Work

Galerkin-Type Solution of the Föppl–von Kármán Equations for Square Plates

Year: 2024

Type: article

Abstract: The solution of the non-linear Föppl–von Kármán equations for square plates in the form of expansion over a system of eigenfunctions, generated by a linear self-adjoint operator, is obtained. The coefficients of the expansion are determined via the reduction method from the infinite-dimensional system of cubic equations. This allows the proposed solution to be considered as a non-linear generalization of the classical Galerkin approach. The novelty of the study is in the strict formulation of the auxiliary boundary problem, which makes it possible to take into account a rigid fixation against any displacements along the boundary. To verify the proposed solution, it is compared with experimental data. The latter is obtained by the holographic interferometry of small deflection increments superimposed on the large deflection caused by initial pressure. Experiment and theory show a good agreement.

Source: Symmetry

DOI: 10.3390/sym17010032

Authors: Sergey A. Lychev, Alexander V. Digilov, Nikolay A. Djuzhev

Institutions: Institute for Problems in Mechanics, National Research University of Electronic Technology

Language: English

Topic: Elasticity and Wave Propagation

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: Ministry of Science and Higher Education of the Russian Federation