High Accuracy Eigenvalue-Analysis Using Non-Positive Definite Mass Matrix.
Yuji Aoyama, Genki YAGAWA · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C · 2000
This paper presents a solution algorithm of generalized eigenvalue problem with non-positive definete mass matrix. The accuracy of the natural frequency is much higher using 20-node hexahedral elements than using 8-node elements. However, lumped mass matrix which reduces the computation cost could not be used combined with the 20-node elements, because the mass matrix would be non-positive definite in the case. Applying the proposed algorithm, the generalized eigenvalue problem with non-positive definite mass matrix can be solved with the same computation cost as for the solution of eigenvalue problem with positive difinite mass matrix.