Active structural vibration control: Robust to temperature variations
d-form augmented piezoelectric constitutive equations which take into account temperature dependence of piezoelectric strain coefficient (d31) and permittivity (?33), are converted into e-form. Using e-form constitutive equations, a finite element model of a smart two dimensional plate instrumented with piezoelectric patches is derived. Equations of motion are derived using Hamilton's variational principle. Coupled equations of motion are uncoupled using modal analysis. Modal state vectors are estimated using the Kalman observer. The first mode of smart cantilevered plate is actively controlled using negative first modal velocity feedback at various temperatures. Total control effort required to do so is calculated using the electro-mechanical impedance method. The temperature dependence of sensor voltage, control voltage, control effort and Kalman observer equations is shown analytically. Simulation results are presented using MATLAB. Variations in (i) peak sensor voltage, (ii) actual and estimated first modal velocities, (iii) peak control voltage, (iv) total control effort and (v) settling time with respect to temperature are presented. Active vibration control performance is not maintained at temperature away from reference temperature when the temperature dependence of piezoelectric stress coefficient e31 and permittivity ?33 is not included in piezoelectric constitutive equations. Active control of vibrations becomes robust to temperature variations when the temperature dependence of e31 and ?33 is included in piezoelectric constitutive equations.
augmented piezoelectric constitutive equations finite element model active vibration control smart structure temperature dependence of piezoelectric strain coefficient and permittivity piezoelectric sensors and actuators