Application of Lanczos Algorithm for the finite element solution of engineering vibration problems

In this thesis the Lanczos Algorithm is demonstrated as a practical tool to solve generalized eigenvalue problems occuring in finite element solutions of engineering vibration problems. The mathematical foundations of the algorithm, implementation in program format, a FORTRAN program and the results for a small size structural vibration problem constitute the major parts of this thesis. A combination of the existing methods and programs is used to reach the objective. Most of the work is dedicated to package the algorithm and the existing codes towards solving small to medium size vibration problems. A two-bay twenty story structure is analyzed successfully to obtain the eigenvectors and eigenvalues at the low end of the spectrum. The algorithm is found to be a suitable tool to solve engineering vibration problems provided the user is familiar with the mechanics of the algorithm and the problem in consideration.