Abstract
For a rod-strip based on the Timoshenko shear model of the first order of accuracy, taking into account the transverse shear and compression in the direction of thickness, the two-dimensional equations of a plane problem of the theory of elasticity, compiled in a simplified geometrically nonlinear quadratic approximation, are reduced to one-dimensional geometrically nonlinear equations of equilibrium and motion. Under static loading, the derived equations make it possible to identify known flexural-shear forms of buckling under compression conditions and purely transverse-shear buckling under bending conditions. When considering stationary low-frequency dynamic processes of deformation, the derived equations in the linearized approximation fall into two systems of equations, of which linear equations describe low-frequency flexural-shear vibrations, and linearized equations describe forced and parametric longitudinal-transverse (“breathing”) vibrations caused by flexural-shear vibrations.
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Funding
This work was supported by the Russian Science Foundation, project no. 22-79-10033 (Sections 1 and 4) and the Strategic Academic Leadership Program of the Kazan Federal University (“PRIORITET-2030”) (Sections 2 and 3).
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Translated by A. Ivanov
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Paimushin, V.N., Makarov, M.V. & Chumakova, S.F. Forced and Parametric Vibrations of a Composite Plate Caused by Its Resonant Bending Vibrations. Russ Math. 66, 73–80 (2022). https://doi.org/10.3103/S1066369X22100085
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DOI: https://doi.org/10.3103/S1066369X22100085