Simulation of an incomplete algebraic problem of eigenvalues and vectors by the method of frequency-dynamic condensation based on FEM in the form of the classical mixed method

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Abstract


Relevance . Dynamic analysis of complex structures using numerical methods leads to the solution of the algebraic problem of eigenvalues and the corresponding eigenvectors of high orders. The solution of this problem for high order matrices is performed using reduction methods. One of the most effective methods is the method of sequential frequency-dynamic condensation, which allows partial consideration of the dynamic properties of the structure in the minor degrees of freedom. This allows for more accurate results compared to static condensation. Frequency-dynamic condensation is traditionally used to reduce frequency equations derived from the finite element method in the form of the displacement method or the force method. Methods. The authors have developed an algorithm for the frequency-dynamic condensation method for the frequency equation obtained on the basis of the FEM in the form of the classical mixed method. That allows to obtain not only the spectrum of the lower vibration frequencies, but also the corresponding vibration modes and the stress-strain state of the structure. Results . This article describes the algorithm and its practical implementation in the problem of dynamic analysis of a rectangular plate. The results of the numerical analysis of the problem are presented. An assessment of the accuracy of the method and recommendations for its use are given.


About the authors

Alexander V Ignatyev

Volgograd State Technical University

Author for correspondence.
Email: alignat@gmail.com
SPIN-code: 9405-9800
28 Lenin Ave., Volgograd, 400005, Russian Federation

PhD in Technical Sciences, Associate Professor, Department of Automated Systems Software

Artem V Chumakov

Volgograd State Technical University

Email: chumakovtema@gmail.com
28 Lenin Ave., Volgograd, 400005, Russian Federation

master student of the Department of Software of Automated Systems

Vadim V Gilka

Volgograd State Technical University

Email: gilka_vv@mail.ru
28 Lenin Ave., Volgograd, 400005, Russian Federation

master student of the Department of Software of Automated Systems

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