Method for determining the parameters of an electrical signal for controlling forced steady-state vibrations of electroviscoelastic bodies. Application to active vibration damping

As a rule, two piezoelectric elements are used in case of implementing an active strategy for controlling the dynamic behavior of structures that include elements made of piezoelectric materials. One of them acts as a sensor and the other one acts as an actuator. In this case, the key problem is in determining the magnitude of the control signal applied to the actuator, and the hardware implementation of the established control law. Due to the need of constructing of complex electrical circuits representing a control unit, preliminary modeling of the mechanical response to a particular control signal becomes attractive. In this paper, the earlier developed approach was extended to the case of using two piezoelectric elements that perform the functions of a sensor and an actuator, and are located accordingly on the surface of the structure.
This approach allows us to obtain expressions for determining the magnitude of the electric potential generated at the moment of resonance on the electroded surface of a piezoelectric element when it is deformed at the vibration mode under consideration in case of forced steady-state vibrations. All the derivations are performed on the basis of solving the problem of natural vibrations of an electro-viscoelastic structure.
Analytical expressions are derived to determine the magnitude of the control signal which is applied to the actuator and provides damping of a given vibration mode. The control signal is generated by converting the signal received from the sensor.
The applicability of the proposed approach is demonstrated at the example of a cantilever plate made of viscoelastic material, the mechanical behavior of which is described by complex dynamic moduli. Piezoelectric elements acting as a sensor and an actuator are placed on both sides of the plate. Numerical implementation of the proposed approach is carried out based on the finite element method using the ANSYS application software package. A good concordance of the results obtained by the derived formulas with the results of the calculation in ANSYS is demonstrated. The proposed approach makes it possible to significantly reduce time and resource costs in case of mathematical modeling of active control of forced steady-state vibrations of electro-viscoelastic bodies, to determine the conditions that the elements of the control unit must satisfy when implementing an active strategy for controlling the dynamic behavior of such smart systems.