes of damped structures are presented. The equation of motion of the structure is transformed into a generalized eigenvalue system Ax = A.Bx in which A and B are symmetric and non positive definite matrices. The block Lanczos method generates a sequence of blocks of orthonormalized vectors and, by a projection on these vectors, we obtain a reduced eigensystem Tz = AZ where T is an unsymmetric block-tridiagonal matrix whose eigenvalues are approximations of those of the initial system. This method provides extraction of multiple frequencies with their multiplicities and, for undamped structures, computation of the frequencies around a given value.
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