Coupled vibrations of viscoelastic three-layer composite plates. 1. Formulation of problem
DOI:
https://doi.org/10.21638/spbu01.2020.309Abstract
A mathematical model of damped oscillations of three-layer plates formed by two rigid anisotropic layers and a soft middle isotropic layer of a viscoelastic polymer is proposed. Each hard layer is an anisotropic structure formed by a finite number of randomly oriented orthotropic viscoelastic composites layers. The model is based on the use of the Hamiltonian variational principle, the refined theory of first-order plates (Reissner-Mindlin theory), the model of complex modules and the principle of elastic-viscoelastic correspondence in the linear theory of viscoelasticity. When describing the physical relationships of hard layer materials, the influence of the vibration frequency and the ambient temperature is considered negligible, while for the soft layer of a viscoelastic polymer, the temperaturefrequency dependence of the elastic-dissipative characteristics is taken into account based on experimentally determined generalized curves. As a special case of the general problem, by neglecting the deformation of the middle surfaces of the rigid layers in one of the directions of the axes of the rigid layers of a three-layer plate, the equations of longitudinal and transverse damped oscillations of a globally orthotropic three-layer beam are obtained. Minimization of the Hamilton functional allows us to reduce the problem of damped vibrations of anisotropic structures to the algebraic problem of complex eigenvalues.
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Литература
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14. Hao M., Rao M.D., “Vibration and Damping Analysis of a sandwich beam containing a viscoelastic constraining layer”, Journal of Composite Materials 39(18), 1621–1643 (2005). https://doi.org/10.1177/0021998305051124
15. Rao M., Echempati R., Nadella S., “Dynamic analysis and damping of composite structures embedded with viscoelastic layers”, Composites. Part B: Engineering 28(5–6), 547–554 (1997).
16. Fotsing E., Sola M., Ross A., Ruiz E., “Lightweight damping of composite sandwich beams: experimental analysis”, Journal of Composite Materials 47(12), 1501–1511 (2012). https://doi.org/10.1177/0021998312449027
17. Li J., Narita Y., “Analysis and optimal design for the damping property of laminated viscoelastic plates under general edge conditions”, Composites. Part B: Engineering 45(1), 972–980 (2013). https://doi.org/10.1016/j.compositesb.2012.09.014
18. Youzera H., Meftah S., Challamel N., Tounsi A., “Nonlinear damping and forced vibration analysis of laminated composite beams”, Composites. Part B: Engineering 43(3), 1147–1154 (2012). https:/doi.org/10.1016/j.compositesb.2012.01.008
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21. Reddy J. N., Mechanics of laminated composite plates and shells. Theory and analysis (2nd ed., CRC Press LLC, 2004).
22. Berthelot J.-M., Dynamics of composite materials and structures (Les Clousures, At the Bottom of Ecrins 4102 m, Vallouise, France, 2015).
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Published
2020-09-04
How to Cite
Ryabov, V. M., Yartsev, B. A., & Parshina, L. V. (2020). Coupled vibrations of viscoelastic three-layer composite plates. 1. Formulation of problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(3), 469–480. https://doi.org/10.21638/spbu01.2020.309
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
