Geodesic
Forced and parametric vibrations of a composite plate caused by its resonant bending vibrations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2022), pp. 86-94.

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For a rod-strip based on the shear model of S.P. Timoshenko of the first order of accuracy, taking into account the transverse shear and compression in the thickness direction, the two-dimensional equations of the 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 reveal known flexural-shear buckling modes under compression conditions and purely transverse-shear buckling modes under flexural conditions. When considering stationary low-frequency dynamic processes of deformation, the derived equations in the linearized approximation are divided 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.
Keywords: forced vibrations, parametric vibrations, Timoshenko model, geometrically nonlinear equations of motion, flexural-shear vibrations, forced breathing vibrations.
Mots-clés : composite plate 
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V. N. Paimushin; M. V. Makarov; S. F. Chumakova. Forced and parametric vibrations of a composite plate caused by its resonant bending vibrations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2022), pp. 86-94. http://geodesic.mathdoc.fr/item/IVM_2022_10_a8/

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