Linearization of the quadratic eigenvalue problem

Abstract The eigenproblem m x + C x + Kx = 0 occurs frequently in the dynamic analysis of structures. It is usually linearized by an augmentation procedure in which a trivial set of equations involving M or K is used to double-up the eigenmatrices. It is shown in this note that the same results may be obtained by augmentation with any arbitrary, non-singular matrix, G. If G is selected judiciously, substantial economy may be achieved in computation time and storage when solving large order problems characteristic of many engineering structures.