Definite Quadratic Eigenvalue Problems

Free vibrations of fluid-solids structures are governed by a nonsymmetric eigenvalue problem. This problem can be transformed into a definite quadratic eigenvalue problem. The present paper considers properties of definite problems and variational characterization for definite quadratic eigenvalue problem. We propose improvement of existing methods which determine whether a quadratic pencil Q(λ) is definite. The improved method is reflected in a better localization of start parameters μ and ξ where Q(μ) > 0 > Q(ξ) and μ > ξ.