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Real Eigenvalues (real + eigenvalue)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

System identification of linear structures based on Hilbert,Huang spectral analysis.

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 10 2003
Part 2: Complex modes
Abstract A method, based on the Hilbert,Huang spectral analysis, has been proposed by the authors to identify linear structures in which normal modes exist (i.e., real eigenvalues and eigenvectors). Frequently, all the eigenvalues and eigenvectors of linear structures are complex. In this paper, the method is extended further to identify general linear structures with complex modes using the free vibration response data polluted by noise. Measured response signals are first decomposed into modal responses using the method of Empirical Mode Decomposition with intermittency criteria. Each modal response contains the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio. Then, each modal response is decomposed in the frequency,time domain to yield instantaneous phase angle and amplitude using the Hilbert transform. Based on a single measurement of the impulse response time history at one appropriate location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex mode shapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the method presented are illustrated through numerical simulations. It is demonstrated that dynamic characteristics of linear structures with complex modes can be identified effectively using the proposed method. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Computing bounds to real eigenvalues of real-interval matrices

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2008
Huinan Leng
Abstract In this study, a new method with algorithms for computing bounds to real eigenvalues of real-interval matrices is developed. The algorithms are based on the properties of continuous functions. The method can provide the tightest eigenvalue bounds and improve some former research results. Numerical examples illustrate the applicability and effectiveness of the new method. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Sufficient conditions of non-uniqueness for the Coulomb friction problem

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2004
Riad Hassani
Abstract We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non-uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non-local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd. [source]