A lanczos‐based technique for exact vibration analysis of skeletal structures

Abstract

Abstract This paper presents and discusses a Lanczos‐based eigensolution technique for evaluating the natural frequencies and modes from frequency‐dependent eigenproblems in structural dynamics. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency‐dependent displacement fields in formulating the system matrices. The method is well suited to the solution of large‐scale problems. The new solution methodology presented here is based on the ability to evaluate a specific set of parameterized non‐linear eigenvalue curves at given values of the parameter through an implicitly restarted Lanczos technique. Numerical examples illustrate that the implicitly restarted Lanczos method with secant interpolation accurately evaluates the exact natural frequencies and modes of the non‐linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models. In addition, the eigenvalue technique presented here is shown to be far more computationally efficient on large‐scale problems than the determinant search techniques traditionally employed for solving exact vibration problems.