539.3 Modal analysis of prestressed 3D structures based on finite element modeling

Dimitrienko Y. I. (Bauman Moscow State Technical University), Bogdanov I. O. (Bauman Moscow State Technical University)

THERMAL DEGRADATION, COMPOSITES, PERIODICITY CELL, FEM, HIGH TEMPERATURES, MANIPULA/SMCM


doi: 10.18698/2309-3684-2025-2-3246


A formulation of a three-dimensional problem for calculating the natural frequencies and natural modes of vibrations of elastic structures is proposed, taking into account their preliminary loading. The problem statement is written in a tensorial index-free form and is derived using the general theory of geometrically nonlinear deformation of structures. The derivation is based on an analogy with the derivation of a three-dimensional problem of the theory of stability of elastic structures, which was proposed earlier by Yu.I. Dimitrienko. A variational formulation of the problem of model analysis of prestressed three-dimensional structures, as well as a methodology for a finite element solution of the problem, are proposed. A software module for solving problems of modal analysis of prestressed structures has been developed as part of the Manipula/SMCM software package, developed at the REC "SIMPLEX" of Bauman Moscow State Technical University. Based on the developed software module, an example of a numerical solution of the modal analysis problem is given for the case of a plate preloaded with a longitudinal compressive load. It is shown that preloading for this problem significantly affects the natural frequencies of vibrations of the plate. A comparison was made with the results of calculations in the Ansys software package, and it was shown that there is good agreement between the results of calculating natural frequencies


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Димитриенко Ю.И., Богданов И.О. Модальный анализ предварительно нагруженных 3D конструкций на основе конечно-элементного моделирования. Математическое моделирование и численные методы, 2025, № 3, с. 32–46.



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