Dynamic analysis of structures using lanczos co-ordinates

A procedure for deriving the Lanczos vectors is explained and their use in structural dynamics analysis as an alternative to modal co-ordinates is discussed. The vectors are obtained by an inverse iteration procedure in which orthogonality is imposed between the vectors resulting from successive iteration cycles. Using these Lanczos vectors the equations of motion are transformed to tridiagonal form, which provides for a very efficient time-stepping solution. The effectiveness of the method is demonstrated by a numerical example.