Статьи на перевод PVDF_P(VDF-TrFE) / Piezoelectric Composites for Sensor and Actuator Applications

58 vol.% PZT showed d33 and d31 of 150 × 10−12 C/N and −70 × 10−12 C/N, respectively. The maximum strain obtained in these composites were 1700 ppm, indicating the e ectiveness of the interdigitated electrodes.

Fine-scale piezoelectric ceramic fiber-polymer composites also have been developed by Advanced Cerametrics Inc. (Lambertville, NJ), where the emphasis has been on the implementation of these composites on conformal surfaces for active vibration damping in sporting goods [155].

H. Electrostrictive/Ceramic Polymer Composites

The electrostrictive materials open up a new direction for transducer applications [146], [156]. By applying an external bias field across the sample, the material becomes piezoelectric. Electrostrictive ceramic-polymer composites with (1-3) connectivity have been developed using the dice and fill method. Deep grooves were cut in a sintered 0.9Pb(Mg1/3Nb2/3)03-0.l PbTiO3 (PMN-PT) ceramic disk in a crisscross pattern and filled with polymer. Composites with 10 and 25% ceramic by volume were fabricated. Fig. 29 shows the dielectric constant and thickness and planar coupling coe cients of the PMN-PT composites. The electromechanical properties of the bulk ceramic also are given for comparison. Composites exhibited very high dielectric constants, and the K value increased linearly with the bias field until saturation of 56% at 5 kV/cm for the composites with 25% ceramic by volume. The polymer phase had e ectively decoupled, causing the planar coupling coe cient to approximate a value of 10% at 5 kV/cm. A higher ratio translates into a more e cient transducer as there is minimal energy lost through planar vibration. Composites showed mechanical quality response of about 8 at 500 kV/cm [157].

I.Other Novel Piezoelectric Composites

1.Moonie and Cymbal Piezoelectric Ceramic-Metal Composite Transducers: Recently, a novel PZT-air composite named Moonie was developed [158], [159]. This composite was constructed using metal (brass) end caps with shallow internal cavities, which were bonded to a piezoelectric ceramic disk (see Fig. 3). The design is based on the

Fig. 29. Field induced (a) dielectric response, and (b) electromechanical response of electrostrictive PMN-PT composites.

concept of a flextensional transducer. In this design, the ceramic is excited in an extensional mode and the metal plates in a flexure mode. The metal plates are used as a mechanical transformer of the high impedance of the ceramic to the low impedance of the load. In this manner, the radial displacement of the piezoelectric ceramic is amplified into a large axial motion of the metal end caps. Essentially, the negative flextensional motion of the metal arising from the radial motion of the ceramic d31 coe - cient is added to the positive longitudinal displacement through d33. This is especially important for hydrophone applications where dh = d33 ± 2d31, and thus a very large hydrostatic piezoelectric charge coe cient is evident.

Moonie composite transducers and actuators were made using electroded PZT or PMN-PT ceramic discs (11 mm in diameter and 1 mm thick), and brass end caps (from 11 mm to 13 mm in diameter with thickness ranging from

0.2 to 3 mm). Brass was chosen as the metal end cap material for its low thermal expansion coe cient (approximately 15 ppm/◦C). Shallow cavities from 6 mm to 8.5 mm in diameter and about 150 µm center depth were machined into the inner surface of each brass cap. Three kinds of bonding materials were used: silver foil/paste, lead-tin- silver solder, and epoxy resin.

The e ective d33 of the composite was found to be inversely proportional to the metal thickness and increased with electroded areas of PZT, evidence that all the PZT was contributing uniformly to the displacement. The e ective d33 values as high as 4000 × 10−12 C/N were obtained with these Moonie composites at the center of the brass end caps, at which flexural motion is largest. Also, dhgh figure of merit values of 50, 000×10−15 m2/N (see Fig. 3 for comparison with other composites) were not uncommon for hydrophones. The lowest flextensional resonance frequency was proportional to the square root of metal thickness and virtually independent of ceramic and bonding layer thickness. This frequency in the PZT-brass composite with the solder bond and without epoxy encapsulation decreased with temperature, which was probably due to the high stress in the PZT ceramic arising from thermal stresses set up by the metal. The Moonie also was examined for its potential as an actuator for micropositioning applications. The displacement of the composite actuator was measured with a linear voltage di erential transducer (LVDT) having a resolution of approximately 0.05 µm, in the low frequency range. The displacement frequency dependence was measured with a double-beam, laser interferometer, and resonant frequencies were obtained with a spectrum analyzer.

The experimental results showed the PMN composite Moonies produced 10-fold amplification in strain with a displacement of 10 µm under a field of 10 kV/cm. For a 124-layer electrostrictive composite, a 30 µm displacement was feasible under an applied voltage of 150 V. By loading these actuators with weights, forces in excess of 2 kgf were created. The displacement amplification was dependent on the thickness of the metal and the cavity diameter with maximum values as large as 20 µm with a force capability of 0.15 kgf for PZT composites were found achievable.

The Cymbal metal-ceramic flextensional composite transducer, a close cousin of the Moonie, has been developed for many actuator and ultrasonic applications [160]. The Cymbal is a descendent of the so-called Moonie trans-

ducer [160], which is composed of a poled piezoelectric disk sandwiched between two metal end caps from the top and bottom. The metal caps have specially designed geometries to accommodate an air cavity between the metal and ceramic as shown in Fig. 3. The reason behind the transition from the Moonie-type transducer to the Cymbal is to eliminate strain gradients near the center of the Moonie caps. Furthermore, Cymbals are simpler in design and more cost e ective to fabricate. Most importantly, the increased sensitivity and amplification of displacements are harnessed through the conversion of radial stresses into large axial motions. When excited electrically with the electric field parallel to the poling direction, the piezoelectric disk expands axially in accordance with the material’s piezoelectric d33 coe cient, and the lateral dimensions shrink in accordance with the piezoelectric d31 coe cient. The lateral contraction is amplified and transferred to the axial direction through the flexing end caps—the central concept for the Cymbal. A large displacement can be obtained, as shown in Figs. 30(a) and (b), along with moderately high generative force in the vicinity of 20 N [160]. It should be noted that the implementation of a single crystal piezoelectric would enhance the displacement of the Cymbal to unprecedented levels.

Although the Cymbal was originally designed for actuator applications, it also has been considered for shallow water sound projector and receiver, where 5 × 20 prototype arrays have been fabricated for testing [161]. It has been found that a broadband response spanning the frequency range 17–100 kHz could be obtained with relative ease. Based on finite-element analyses, variations of the Cymbal such as the double-dipper (deep submergence), the double driver (unidirective beam pattern), and the smart caps (adjustable resonance frequency) [161]. Each of these Cymbal derivatives is based on the di erent placements of the metal end caps on the ceramic. For instance, the double dipper is essentially an inverted Cymbal in which the metal end caps are adhered to the ceramic driver with the cavity pointing away from the ceramic, resulting in better depth capability for the transducer. However, in the case of smart caps design, the inactive metal end caps (typically steel or brass) are replaced by shape memory alloy such as nitinol. This substitution imparts temperature tunability up to 25% to the device. Furthermore, the transducer is rendered self-healing when excessive hydrostatic pressure collapses the end caps [161].

Fig. 30. (a) Comparison of field-induced displacement for various Cymbal composite actuators. (b) Comparison of field-induced displacement for various Cymbal composite actuators and single crystal piezoelectric.

Moonie and Cymbal composite transducers are most amenable, particularly for actuator applications in which a reasonably high force and high displacement are called for [160]. Furthermore, they also can be e ectively used as sound projectors as well as receivers. Hence, the Moonie and Cymbal provide a backbone from which applicationspecific transducers can be built. It should be noted that these remarkable and tailorable properties could be brought to bear only because the said transducers are fundamentally ceramic-metal composite.

2. Hollow Sphere Composite: Miniature piezoelectric hollow spheres, also known as BBs due to their similarity in size to the pellets used in buckshot, are made using a coaxial nozzle slurry technique with a diameter of 1–6 mm and a wall thickness of 40 to 150 mm [162]. Spheres with both tangential and radial poling configurations, shown in Fig. 31, exhibit a very large hydrophone figure of merit (dhgh). The amplification of dh and figure of merit of BBs results purely from the spherical geometry. An applied hydrostatic pressure is transformed into radial and tangential

Fig. 31. Schematic showing the cross-sectional structure of a BB ceramic-metal composite actuator.

stress components, which are amplified with a factor that can be defined as the ratio of radius to wall thickness (r/t). Properties of the BBs are reported to remain stable up to 7 MPa. The dhgh value of such metal ceramic composites is300,000 (mks units) making it one of the most prominent for transducer applications [162], [163].

J. Theoretical Studies on Piezoelectric Composites

Substantial advances have been made in theoretical studies on piezoelectric composites thanks to the widespread availability of finite-element analysis software, and readily accessible, cheap, computational power. Most theoretical studies have concentrated on composites with (0-3), (1-3), and (2-2) connectivity because of their importance in commercial and military applications [13], [91], [154], [164]–[210]. In what follows, selected examples of theoretical work pertaining to (1-3) and (2-2) composites are given to briefly expose the reader to the wealth of information in the literature. A detailed review of the theory is beyond the scope of this article, and the interested reader is referred to the references provided.

Hosak and Hayward [208], who studied the vibrational and electromechanical characteristics of a wide range of (1-3) structures with (1-3) connectivity, were among the first to apply finite-element analysis to the modeling of such composites. In Fig. 32, the modes of vibration analyzed by Hosak and Hayward [208] are shown, and the corresponding pillar aspect ratio dependence of resonance and antiresonance frequencies is shown. In Figs. 33 and 34, the pillar aspect ratio dependence of coupling coe cients is depicted. In their work, the e ects of pillar geometry, ceramic volume fraction, and pillar orientation were studied, and it was found that a small pillar aspect ratio and a relatively high volume fraction provides the most satisfactory

Fig. 32. Resonant modes of 20 volume percent, 3-mm thick composite with pillar aspect ratio of 0.5. (a) Mode 1: 472 kHz, (b) Mode 2: 520 kHz, (c) Mode 3: 565 kHz, (d) Mode 4: 677 kHz [208].

Fig. 33. Dependence of resonant (fr ) and anti-resonant (fa ) frequencies on pillar aspect ratio in 20 vol.% composite with modes of vibration for: (1) thickness mode fr for an isolated pillar, (2) antiresonance fa for mode 1, (3) thickness mode antiresonance fa for an isolated pillar, (4) antiresonance fa for mode 3, and (5) antiresonance fa for mode 4.

Fig. 34. Dependence of coupling coe cients on pillar aspect ratio in 20 vol.% composite with modes of vibration for modes 1-3, with polymer modulus of elasticity of 2.5 × 109 J/m3.

performance in terms of electromechnical e ciency and uniformity of thickness dilation. It was shown that the use of wide aspect ratio pillars in low ceramic fraction composites is not useful because the pillars in such composites are su ciently spaced, resulting in a strong lateral resonant activity within the polymer at frequencies near the thickness resonance. Furthermore, it also was determined that isolated ceramic pillars tend to vibrate more strongly at the frequency associated with the vibration. Consequently, the thickness coupling coe cient is reduced, and surface displacements become very uneven—an unwanted e ect. However, if a high ceramic volume fraction is used, the pillars become closely spaced, causing the parasitic secondary resonances to be much weaker. As such, the use of a wider aspect ratio (see Figs. 33, 34) is practical.

The finite-element method also has been successfully used in the modeling of the dynamical behavior of (2-2) composites as exemplified by the work of Geng and Zhang [137], who studied the e ects of series modes associated with the periodic structure of a piezoelectric composite that is beyond the stop-band edge resonance. They have addressed the challenge pertaining to the surface vibration profile changes with frequency, and how that is influenced by the aspect ratio of the ceramic plate. Their results indicated that, as long as the thickness resonance is below the first lateral mode frequency, there always is a frequency f1 near the thickness resonance, and at which the polymer and ceramic vibrate in unison. Geng and Zhang [137] also have found that, in a fluid medium such as water, there will be a resonance mode, which has a frequency determined by the velocity of the fluid medium and the unit cell length, and is associated with the oscillation of the fluid.

We also would like to point out that the application of finite-element methods in the modeling of the dynamic response of piezoelectric composites will increase at a fast pace because its use has been proven to be most e ective. The widespread implementation of numerical techniques results is drastic reductions in the time needed for the

design e orts, thereby eliminating the trial-and-error stage in making such piezocomposites.

V. Summary

In the last 25 years, piezoelectric ceramic-polymer composites have been conceptualized, prototyped, fabricated, and implemented in applications encompassing medical imaging and military missions, among others.

A detailed view of the materials used in piezoelectric transducer applications was provided, and indicated that, in the near future, the focus would be on single crystal ferroelectrics in many piezoelectric transducer applications. Therefore, it is reasonable to expect a second generation of research on single crystal-polymer composites, probably with emphasis on (1-3) and (2-2) connectivity.

The salient steps involved in the processing of piezoelectric composites were summarized. The properties of the resultant composites were presented following the time line of its historical evolution, and by using the context of connectivity as the unifying central concept. It is safe to say that great success has been obtained in developing composites with a very wide range of properties, meeting the needs of a diverse array of applications—civilian and military. Most likely, the immediate thrust in this area of research will be to reduce further the scale of such composites for higher-frequency operation (>100 MHz). The major challenges in that quest, of course, will be to devise cost-e ective means of industrial-level production, and the development of low-loss materials.

A detailed account on CAD-based composite fabrication methods has been provided to introduce the reader to novel concepts in processing that surpasses the structural complexity obtained with traditional methods by far. It should be pointed out that the application of SFF methods in prototyping and fabrication of piezoelectric transducers is a very new concept, and more research certainly is needed to benchmark its full potential. However, the potential for its successful, full-scale implementation has been demonstrated, opening new avenues for future research in piezoelectric transducers. A new area of use for SFF-based piezocomposites, hence, might be in nonlinear acoustic transducers in which complex asymmetric piezoelectric elements are needed.

In the last 10 years, there has been remarkable success in the development of flextensional transducers such as the Moonie and Cymbal transducers, which are essentially pseudo (2-2) ceramic-metal composites. These transducers enable one to combine key parameters such as high sensitivity, high displacement, moderately high generative force, and miniaturization into a compact system. And, as such, they have great potential for use in commercial and military applications.

There also have been substantial advances in theoretical and computational methods paralleling the advances in synthesis and fabrication. The widespread availability of finite-element analysis software, along with readily ac-

cessible cheap computational power, resulted in extensive studies on commercially important composites with primarily (0-3), (1-3), and (2-2) connectivity patterns. It is fair to say that the theory now has caught up with the experiment, so there is more quantitative insight into the dynamic behavior of such composites. We, therefore, expect the progress in piezoelectric composites to be much faster in the next decade in light of the theoretical advances made thus far. It also is expected that the theoretical studies will be very useful in miniaturization of piezoelectric composites in which the scales involved may result in very complex interaction phenomena among resonating elements.

References

[1]K. Uchino, Piezoelectric Actuators and Ultrasonic Motors. New York: Kluwer Academic, 1996.

[2]B. Ja e, W. R. Cook, and H. Ja e, Piezoelectric Ceramics. Marietta, OH: R.A.N. Publ., 1971.

[3]Y. Xu, Ferroelectric Materials and Their Applications. Amsterdam: North-Holland, 1991.

[4]L. E. Cross, Ferroelectric Ceramics: Tailoring Properties for Specific Applications. N. Setter and E. L. Colla, Eds. Basel, Switzerland: Birkh¨auser Verlag, 1993, pp. 1–85.

[5]S.-E. Park and T. R. Shrout, “Relaxor based ferroelectric single crystals with high piezoelectric performance,” presented at 8th US-Japan Seminar on Dielectric and Piezoelectric Ceramics, Plymouth, MA, 1997.

[6]S.-E. Park, M. L. Mulvihill, G. Risch, and T. R. Shrout, “The e ect of growth conditions on the dielectric properties of

Pb(Zn1/3Nb2/3)O3 single crystals,” Jpn. J. Appl. Phys., vol. 36, pp. 1154–1158, 1997.

[7]S.-E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor-based ferroelectric single crystals,” J. Appl. Phys., vol. 84, pp. 1804–1811, 1997.

[8]S.-E. Park and T. R. Shrout, “Relaxor-based ferroelectric single crystals for electromechanical actuators,” Mater. Res. Innovations, vol. 1, no. 1, pp. 20–25, 1997.

[9]G. Goodman, “Ferroelectric properties of lead metaniobate,” J. Amer. Ceram. Soc., vol. 36, pp. 368–372, 1960.

[10]E. C. Subbarao, “X-ray study of phase transitions in ferroelectric lead metaniobate and related materials,” J. Amer. Ceram. Soc., vol. 43, pp. 439–442, 1960.

[11] G. Y. Xu, Z. Zhong, Y. Bing, Z. G. Ye, C. Stock, and G. Shirane, “Ground state of the relaxor ferroelectric Pb(Zn1/3Nb2/3)O3,” Phys. Rev. B, vol. 67, pp. 104102-1– 104102-5, 2003.

[12]Z. G. Ye, Y. Bing, J. Gao, A. A. Bokov, P. Stephens, B. Noheda, and G. Shirane, “Development of ferroelectric order in relaxor

(1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3) (0 < x < 0.15),” Phys. Rev. B, vol. 67, pp. 104104-1–104104-5, 2003.

[13]H. M. Ji, Z. Bing, and M. X. Xu, “The influence of di erent substrates on preparation of SrBi2Ta2O9 ferroelectric thin films,” Rare Metal Mater. Eng., vol. 31, pp. 292–295, 2002.

[14]Y. H. Bing, R. Guo, and A. S. Bhalla, “Optical properties of relaxor ferroelectric crystal: Pb(Zn1/3Nb2/3)O3- 4.5%PbTiO3,” Ferroelectrics, vol. 242, pp. 1–11, 2000.

[15]Y. H. Bing and Z. G. Ye, “E ects of chemical compositions on

the growth of relaxor ferroelectric Pb(Sc1/2Nb1/2)(1-x)TixO3 single crystals,” J. Cryst. Growth, vol. 250, pp. 118–125, 2003.

[16]N. Yasuda, N. Uemura, H. Ohwa, Y. Yamashita, M. Iwata, M. Maeda, I. Suzuki, and Y. Ishibashi, “Domain observation in PINPT mixed crystal near a morphotropic phase boundary,” J. Korean Phys. Soc., vol. 42, pp. S1261–S1265, 2003.

[17]M. Iwata, N. Tomisato, H. Orihara, H. Ohwa, N. Yasuda, and Y. Ishibashi, “A Raman study of phase transition in the

(1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3) system,” Ferroelectrics, vol. 261, pp. 747–752, 2001.

[18]M. Iwata, N. Tomisato, H. Orihara, N. Arai, N. Tanaka, H. Ohwa, N. Yasuda, and Y. Ishibashi, “Raman scattering in (1-

x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 mixed crystal system II,” Jpn.

J.Appl. Phys. Part 1, vol. 40, pp. 5819–5822, 2001.

[19]H. Ohwa, M. Iwata, H. Orihara, N. Yasuda, and Y. Ishibashi,

“Raman scattering in (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3,” J. Phys. Soc. Jpn., vol. 70, pp. 3149–3154, 2001.

[20]R. E. Eitel, C. A. Randall, T. R. Shrout, and S. E. Park, “Preparation and characterization of high temperature perovskite ferroelectrics in the solid-solution (1-x)BiScO3-xPbTiO3,” Jpn. J. Appl. Phys. Part 1, vol. 41, pp. 2099–2104, 2002.

[21]S. J. Zhang, L. Lebrun, S. Rhee, R. E. Eitel, C. A. Randall, and

T.R. Shrout, “Crystal growth and characterization of new high Curie temperature (1-x)BiScO3-xPbTiO3 single crystals,” J. Cryst. Growth, vol. 236, pp. 210–216, 2002.

[22]S. J. Zhang, P. W. Rehrig, C. Randall, and T. R. Shrout,

“Crystal growth and electrical properties of Pb(Yb1/2Nb1/2)O3- PbTiO3 perovskite single crystals,” J. Cryst. Growth, vol. 234, pp. 415–420, 2002.

[23]S. J. Zhang, S. Rhee, C. A. Randall, and T. R. Shrout, “Dielectric and piezoelectric properties of high Curie temperature

single crystals in the Pb(Yb1/2Nb1/2)O3-xPbTiO3 solid solution series,” Jpn. J. Appl. Phys. Part 1, vol. 41, pp. 722–726, 2002.

[24]S. J. Zhang, C. A. Randall, and T. R. Shrout, “High Curie temperature piezocrystals in the BiScO3-PbTiO3 perovskite system,” Appl. Phys. Lett., vol. 83, pp. 3150–3152, 2003.

[25]Properties of Raytheon Polyvinylidene Fluoride (PVDF). Lexington, MA: Raytheon Research Division, 1990.

[26]L. F. Brown, “Ferroelectric polymers: Current and future ultrasonic applications,” presented at Proc. IEEE Ultrason. Symp., New York, 1992.

[27]T. Furukawa, “Structure and functional properties of ferroelectric polymers,” Adv. Colloid Polymer Sci., vol. 71-72, pp. 183– 208, 1997.

[28]P. N. T. Wells, Ultrasonic Transducers. New York: Academic, 1977.

[29]T. R. Gururaja, “Piezoelectric composite materials for ultrasonic transducer applications,” Ph.D. dissertation, Pennsylvania State University, State College, PA, 1984.

[30]J. Su, Q. M. Zhang, and R. Y. Ting, “Space charge enhanced electromechanical response in thin film polyurethane elastomers,” Appl. Phys. Lett., vol. 71, pp. 386–388, 1997.

[31]J. Su, Q. M. Zhang, C. H. Kim, R. Y. Ting, and R. Capps, “E ects of transitional phenomena on the electric field induced strain—Electrostrictive response of a segmented polyurethane elastomer,” J. Appl. Poly. Sci., vol. 65, pp. 1363–1370, 1997.

[32]H. R. Gallantree, “Review of transducer applications of polyvinylidene fluoride,” Proc. IEEE, vol. 130, pp. 219–224, 1983.

[33]T. R. Gururaja, “Piezoelectrics transducers for medical ultrasonic imaging,” Amer. Ceram. Soc. Bull., vol. 73, pp. 50–54, 1994.

[34]M. J. Haun, “Transverse reinforcement of 1-3 and 1-3-0 PZT polymer composites with glass fibers,” M.S. thesis, Pennsylvania State University, State College, PA, 1983.

[35]A. Safari, “Perforated PZT-polymer composites with 3-1 and 3- 2 connectivity for hydrophone applications,” Ph.D. dissertation, Pennsylvania State University, State College, PA, 1983.

[36]A. S. Bhalla and R. Y. Ting, “Hydrophone figure of merit,” Sens. Mater., vol. 4, pp. 181–185, 1988.

[37]W. A. Smith, “New developments in ultrasonic transducers and transducer systems,” Proc. SPIE, vol. 1773, 1992.

[38]W. A. Smith, “Composite piezoelectrics utilizing a negative Poisson ratio polymer,” U.S. Patent 5334903, Dec. 4, 1992.

[39]W. A. Smith, “Composite piezoelectric materials for medical ultrasonic-imaging transducers—A review,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 33, pp. 812–813, 1986.

[40]W. A. Smith and A. A. Shaulov, “Ultrasonic transducer arrays made from composite piezoelectric materials,” presented at Proc. IEEE Ultrason. Symp., San Francisco, CA, 1985.

[41]W. A. Smith and A. A. Shaulov, “Ultrasonic transducer arrays made from composite piezoelectric materials,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 33, pp. 100–101, 1986.

[42]W. A. Smith, A. A. Shaulov, and B. A. Auld, “Tailoring the properties of composite piezoelectric materials for medical ultrasonic transducers,” presented at Proc. IEEE Ultrason. Symp., San Francisco, CA, 1985.

[43]J. D. Wicks and K. S. Howe, Fundamentals of Ultrasonic Technique. New York: Academic, 1971.

[44]D. A. Berlincourt, D. R. Curren, and H. Ja e, Piezoelectric and Piezomagnetic Materials and Their Function in Transducers. vol. 1, New York: Academic, 1964.

[45]T. R. Gururaja, A. Safari, R. E. Newnham, and L. E. Cross, “Piezoelectric ceramic-polymer composites for transducer applications,” in Electronic Ceramics. R. C. Buchanan, Ed. New York: Marcell Dekker, 1988, pp. 63–79.

[46]D. P. Skinner, R. E. Newnham, and L. E. Cross, “Connectivity and piezoelectric-pyroelectric composites,” Mater. Res. Bull., vol. 13, pp. 599–607, 1978.

[47]R. E. Newnham, “Composite electroceramics,” Ferroelectrics, vol. 1, pp. 1–32, 1986.

[48]S. M. Pilgrim, R. E. Newnham, and L. L. Rohlfing, “Extension of the composite nomenclature scheme,” Mater. Res. Bull., vol. 22, pp. 677–684, 1987.

[49]K. A. Klicker, “Piezoelectric composites for hydrostatic transducer applications,” M.S. thesis, Pennsylvania State University, University Park, PA, 1980.

[50]K. A. Klicker, J. V. Biggers, and R. E. Newnham, “Composites of PZT and epoxy for hydrostatic transducer applications,” J. Amer. Ceram. Soc., vol. 64, pp. 5–9, 1981.

[51]K. A. Klicker, R. E. Newnham, L. E. Cross, and J. V. Biggers, “PZT composites and a fabrication method thereof,” U.S. Patent 4412148, Oct. 25, 1983.

[52]H. P. Savakus, K. A. Klicker, and R. E. Newnham, “PZTEpoxy piezoelectric transducers: A simplified fabrication approach,” Mater. Res. Bull., vol. 16, pp. 677–686, 1981.

[53]J. W. Sliwa, S. Ayter, and J. P. Mohr, “Method for making piezoelectric composites,” U.S. Patent 5239736, Aug. 31, 1993.

[54]R. L. Gentilman, D. F. Fiore, H. T. Pham, K. W. French, and

L.J. Bowen, “Fabrication and properties of 1-3 PZT-polymer composites,” in Ceramic Transactions, Ferroic Materials: Design, Preparation, and Characteristics. vol. 43, A. S. Bhalla,

K.M. Nair, I. K. Lloyd, H. Yanagida, and D. A. Payne, Eds. Westerville, OH: American Ceramic Society, 1994, pp. 112–116.

[55]L. J. Bowen and K. W. French, “Fabrication of piezoelectric ceramic/polymer composites by injection molding,” in Proc. IEEE Int. Symp. Appl. Ferroelect., 1992, pp. 160–163.

[56]L. J. Bowen, R. L. Gentilman, H. T. Pham, D. F. Fiore, and

K.W. French, “Injection molded fine-scale piezoelectric composite transducers,” in Proc. IEEE Ultrason. Symp., 1993, pp. 499–501.

[57]R. L. Gentilman, D. Fiore, H. Pham, W. Serwatka, and L. Bowen, “Manufacturing of 1-3 piezocomposite sonopanel transducers,” Proc. SPIE: Indust. Commercial Appl. Smart Struct. Technol., vol. 2447, pp. 274–281, 1995.

[58]W. Wersing, “Composite piezoelectrics for ultrasonic transducers,” in Proc. IEEE Int. Symp. Appl. Ferroelect., 1986, pp. 212– 214.

[59]E. W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, and D. Munchmeyer, “Fabrication of microstructures with high aspect ratios and great structural heights by synchrotron radiation lithography, galvanoforming, and plastic moulding (LIGA process),” Microelectron. Eng., vol. 4, pp. 35–56, 1986.

[60]U. Bast, D. Cramer, and A. Wol , “A new technique for production of piezoelectric composites with 1-3 connectivity,” in

Ceramics Today—Tomorrow’s Ceramics. vol. 66C, P. Vincenzini, Ed. Amsterdam: Elsevier Sci. Publ., 1991, pp. 67–73.

[61]U. Bast, H. Kaarmann, K. Lubitz, M. Vogt, W. Wersing, and

D.Cramer, “Composite ultrasonic transducer and method for manufacturing a structured component therefore of a piezoelectric,” U.S. Patent 5164920, Nov. 17, 1992.

[62]K. Lubitz, A. Wol , and G. Preu, “New piezoelectric composites for ultrasonic transducers,” Ferroelectrics, vol. 133, pp. 27–31, 1992.

[63]K. Lubitz, A. Wol , and G. Preu, “Microstructure technology,” presented at Proc. IEEE Ultrason. Symp., Piscataway, NJ, 1993.

[64]K. Lubitz, A. Wol , and B. Schulmeyer, “New piezoelectric composites for ultrasonic transducers,” Ferroelectrics, vol. 133, pp. 21–26, 1992.

[65]K. A. Lubitz, A. Wol , and G. Preu, “Microstructure technology,” presented at Proc. IEEE Ultrason. Symp., 1993.

[66]D. J. Waller, “Lead zirconate titanate ceramic fiber/polymer composites for transducer applications,” M.S. thesis, Rutgers University, New Brunswick, NJ, 1991.

[67]D. J. Waller, A. Safari, R. J. Card, and M. P. O’Toole, “Lead zirconate titanate fiber/polymer composites prepared by a replication process,” J. Amer. Ceram. Soc., vol. 73, no. 11, pp. 3503– 3506, 1990.

[68]J. Zola, “Transducer comprising composite electrical materials,” U.S. Patent 4572981, Feb. 25, 1986.

[69]S. Livneh, V. F. Janas, and A. Safari, “Development of fine scale PZT ceramic fiber/polymer shell composite transducers,” J. Amer. Ceram. Soc., vol. 78, pp. 1800–1804, 1995.

[70]S. S. Livneh, “Fine scale PZT ceramic fiber/polymer shell composite transducers,” M.S. thesis, Rutgers University, New Brunswick, NJ, 1994.

[71]S. S. Livneh, S. M. Ting, and A. Safari, “Development of fine scale and large area piezoelectric ceramic fiber/polymer composites for transducer applications,” Ferroelectrics, vol. 157, pp. 421–426, 1994.

[72]J. W. Stevenson, M. R. Reidmeyer, and W. Huebner, “Fabrication and characterization of PZT/thermoplastic polymer composites for high frequency phased linear arrays,” J. Amer. Ceram. Soc., vol. 77, pp. 2491–2495, 1994.

[73]C. A. Randall, D. V. Miller, J. H. Adair, and A. S. Bhalla, “Processing of electroceramic-polymer composites using the electrorheological e ect,” J. Mater. Res., vol. 8, pp. 899–904, 1993.

[74]C. A. Randall, C. P. Bowen, T. R. Shrout, A. S. Bhalla, and

R.E. Newnham, “Dielectrophoresis: A means to assemble novel electroceramic composite materials,” in Proc. 6th U.S. Japan Seminar Dielectric Piezoelectric Ceram., 1993, pp. 152–154.

[75]M. Eyett, D. Bauerle, and W. Wersing, “Excimer laser induced etching of ceramic PZT,” J. Appl. Phys., vol. 62, pp. 1511–1514, 1987.

[76]Y. Ohara, M. Miyayama, K. Koumoto, and H. Yanagida, “PZTpolymer composites fabricated with YAG laser cutter,” Sens. Actuators A, vol. 40, pp. 187–190, 1994.

[77]Y. Ohara, M. Miyayama, K. Koumoto, and H. Yanagida, “Partially stabilized zirconia stabilized composites fabricated with an ultrasonic cutter,” J. Mater. Sci. Lett., vol. 12, pp. 1279–1282, 1993.

[78]M. J. Creedon, S. Gopalakrishan, and W. A. Schulze, “3-3 Composite hydrophones from distorted reticulated ceramics,” presented at IEEE Int. Symp. Appl. Ferroelect., Pennsylvania State University, State College, PA, 1994.

[79]M. J. Creedon and W. A. Schulze, “Axially distorted 3-3 piezoelectric composites for hydrophone applications,” Ferroelectrics, vol. 153, pp. 333–339, 1994.

[80]J. D. Ervin, D. Brei, C. A. V. Hoy, J. R. Mawdsley, and

J.W. Halloran, “New fabrication process for active microsized metal/ceramic devices,” in Proc. ASME Aerosp. Division, American Society of Mechanical Engineers, 1996, pp. 695–697.

[81]C. A. V. Hoy, A. Barda, M. Gri th, and J. W. Halloran, “Microfabrication of ceramics by co-extrusion,” J. Amer. Ceram. Soc., vol. 81, pp. 152–156, 1998.

[82]R. K. Panda, “Novel piezoelectric ceramics by solid freeform fabrication,” Ph.D. dissertation, Rutgers University, New Brunswick, NJ, 1998.

[83]K. A. Klicker, W. A. Shultze, and J. V. Biggers, “Piezoelectrics composites with 3-1 connectivity and a foamed polyurethane matrix,” J. Amer. Ceram. Soc., vol. 65, pp. C208–C210, 1982.

[84]K. Rittenmyer, T. Shrout, W. A. Schulze, and R. E. Newnham, “Piezoelectric 3-3 composites,” Ferroelectrics, vol. 41, pp. 323– 329, 1982.

[85]Materials System Inc., Injection Molded Piezoceramic Components, www.matsysinc.com/im.html, 2004.

[86]W. Hackenberger, P. Ming-Jen, D. Kuban, T. Ritter, and T. Shrout, “Novel method for producing high frequency 2-2 composites from PZT ceramic,” in Proc. IEEE Ultrason. Symp., vol. 2, 2000, pp. 969–972.

[87]R. P. Schae er, V. F. Janas, and A. Safari, “Engineering of fine structured 2-2 and 2-0-2 piezoelectric ceramic/polymer composites by tape casting,” presented at 10th IEEE Int. Symp. Appl. Ferroelect., East Brunswick, NJ, pt. 2 (of 2), 1996.

[88]W. Huebner, M. R. Reidmeyer, J. W. Stevenson, and L. Busse, “Fabrication of 2-2 connectivity PZT/thermoplastic composites for high frequency linear arrays,” presented at 9th IEEE Int. Symp. Appl. Ferroelect., State College, PA, 1994.

[89]D. M. Mills and S. W. Smith, “Multi-layered PZT/polymer composites to increase signal-to-noise ratio and resolution for medical ultrasound transducers. II. Thick film technology,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 49, pp. 1005– 1014, 2002.

[90]C. Van Hoy, A. Barda, M. Gri th, and J. W. Halloran, “Microfabrication of ceramics by co-extrusion,” J. Amer. Ceram. Soc., vol. 81, pp. 152–158, 1998.

[91]J. W. Halloran, “Freeform fabrication of ceramics,” Br. Ceram. Trans., vol. 98, pp. 299–303, 1999.

[92]H. L. Marcus, J. J. Beaman, J. W. Barlow, D. L. Bourell, and

R.H. Crawford, “Rapid prototyping using FDM: A fast, precise, safe technology,” presented at Solid Freeform Fabrication, Austin, TX, 1992.

[93]H. L. Marcus, J. J. Beamen, J. W. Barlow, D. L. Bourell, and

R.H. Crawford, “Rapid prototyping using FDM: A fast, precise, safe technology,” in Proc. Solid Freeform Fabrication, 1992, pp. 66–69.

[94]H. L. Marcus, J. J. Beamen, J. W. Barlow, D. L. Bourell, and

R.H. Crawford, “Fast, precise, safe prototypes with FDM,” in

Proc. Solid Freeform Fabrication, 1991, pp. 92–96.

[95]H. L. Marcus and D. L. Bourell, “Solid freeform fabrication finds new applications,” Adv. Mater. Process., vol. 9, pp. 677–684, 1993.

[96]S. Ashely, “Rapid prototyping is coming of age,” Mechan. Eng., vol. 117, pp. 62–65, 1995.

[97]D. L. Bourell, J. J. Beamen, H. L. Marcus, and J. W. Barlow, “Solid freeform fabrication, an advanced manufacturing approach,” in Solid Freeform Fabrication Symp. Proc., Austin, TX, 1990.

[98]P. F. Jacobs, Stereolithography and Other RP & M Technologies from Rapid Prototyping to Rapid Tooling. Dearborn, MI: Soc. Manufacturing Eng., 1995.

[99]P. F. Jacobs, Rapid Prototyping & Manufacturing: Fundamentals of StereoLithography. Dearborn, MI: Soc. Manufacturing Eng., 1992.

[100]M. Feygin and B. Hsieh, “Laminated object manufacturing (LOM): A simpler process,” in Proc. Solid Freeform Fabrication Symp., 1991, pp. 123–130.

[101]M. Feygin, “Apparatus and method for forming an integral object from laminatos,” U.S. Patent 5354414, Oct. 10, 1994.

[102]J. Cesarano, T. A. Baer, and P. Calvert, Proc. Solid Freeform Fabrication Symp.. vol. 8, D. L. Bourell, J. J. Beamen, H. L. Marcus, R. H. Crawford, and J. W. Barlow, Eds. 1997, pp. 25– 28.

[103]J. Cesarano, B. H. King, and H. B. Denham, Proc. Solid Freeform Fabrication Symp.. vol. 9, D. L. Bourell, J. J. Beamen, H. L. Marcus, R. H. Crawford, and J. W. Barlow, Eds. Austin, TX, 1998, pp. 697–700.

[104]E. M. Sachs, M. J. Cima, P. Williams, D. Brancazio, and J. Cornie, “Three dimensional printing: Rapid tooling and prototypes directly from a CAD model,” J. Eng. Ind., vol. 114, pp. 481–488, 1992.

[105]J. Cesarano and P. Calvert, “Freeforming objects with lowbinder slurry,” U.S. Patent 6027326, Feb. 22, 2000.

[106]T. Kitayama and Sugawara, Rept. Prof. Gr. Inst. Elec. Comm. Eng. Japan, pp. CPM 72–77, 1972. (in Japanese)

[107]L. A. Pauer, “Flexible piezoelectric material,” presented at IEEE Int. Conv. Rec., 1973.

[108]W. B. Harrison, “Flexible piezoelectric organic composites,” in

Proc. Workshop on Sonar Transducer Mat., Naval Research Laboratory, Arlington, VA, 1976.

[109]H. Banno and S. Saito, “Piezoelectric and dielectric properties of composites of synthetic rubber and PbTiO3 or PZT,” Jpn. J. Appl. Phys., vol. 22, pp. 67–69, 1983.

[110]H. Banno, “Recent developments of piezoelectric ceramic products and composites of synthetic rubber and piezoelectric ceramic particles,” Ferroelectrics, vol. 50, pp. 3–12, 1983.

[111]H. Banno, K. Ogura, H. Sobue, and K. Ohya, “Piezoelectric and acoustic properties of piezoelectric flexible composites,” Jpn. J. Appl. Phys., vol. 26, pp. 153–155, 1987.

[112]J. R. Giniewicz, K. Duscha, R. E. Newnham, and A. Safari, “0- 3 Composites for hydrophone applications,” presented at IEEE Int. Symp. Appl. Ferroelect., Bethlehem, PA, 1986.

[113]A. Safari, T. R. Gururaja, C. Hakun, A. Halliyal, and R. E. Newnham, “0-3 Piezoelectric-polymer composites prepared by

new method: Fired composites,” presented at IEEE Int. Symp. Appl. Ferroelect., Bethlehem, PA, 1986.

[114]K. H. Han, “Colloidal processing of (0-3) piezoelectric composites,” Ph.D. dissertation, Rutgers University, New Brunswick, NJ, 1992.

[115]K. H. Han, A. Safari, and R. E. Riman, “Colloidal processing for improved piezoelectric propenies of flexible 0-3 ceramic/polymer composites,” J. Amer. Ceram. Soc., vol. 74, pp. 1699–1702, 1991.

[116]G. Sa-Gong, A. Safari, S. J. Jang, and R. E. Newnham, “Easily poled flexible piezoelectric composites,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 33, pp. 805–809, 1986.

[117]G. Sa-Gong, A. Safari, S. J. Jang, and R. E. Newnham, “Poling flexible piezoelectric composites,” Ferroelectrics, vol. 5, pp. 131– 142, 1986.

[118]A. Safari, Y. H. Lee, A. Halliyal, and R. E. Newnham, “0- 3 Piezoelectric composites prepared by coprecipitated lead titanate powder,” Amer. Ceram. Soc. Bull., vol. 66, no. 4, pp. 668–670, 1987.

[119]M. H. Lee, A. Halliyal, and R. E. Newnham, “Poling studies

of piezoelectric composites prepared by coprecipitated PbTiO3 powder,” Ferroelectrics, vol. 87, pp. 71–80, 1988.

[120]Y. H. Lee, M. J. Haun, A. Safari, and R. E. Newnham, “Preparation of lead titanate powder for a flexible 0-3 piezoelectric composite,” presented at IEEE Int. Symp. Appl. Ferroelect., Bethlehem, PA, 1986.

[121]Y. Chen, J. Li, H. L. W. Chan, C. L. Choy, and K. Y. Tong, “PT/P(VDF-TrFE) 0-3 nanocomposite thin film pyroelectric sensors,” J. De Physique IV, vol. 8, pp. 139–142, 1998.

[122]H. Kawai, “The piezoelectricity of PVDF,” Jpn. J. Appl. Phys., vol. 8, pp. 975–976, 1969.

[123]S. Y. Lynn, “Polymer-piezoelectrics with 1-3 connectivity for hydrophone applications,” M.S. thesis, Pennsylvania State University, State College, PA, 1981.

[124]C. Richard, P. Eyrand, L. Eyrand, D. Audigier, and M. Richard, “An optimization of 1.3.1 PZT-polymer composite for deep underwater hydrophone application,” in Proc. 8th Int. Symp. Appl. Ferroelect., Honolulu, HI, 1992, pp. 255–258.

[125]W. A. Smith, “The role of piezocomposites in ultrasonic transducers,” presented at Proc. IEEE Ultrason. Symp., Montreal, Canada, 1989.

[126]H. Ohigashi, K. Koga, M. Suzuki, T. Nakanishi, K. Kimura, and N. Hashimoto, “Piezoelectric and ferroelectric properties of (PVDF-TrFE) copolymers and their application to ultrasonic transducers,” Ferroelectrics, vol. 60, pp. 263–276, 1984.

[127]A. Safari, “Development of piezoelectric composites for transducers,” J. Phys. III, vol. 4, pp. 1129–1149, 1994.

[128]M. Kahn, A. Dalzell, and B. Kovel, “PZT Ceramic-air composites for hydrostatic sensing,” Adv. Ceram. Mater., vol. 2, pp. 836–839, 1987.

[129]M. Kahn, “E ects of heat treatments on multilayer piezoelectric ceramic-air composites,” J. Amer. Ceram. Soc., vol. 75, pp. 649–656, 1992.

[130]W. Schulze, “The incorporation of rigid composites into a conformal hydrophone,” Ferroelectrics, vol. 50, pp. 33–37, 1983.

[131]T. R. Shrout, L. J. Bowen, and W. A. Schulze, “Extruded PZTpolymer composites for electro-mechanical transducer applications,” Mater. Res. Bull., vol. 15, pp. 1371–1379, 1980.

[132]A. Safari, A. Halliyal, R. E. Newnham, and J. M. Lachlan, “Transverse honeycomb composite transducers,” Mater. Res. Bull., vol. 17, pp. 301–308, 1982.

[133]W. Qi and W. Cao, “Finite element analysis and experimental studies on the thickness resonance of piezocomposite transducers,” Ultrason. Imag., vol. 18, pp. 1–5, 1996.

[134]W. Qi and W. Cao, “Finite element study of random design of 2-2 composite transducer,” in Proc. SPIE, Ultrasonic Transducer Materials, 1997, pp. 176–180.

[135]Q. Zhang and X. Geng, “Acoustic properties of the interface of a uniform medium 2-2 piezocomposite and the field distributions in the composite,” Jpn. J. Appl. Phys., vol. 11, pt. 1, no. 11, pp. 6853–6861, 1997.

[136]Y. Shui and Q. Xue, “Dynamic characteristics of 2-2 piezoelectric composite transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, pp. 1110–1119, 1997.

[137]X. C. Geng and Q. M. Zhang, “Evaluation of piezocomposites for ultrasonic transducer applications—Influence of the unit

cell dimensions and the properties of constituents on the performance of 2-2 piezocomposites,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, pp. 857–872, 1997.

[138]S. Turcu, “Oriented (2-2) and (3-3) piezoelectric composites by fused deposition of ceramics,” M.S. thesis, Rutgers University, New Brunswick, NJ, 2002.

[139]S. Turcu, B. Jadidian, S. C. Danforth, and A. Safari, “Piezoelectric properties of novel oriented ceramic-polymer composites with 2-2 and 3-3 connectivity,” J. Electroceram., vol. 9, pp. 165– 171, 2002.

[140]C. W. Nan, L. Liu, and L. Li, “Calculations of the e ective properties of 1-3 type piezoelectric composites with various rod/fibre orientations,” J. Phys. D, vol. 33, pp. 2977–2984, 2000.

[141]C. W. Nan and G. W. Weng, “Influence of polarization orientation on the e ective properties of piezoelectric composites,” J. Appl. Phys., vol. 88, pp. 2977–2984, 2000.

[142]R. E. Newnham, D. P. Skinner, and L. E. Cross, “Flexible composite transducers,” Mater. Res. Bull., vol. 13, pp. 559–607, 1978.

[143]M. Miyashita, K. Takano, and T. Toda, “Preparation and properties of PZT ceramics with ladder type structure,” Ferroelectrics, vol. 28, p. 397, 1980.

[144]K. Hikita, K. Yamada, M. Nishioko, and M. Ono, “Piezoelectric properties of the porous PZT and the porous PZT composite with silicone rubber,” Ferroelectrics, vol. 1, pp. 265–272, 1983.

[145]Y. Q. Zhuang, “Solid porous-solid sandwich PZT and its application to transducers,” Ferroelectrics, 1981.

[146]H. Masuzawa, “Electrostrictive materials for ultrasonic probes

(II)applications,” presented at Fifth U.S.-Japan Seminar Dielectric and Piezoelectric Ceramics, Kyoto, Japan, 1990.

[147]A. Bandyopadhyay, R. K. Panda, V. E. Janas, M. K. Agarwala, S. C. Danforth, and A. Safari, “Processing of piezocomposites by fused deposition technique,” J. Amer. Ceram. Soc., vol. 80, pp. 1366–1372, 1997.

[148]A. Safari, V. F. Janas, and R. K. Panda, “Fabrication of fine scale 1-3 PZT ceramic/polymer composites using a modified lost mold method,” presented at SPIE Symp. Smart Struct. Mater., San Diego, CA, 1996.

[149]A. Safari, J. Cesarano, III, P. G. Clem, and B. Bender, “Fabrication of advanced functional electroceramic components by layered manufacturing (LM) methods,” presented at 13th IEEE Int. Symp. Appl. Ferroelect., Nara, Japan, 2002.

[150]R. J. Card and M. P. O’Toole, “Solid ceramic fibers via impregnation of activated carbon fibers,” J. Amer. Ceram. Soc., vol. 73, pp. 665–668, 1990.

[151]R. J. Card, M. P. O’Toole, and A. Safari, “Method of making piezoelectric composites,” U.S. Patent 408422, Sep. 17, 1986.

[152]S. Ting, “Fine scale and large area piezoelectric fiber/polymer composites,” M.S. thesis, Rutgers University, New Brunswick, NJ, 1995.

[153]B. Jadidian, “Design and fabrication of a flexible large area fabric transducer for bone healing applications,” Ph.D. dissertation, Rutgers University, New Brunswick, NJ, 1998.

[154]A. A. Bent, N. W. Hagood, and J. P. Rodgers, “Anisotropic actuation with piezoelectric fiber composites,” J. Intelligent Mater. Syst. Struct., vol. 6, pp. 338–349, 1995.

[155]F. Mohammadi and E. K. Akdogan, Private communication, 2004.

[156]H. Takeuchi, “Electrostrictive materials for ultrasonic probes

(I)material properties,” presented at Fifth U.S.-Japan Seminar on Dielectric and Piezoelectric Ceramics, Kyoto, Japan, 1990.

[157]J. C. Shannon, “Electrostrictive-polymer composites,” M.S. thesis, Rutgers University, New Brunswick, NJ, 1992.

[158]Y. Sugawara, K. Onitsuka, S. Yoshikawa, Q. Xu, R. E. Newnham, and K. Uchino, “Metal-ceramic composite actuators,” J. Amer. Ceram. Soc., vol. 75, pp. 996–1001, 1992.

[159]Q. C. Xu, S. Yoshikawa, J. R. Belsick, and R. E. Newnham, “Piezoelectric composites with high sensitivity and high capacitance for use at high pressures,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 38, pp. 634–639, 1991.

[160]R. J. Meyer, Jr., A. Dogan, C. Yoon, S. M. Pilgrim, and R. E. Newnham, “Displacement amplification of electroactive materials using the cymbal flextensional transducer,” Sens. Actuators A-Phys., vol. 87, pp. 157–162, 2001.

[161]R. E. Newnham and J. Zhang, “Cymbal transducers: A review,” in Proc. IEEE Int. Symp. Appl. Ferroelect., 2000, pp. 29–32.

[204]D. Varelis and D. A. Saravanos, “Coupled buckling and postbuckling analysis of active laminated piezoelectric composite plates,” Int. J. Solids Struct., vol. 41, pp. 1519–1538, 2004.

[205]W. M. D. Wright, D. A. Hutchins, A. Gachagan, and G. Hayward, “Polymer composite material characterisation using a laser/air-transducer system,” Ultrasonics, vol. 34, pp. 825–833, 1996.

[206]Q. M. Zhang and X. C. Geng, “Acoustic properties of the interface of a uniform medium-2-2 piezocomposite and the field distributions in the composite,” Jpn. J. Appl. Phys. Part 1-Reg. Papers Short Notes Rev. Papers, vol. 36, pp. 6853–6861, 1997.

[207]D. D. N. Hall, G. Hayward, and Y. Gorfu, “Theoretical and experimental evaluation of a two-dimensional composite matrix array,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 40, pp. 704–709, 1996.

[208]J. A. Hosak and G. Hayward, “Finite element analysis of 1-3 piezoelectric composites,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 38, p. 618, 1991.

[209]R. L. O’Leary and G. Hayward, “Investigation into the e ects of modification of the passive phase of improved manufacture of 1-3 connectivity piezocomposite transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 46, pp. 511–516, 1999.

[210]D. J. Powell, G. Hayward, and R. Y. Ting, “Unidimensional modeling of multi-layered piezoelectric transducer structures,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 45, pp. 667–677, 1998.