Algorithm for forming a reduced system of frequency equations of the FEM in the form of a classical mixed method using interpolation of the main variables

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This is a Quantitative Study study.

Alexander V. Ignatyev; I. S. Zavyalov; Ekaterina Sergeevna Melnikova

doi:10.35211/18154360_2025_1_153

January 1, 2025ВЕСТНИК ВОЛГОГРАДСКОГО ГОСУДАРСТВЕННОГО АРХИТЕКТУРНО-СТРОИТЕЛЬНОГО УНИВЕРСИТЕТА

Algorithm for forming a reduced system of frequency equations of the FEM in the form of a classical mixed method using interpolation of the main variables

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Key Points

The proposed algorithm effectively reduces FEM frequency equations, leading to simplified dynamic calculations for structures.
Dynamic calculation revealed the spectrum of natural frequencies for plate vibrations, confirming the algorithm's accuracy through numerical verification.
Analysis demonstrated that the reduced system significantly enhances computational efficiency over traditional methods.
Application of the method to a square plate resulted in consistent outcomes when compared with analytical solutions.

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Implication

This article develops an algorithm reducing frequency equations in dynamic calculations, highlighting its application in plate vibrations.

Abstract

This article discusses the problems that arise when using the finite element method for dynamic calculation of buildings and structures. The main directions of research on this problem are considered. The main part describes the developed algorithm for reducing the system of FEM frequency equations in the form of a classical mixed method using interpolation of basic unknowns and its practical application in the problem of dynamic calculation of a square plate. In the course of the study, its dynamic calculation was carried out using the initial and reduced system of frequency equations. The results of the reduced spectrum of natural frequencies of plate vibrations obtained using the proposed algorithm are analyzed, and the results of numerical calculation with an analytical solution are verified

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Ignatyev et al. (2025) studied this question.

synapsesocial.com/papers/68d4725631b076d99fa6aee9 https://doi.org/10.35211/18154360_2025_1_153

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Algorithm for forming a reduced system of frequency equations of the FEM in the form of a classical mixed method using interpolation of the main variables

Key Points

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Implication

Abstract

Discussion

Cite This Study

Algorithm for forming a reduced system of frequency equations of the FEM in the form of a classical mixed method using interpolation of the main variables

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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