The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress Keywords: circular plate, resonant vibrations, dissipative heating, piezoelectric actuator Introduction. Solid and compound piezoceramic plates of various configurations are widely used in many kinds of energy converters, piezoelectric transformers, vibration recording and exciting devices, etc. The achievements in research on the resonant vibrations of such elements based on the theory of coupled electroelasticity are reviewed in [14]. Under intensive resonant vibrations, the stressing and straining of a structural element is accompanied by vibrational heating due to electromechanical losses in the material [6]. The theory of coupled thermoelectroviscoelasticity is used in [3, 4, 8-10, 13, 15, 17-19] to study and discuss the influence of vibrational heating and various inhomogeneities on the electrothermomechanical processes in inelastic thin-walled piezoelectric elements. The possibility of controlling the thermoelectromechanical processes in circular bimorph piezoplates with inhomogeneous electrode coating under single-frequency electric loading is examined in [11,[16][17][18].Recently, compound plates that are inhomogeneous structures with passive and piezoactive layers have come to be widely used in vibration recording and damping devices. To damp stationary and nonstationary vibrations, inhomogeneous structures often incorporate piezoactive layers (actuators) to which voltage of appropriate amplitude and phase is applied to compensate for the most power-intensive modes [20,21]. Under such loading, dissipative (or external) heating may considerably affect the functional capability of the compound element as a whole and the actuator in particular. The paper [5] was apparently the first to analyze the effect of temperature on the efficiency of damping the fundamental flexural mode of a clamped circular plate with a thin piezoelectric actuator with stiffness characteristics independent of the thickness. The analytic solution of the problem found by a variational method was used there to derive a formula for the calculation of the electric potential applied to the actuator to compensate for the ...
A mathematical formulation of a new nonlinear problem for active vibration damping (ACD) of thin viscoelastic plates by distributed piezoelectric sensors and actuators is given. The influence of dissipative heating on ACD is considered. The nonlinearity of the problem is caused by the temperature dependence of the material properties and the nonlinearity of the dissipative function. The thermomechanical behavior of the materials under harmonic loading is described by the concept of complex characteristics. Numerical and analytical methods are used for solving this problem. As an example, the influence of dissipative heating on damped axisymmetric bending vibrations of a circular viscoelastic plate is investigated. It is shown that this influence can be significant in the case of ACD of polymeric plates.
The paper addresses the forced flexural vibrations and dissipative heating of a circular viscoelastic plate with piezoactive actuators under axisymmetric loading. A refined formulation of this coupled problem is considered. The viscoelastic behavior of materials is described using the concept of complex moduli dependent on the temperature of dissipative heating. The electromechanical behavior of the plate is modeled based on the Timoshenko hypotheses for the mechanical variables and analogous hypotheses for the electric-field variables in the piezoactive layers of the actuator. The temperature is assumed constant throughout the thickness. The nonlinear problem is solved by a time stepping method using, at each step, the discrete-orthogonalization and finite-difference methods to solve the elastic and heat-conduction equations, respectively. A numerical study is made of the effect of the shear strain, the temperature dependence of the material properties, fixation conditions, and geometrical parameters of the plate on the vibrational characteristics and the electric potential applied to the actuator electrodes to balance the mechanical load
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