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 
@article{IVM_2022_10_a8,
     author = {V. N. Paimushin and M. V. Makarov and S. F. Chumakova},
     title = {Forced and parametric vibrations of a composite plate caused by its resonant bending vibrations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--94},
     publisher = {mathdoc},
     number = {10},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_10_a8/}
}
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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/