000021591 001__ 21591
000021591 005__ 20170622131254.0
000021591 04107 $$aeng
000021591 046__ $$k2017-06-15
000021591 100__ $$aStanoev, Evgueni
000021591 24500 $$aMODAL ANALYSIS PROCEDURE USING COMPLEX LEFT AND RIGHT EIGENVECTORS OF NON-PROPORTIONALLY DAMPED STRUCTURES

000021591 24630 $$n6.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000021591 260__ $$bNational Technical University of Athens, 2017
000021591 506__ $$arestricted
000021591 520__ $$2eng$$aIn the general case of non-proportionally damped structural model the associated quadratic eigenvalue problem leads to complex eigenvalues and eigenvectors. The modal decomposition of the equations of motion is usually to be performed in complex space. In this paper are presented possible variants of a general method [2] - [5] for modal transformation of damped multi-degree-of-freedom-systems (MDOFS) with non-modal symmetric damping matrix. The assembly of a modal transformation matrix in real space is based either on the conjugated complex left eigenvectors, or on the right eigenvectors, or on a combination of the left and right eigenvectors of the system. The eigenvector normalization can be performed with respect to the general mass or to the general stiffness matrix. The equations of motion are stated in state-space formulation. The developed real-space modal transformation matrix is always built by a combination of two complex transformations. Analytically expressions for all presented variants of the modal transformation basis are developed be the aid of computer algebra software. Those formulas operate with the real and the imaginary parts of the eigenvectors and the associated eigenvalues. All variants of the suggested modal procedure retain the common advantages of the classic modal decomposition of the equations of motion. The vibrations of a rotor blade of a wind turbine subjected to wind thrust loads have been calculated in two variants to demonstrate the performance of the presented modal analysis procedures. The initial computation of the complex eigenvalue solution of the FEM beam model and all subsequent computations are done by the aid of computer algebra software. The suggested procedures can be applied in structural systems containing different damping and energy-loss mechanism in various parts of the structure, described by non-proportional damping matrix.

000021591 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000021591 653__ $$amodal decomposition of the equations of motion, modal transformation method, left and right complex eigenvectors, complex eigenvalue problem, proportional/nonproportional damping.

000021591 7112_ $$aCOMPDYN 2017 - 6th International Thematic Conference$$cRhodes Island (GR)$$d2017-06-15 / 2017-06-17$$gCOMPDYN2017
000021591 720__ $$aStanoev, Evgueni
000021591 8560_ $$ffischerc@itam.cas.cz
000021591 8564_ $$s1545353$$uhttps://invenio.itam.cas.cz/record/21591/files/17160.pdf$$yOriginal version of the author's contribution as presented on CD, section: [RS12] Numerical simulation methods for dynamic problems
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000021591 962__ $$r21500
000021591 980__ $$aPAPER