FORCED VIBRATIONS AND VIBROHEATING OF VISCOELASTIC PLATE WITH PIEZOSENSORS WITH TAKING INTO ACCOUNT GEOMETRICAL NONLINEARITY AND SHEAR STRAINS - Karnaykhov, V. G.; Кozlov, V. І.; Karnaykhova, T. V. (Computer Science and Applied Mathematics, 2017)
With oscillations, the piezosensors have hysteresis losses. These losses are significantly increased for inelastic materials. Sometimes this lead to a significant increase in temperature of dissipative warming up. This temperature affects the performance of the sensors. If temperature reaches the Curie value of the material, the sensor loses its functional purpose due to depolarization of the material. Due to the resonance oscillations of not enough thin plates and an anisotropy of the material, it is necessary to take into account a geometric nonlinearity and deformation of the transverse displacement in the study of their resonant oscillations and dissipative warming. The article studies a three-layer plate. The plate is composed of an orthotropic viscoelastic core-layer and two outer transversally isotropic layers (facesheets). The core is passive without piezoelectric effect, and facesheets are piezoelectric. Facesheets are opposite polarized. The plate is loaded by pressure. Pressure is uniform and harmonic over time. A frequency of pressure is close to the resonance. The visco-elastic properties of a material are described by Voltaire's operators. We developed Based a model of forced resonant oscillations of flexible viscoelastic rectangular plates with piezoelectric sensors. In the model, refined hypothesis of S. Tymoshenko are employed. Using the Bubnov-Galerkin method, the problem is reduced to a nonlinear integro-differential equation with cubic nonlinearity of the transverse deflection. We use asymptotic methods of nonlinear mechanics solving this equation. We obtain a cubic algebraic equation where the unknown is the square power of the transverse oscillations’ amplitude. Using the obtained solution of the problem of electromechanics, a dissipative function is obtained. Finally, an analytical solution of the heat equation with a known heat source is also obtained.