Definite Quadratic Eigenvalue Problems

• DOI: 10.1016/j.proeng.2015.01.342
• Publication Date: 2015-02-24T05:09:07Z
• Authors: Aleksandra Kostić; Šefko Šikalo
• Keywords: free vibrations; definite quadratic pencil; eigenvalue; methods for detection; 0101 mathematics; 01 natural sciences; Engineering(all); variational characterization

AbstractFree 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.