Abstract

AbstractThis paper describes the way in which an unsymmetric block Lanczos algorithm can be employed for approximate eigensolutions or dynamic response solutions for large systems having arbitrary damping and/or repeated (or closely spaced) eigenvalues. To reduce a square, unsymmetric matrix which may have repeated eigenvalues to block‐tridiagonal form, an unsymmetric block Lanczos algorithm is developed. Right and left Lanczos vectors, generated by the reduction process, are employed to define the reduced‐order model based on a discrete analytical model of general linear, time‐invariant dynamic systems. A special type of starting vector is also introduced, which automatically includes the static displacement. This reduced‐order model is employed to compute approximate eigenvalues/vectors and dynamic responses of the original system. To verify the proposed algorithm, examples of an 8‐DOF beam‐rotor system are provided for eigensolutions and dynamic responses due to step and random external forces. These examples showed promising results, indicating that the proposed algorithm is worthy of further study.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.