Refined Geometrically Nonlinear and Linear Equations of Motion of an Elongated Rod-Type Plate

New refined geometrically nonlinear equations of motion of composite elongated rod-type plates in plane stress-strain state are derived for the case when the axes of the selected coordinate system coincide with the axes of the orthotropy of the plate material. The equations are based on the previous...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023-10, Vol.44 (10), p.4469-4477
Main Authors: Paimushin, V. N., Kamalutdinov, A. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Composite structures
Coordinates
Deformation
Elongation
Equations of motion
Geometry
Linear equations
Mathematical Logic and Foundations
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear equations
Plane stress
Plate material
Probability Theory and Stochastic Processes
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Summary:New refined geometrically nonlinear equations of motion of composite elongated rod-type plates in plane stress-strain state are derived for the case when the axes of the selected coordinate system coincide with the axes of the orthotropy of the plate material. The equations are based on the previously proposed relations of a consistent version of the geometrically nonlinear theory of elasticity under small deformations and on the refined shear model of S.P. Timoshenko. Such equations describe the high-frequency torsional vibrations in elongated rod-type plates that can occur during low-frequency flexural vibrations. By limit transition to the classical model of the theory of rods, the derived equations simplified to a system of equations of a lower order. For the case of the same deformation models for a composite plate with inclined reinforcement, similar equations of motion in a linear approximation are obtained. It is shown that they describe the coupled flexural-torsional vibrations in the case of small displacements.
ISSN:1995-0802
1818-9962
DOI:10.1134/S199508022310030X