The influence of the relative thickness of a stiff viscoelastic polymer layer and the orientation of reinforcing layers of the bearing layer on the values of their natural frequencies and loss factors of damped vibrations of an unsupported two-layered composite plate has been investigated. It has been established that each natural vibration mode of a two-layered plate corresponds to a certain effective relative thickness of an isotropic viscoelastic polymer layer. A further increase in the relative thickness of plates with an orthotropic bearing layer depending on ambient temperature may result in both an increase and decrease in natural frequencies without any considerable change in their energy dissipation. For plates with a monoclinic bearing layer, the increase in relative thickness of the isotropic viscoelastic polymer layer is accompanied by both a decrease and increase of loss factor for different vibration modes. It is shown that a change in the stacking sequence of reinforcing layers in the bearing layer brings about mutual transformation domains of coupled vibration modes. It has been established that the mutual transformation of the natural shapes of coupled modes of an unsupported quasi-uniform rectangular plate vibrations appears if one of the natural shapes has an even number of quarter-wavelengths in at least one of the plate directions, whereas another natural shape has an odd number of those. It has been demonstrated that the temperature-frequency relationship of elastic-dissipative characteristics of the stiff viscoelastic polymer has a considerable effect upon natural frequencies and loss factors of all the investigated vibration modes for an unsupported rectangular two-layered plate.
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