Bending vibrations of viscoelastic plates within the Kirchhoff-Love model

Pyatetska, O. V. (2019). Bending vibrations of viscoelastic plates within the Kirchhoff-Love model. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(4), 64–67. https://doi.org/10.17721/1812-5409.2019/4.8

Within the framework of the hypotheses of the classical Kirchhoff-Love theory, complete systems of resolving equations are constructed to determine the stress-strain state and the temperature of dissipative heating under steady transverse vibrations of plates made of a linear viscoelastic material, the properties of which depend on the frequency of external excitation and temperature. The equations were obtained without any preliminary suggestions about the law of temperature variation over the plate thickness. This law is determined in the process of solving the problem. The unrelated problem of vibrational bending of viscoelastic plates for complicated way of fixing a contour and different types of thermal boundary conditions is considered. Mathematical models of problems on the steady-state transverse vibrations of plates made of a linear viscoelastic material, the properties of which depend on temperature for an arbitrary law of its change over the thickness of the object. If the material characteristics depend on temperature, investigation of the influence of temperature of dissipative heating is reduced to solution of complicated non-linear systems of differential equations.Key words: viscoelastic plates, dissipative heating, Kirchhoff-Love theory.Pages of the article in the issue: 64 - 67Language of the article: Ukrainian