Characterization of Piezoelectric Wafer Active Sensors

In the beginning, the classical one-dimensional analysis of piezoelectric active sensors is reviewed. The complete derivation for a free-free sensor is then extended to cover the cases of clamped and elastically constrained sensors. An analytical model based on structural vibration theory and theory of piezoelectricity was developed and used to predict the electro-mechanical (E/M) impedance response, as it would be measured at the piezoelectric active sensor’s terminals. The model considers one-dimensional structures and accounts for both axial and flexural vibrations. The numerical analysis was performed and supported by experimental results. Experiments were conducted on simple beam specimens to support of the theoretical investigation, and on thin gauge aluminum plates to illustrate the method’s potential. It was shown that E/M impedance spectrum recorded by the piezoelectric active sensor accurately represents the mechanical response of a structure. It was further proved that the response of the structure is not modified by the presence of the sensor, thus validating the sensor’s non-invasive characteristics. The sensor calibration procedure is outlined and statistical analysis was presented. It was found that PZT active sensors have stable and repeatable characteristics not only in as-received condition, but also while mounted on 1-D or 2-D host structure. It is shown that such sensors, of negligible mass, can be permanently applied to the structure creating a non-intrusive sensor array adequate for on-line automatic structural identification and health monitoring. * Author to whom correspondence should be addressed, Email victorg@sc.edu JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 11 – December 2000 INTRODUCTION The advent of commercially available low-cost piezoceramics has opened new opportunities for dynamic structural identification using embedded active sensors. Embedded active sensors are small piezoelectric (PZT) ceramic wafers that can be permanently attached to the structure (Figure 1). Through their intrinsic electromechanical (E/M) coupling, these piezoelectric wafers act as both sensors and actuators. In addition, their frequency bandwidth is orders of magnitude larger than that of conventional modal analysis equipment. They can form sensor and actuator arrays that permit effective modal identification in a wide frequency band. Crawley and Luis (1987) proposed the use of piezoceramic wafers as elements of intelligent structures. Dimitriadis et al. (1991) and D’Cruz (1993) used piezoelectric wafers for structural excitation. Zhou et al. (1996) performed experiments in which a PZT wafer produced the excitation, while a laser velocimeter picked up the vibration response. Several investigators (Collins et al. (1992), Clark et al. (1993)) and others used piezopolymer films for vibration sensing. Banks (1996) describes experiments in which the PZT wafer was used initially for excitation, and then for sensing the free decay response. Wang and Chen (2000) used a PZT wafer to excite the structure and an array of PVDF film sensors to pick up the forced vibration response to generate the frequencies and mode shapes through multi-point signal processing. Liang et al. (1994) performed the coupled E/M analysis of adaptive systems driven by a surface-attached piezoelectric wafer. The aim of the analysis was to determine the actuator power consumption and system energy transfer. A 1-degree of freedom (1-DOF) analysis was performed, and the electrical admittance, as measured at the terminals of the PZT wafer attached to the structure, was expressed as: 2 31 ( ) ( ) 1 ( ) ( ) str str A Z Y i C Z Z ω ω ω κ ω ω   = −   +   (1) where C is the electrical capacitance of the PZT active sensor, Zstr(ω) is the 1-DOF structural impedance as seen by the sensor, and ZA(ω) is the sensor impedance. A 1DOF numerical example, using a quasi-static sensor impedance formulation, was used to show that the E/M admittance response accurately reflects the system dynamic response. At coupled-system resonance, the real part of the E/M admittance was shown to have a distinct peak. However, due to the additional stiffness contributed by the PZT wafer, the system natural frequency shifted from 500 Hz (without PZT wafer) to 580 Hz (with PZT wafer). Experimental curve-fitting results were also presented. No modeling of the structural substrate was included, and no prediction of Zstr(ω) for a multi-DOF structure was presented. This work was continued and extended by Sun et al. (1994) who used the half-power bandwidth method to accurately determine the natural frequency and damping values. Mode shape extraction methods, using the self and across admittance of multiple sensors, were explored. Experiments were performed on aluminum beams at frequencies up to 7 kHz. These two papers were the first to conceptualize that the E/M admittance as seen at the sensor terminals reflects the coupled-system dynamics, and that an embedded PZT wafer could be used as structural-identification sensor. However, no theoretical modeling of the E/M 960 VICTOR GIURGIUTIU AND ANDREI N. ZAGRAI impedance/admittance response for comparison with experimental data was attempted. PZT wafer active sensor