Electroelasticity relations and fracture mechanics of piezoelectric structures

Applied Mechanics Reviews

Volumn 60, Issue 1-6, 2007, Pages 21-36

  Bogomol'nyi, V M ^a  

^a RUSSIAN STATE UNIVERSITY OF TOURISM AND SERVICE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTITUTIVE EQUATIONS; FRACTURE MECHANICS; PLATES (STRUCTURAL COMPONENTS); SHELLS (STRUCTURES); THREE DIMENSIONAL;

ELECTROELASTICITY; PIEZOEFFECTS; PIEZOELECTRIC STRUCTURES;

PIEZOELECTRIC MATERIALS;

EID: 35448935272     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2375142     Document Type: Review

References (301)

1. Adirovich, E. I., 1960, "An Electrical Field and Currents Caused by Injection-Controlled Polarization," Sov. Phys. Solid State, 28(2), pp. 1410-1422.
2. Wright, G., 1961, "Mechanisms of Space-Charge-Limited Current in Solids," Solid-State Electron., 2(2/3), pp. 165-189.
3. Sutton, P. M., 1964, "Space Charge and Electrode Polarization in Glass. II," J. Am. Ceram. Soc., 47(5), pp. 219-230.
4. Gifeisman, Sh. M., 1969, "Distribution of the Field in a Contact Metal-Dielectric-Metal System," Sov. Phys. Solid State, 11(8), pp. 2097-2102.
5. Chenskii, E. V., 1970, "On the Monodomain Polarization of Ferroelectrics With Phase Transition of the First Kind," Sov. Phys. Solid State, 12(2), pp. 586-591.
6. Lampert, M., and Mark, P., 1970, Current Injection in Solids, Academic, New York.
7. Lampert, M. A., and Shilling, R. B., 1970, "Current Injection in Solids. The Regional Approximation Method," Semiconductors and Semimetals, R. K. Willardson, and A. C.Beer, eds., Vol. 6, Injection Phenomena, Academic, New York.
8. Simmons, J. G., 1971, "Theory of Metallic Contacts on High Resistivity Solids. I: Shallow Traps," J. Phys. Chem. Solids, 32(8), pp. 1987-1999.
9. Godlewski, J., and Kalinowski, J., 1978, "An Extension of Theoretical Description of Space-Charge-Limited Currents in Insulators," Solid State Commun., 25(7), pp. 473-475.
10. Arkhipov, V. I., and Rudenko, A. I., 1978, "Negative Currents Caused by Injection-Controlled Polarization," Solid State Commun., 28(8), pp. 675-676.
11. Lee, H. S., and Marin, S. P., 1980, "Electrode Shape Effects on Oxide Conduction in Films Thermally Grown from Polycrystaline Silicon," J. Appl. Phys., 51(7), pp. 3746-3750.
12. Mead, C. A., 1961, "Operation of Tunnel-Emission Devices," J. Appl. Phys., 32(4), pp. 646-652.
13. Mead, C. A., 1962, "Electron Transport in Thin Insulating Films," Phys. Rev., 128, pp. 2088-2091.
14. Romanov, V. P., and Chaplygin, Ju. A., 1979, "Stationary Distribution of the Mobile Charge in the Dielectric of MOS Structures," Phys. Status Solidi A, 53, pp. 493-498.
15. Romanov, V. P., 1981, "Stationary Distribution of the Noncompensated Mobile Charge in Two-Layer Dielectrics," Russian Microelectronics, 10, pp. 132-134.
16. Romanov, V. P., 1982, "Stationary Distribution of the Mobile Ions in a Dielectric With Regard to Their Elastic Interaction With a Medium," Phys. Status Solidi A, 70, pp. 525-532.
17. Naidjuk, Ju. G., Gribov, N. N., Shklarevskii, O. I., Jansen, A. G., and Janson, I. K., 1985, "Thermoelectrical Effects Ad Asymmetry of the Volt-Amper Characteristics of Metal Microcontacts," Phys. Low Temperat, 11(11), pp. 1053-1062.
18. Bogomol'nyi, V. M., 1995a, "Calculation and Design of PZ Actuators on the Basis of Thin Layer MDM Structures," Proc. SPIE, 2442, pp. 518-524.
19. Bogomol'nyi, V. M., and Serebryakov, Ju., N., 1996, "Calculation of Electrical Field in MDM Structures," Meas. Tech., 1, pp. 46-47 (translated in English).
20. Wu, C. Y., and Chen, C. F., 1987, "Transport Properties of Thermal Oxide Films Growth on Polycrystalline Silicon," IEEE Trans. Electron Devices, ED34(7), pp. 1520-1527.
21. Joo, J. H., et al., 2001, "Rugged Metal Electrode (RME) in High Density Memory Devices," Jpn. J. Appl. Phys., Part 2, 40(8A), pp. L826-L828.
22. Brezzi, F., Marini, L. D., and Pietra, P., 1989, "Numerical Simulation of Semi-conductor Devices," Comput. Methods Appl. Mech. Eng., 75, pp. 493-514.
23. Dong, S., Wang, S., Shen, Wenjaang, and Li, Lonati, 2000, "A Miniature PZ Ultrasonic Motor Based on Circular Bending Vibration Mode," IEEE/ASME Trans. Mechatron., 5(4), pp. 325-330.
24. Mock, M. S., 1983, Analysis of Mathematical Models of Semiconductor Devices, Boole Press, Dublin,
25. Esener, S., and Lee, S. H., 1985, "Punch-Through Current Under Diffusion-Limited Injection," J. Appl. Phys., 58(3), pp. 1380-1387.
26. Kao, K., and Hwang, W., 1981, Electrical Transport in Solids. Part 1,2, Pergamon, Oxford.
27. Benveniste, Y., 1992, "The Termination of the Elastic and Electric Fields in PZ Inhomogeneity," J. Appl. Phys., 72, pp. 1086-1095.
28. Benveniste, Y., 1993, "Universal Relations in PZ Composites With Eigenstress and Polarization Fields. Part I: Binary-Media-Local Fields and Effective Behavior. Part II: Multiphase Media Effective Behavior," Trans. ASME, J. Appl. Mech., 60(2), pp. 265-275.
29. Bogomol'nyi, V. M., 1995b, "On Calculation of Uneven Polarized Through Thickness Piezoceramic Transducers," Meas. Tech., 6, pp. 52-54.
30. Bogomol'nyi, V. M., 1995c, "On Calculation of PZ Modulators of Infrared Radiation," Meas. Tech., 7, pp. 58-60.
31. Furukawa, T., Yematsu, Y., and Asakawa, K., 1968, "Piezoelectricity, Pyro-electricity and Thermoelectricity of Polymer Films," J. Appl. Polym. Sci., 12(12), pp. 2675-2689.
32. 3 Thin Films. Analysis of Charge Carrier Trapping Phenomenon," Integr. Ferroelectr., 35(1-4), pp. 283-297.
33. Bugdacy, N., and Bogy, D. B., 1981a, "A Two-Dimensional Theory For PZ Layers Used in Electromechanical Transducers. Part I: Derivation, Part II: Application," Int. J. Solids Struct., 17(12), pp. 1159-1202.
34. Ebeneser, D. D., and Pushpa, A., 1999, "PZ Thin Shell Theoretical Model and Eigenfunction Analysis of Radially Polarized Cylinder," J. Acoust. Soc. Am., 105(1), pp. 154-163.
35. Hazony, D., and Raya, J., 1988, "Electromechanical Modelling of Distortion-less PZ Transducers With Non-Uniform Parameters," J. Acoust. Soc. Am., 84(1), pp. 20-25.
36. Joffe, A. F., 1928, The Physics of Crystals, McGraw-Hill, New York.
37. Mason, W. P., 1950, Piezoelectric Crystals and their Applications in Ultrasonics, Princeton, New Jersey.
38. Mason, W. P., and Wick, R. F., 1954, "Ferroelectric and Dielectric Amplifiers," Proc. IRE, 42(11), pp. 1606-1611.
39. Mason, W. P., 1981, "Piezoelectricity, Its History and Applications," J. Acoust. Soc. Am., 70, (pp. 1561-1566).
40. Holmes, J., Pearce, D., and Button, T., 1999, "Novel PZ Structures for Sensors and Actuators Applications," Ferroelectrics, 224(1-4), pp. 21-28.
41. Weinberg, M. S., 1999, "Working Equations for PZ Actuators and Sensors," J. Microelectromech. Syst., 8(4), pp. 529-533.
42. Barfoot, J., and Taylor, G., 1979, Polar Dielectrics and their Applications, Macmillan Press, New York.
43. Ming-Jen, Pa., et al., 2000, "Comparison of Actuators Properties for PZ and Electrostrictive Materials," Proc. SPIE, 3992, pp. 80-90.
44. Miy, D. K., 1993, Mechatronics, Electromechanics, Springer, New York.
45. Takano, T., Hirata, H., and Tomikawa, Y., 1990, "Non-axisymmetric Contour Vibrations of Clamped PZ Annular Plates," J. Acoust. Soc. Jpn., 11(3), pp. 161-172.
46. Uchino, K., 1996, PZ Actuators and Ultrasonic Motors, Kluwer Academic, Dordrecht, Netherlands.
47. Burdess, J. S., 1986, "The Dynamics of a Thin PZ Cylinder Gyroscope," Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 4, pp. 271-280.
48. Chiba, M., and Wakatsuki, N., 2000, "Temperature Self Compensated Lithium-Tantalate PZ Gyroscope With Higher Stability," Jpn. J. Appl. Phys., Part 1, 39(5B), pp. 3069-3072.
49. Cho, Y. S., and Yoon, K. H., 2001, "Dielectric Ceramics," Handbook of Advanced Electronics and Photonics Materials and Devices, 4, Ferroelectrics and Dielectrics, H. S. Nalwa, ed., Academic Press, San Diego.
50. Cassedy, E. S., 1959, "A Surface Wave Parametric Amplifier," Proc. IRE, 47(8), pp. 374-380.
51. Ingebritsen, K. A., 1969, "Surface Wave in Piezoelectrics," J. Appl. Phys., 40(7), pp. 2681-2686.
52. Sharma, A. K., and Wilson, M. G. F., 1970, "Linear Theory of the Acousto-electric Oscillator," Proc. IEEE, 117(12), pp. 2216-2220.
53. Zjurjukin, Ju. A., Najanov, V. I., and Polotnjagin, V. A., 1970, "To Theory of Hypersound Waves Excitation With PZ Transducers," J. Commun. Technol. Electron., 15(4), pp. 795-804 (in Russian).
54. Zjurjukin, Ju. A., Starukhin, Ju. I., Stephko, V. V., and Khitrin, V. S., 1974, "Investigation of the Operation of Acoustoelectronic Generator of CdS," Sov. Phys. Semicond., 8(6), pp. 1196-1198.
55. Zjurjukin, Ju. A., Stephko, V. V., and Khitrin, V. S., 1973, "To Theory of Acoustoelectronic Generator in for Generation Regime," J. Commun. Technol. Electron., 18(7), pp. 1459-1467.
56. Zjurjukin, Ju. A., Khitrin, V. S., and Shevchik, V. N., 1976, "On Synchronization of the Acoustical Waves in PZ Semiconductors," J. Commun. Technol. Electron., 21(3), pp. 571-573.
57. Brittain, R. H., and Weight, J. P., 1987, "Fabrication of the Non-Uniformly Excited Wide-Band Ultrasonics Transducers," Ultrasonics, 25(2), pp. 100-106.
58. Khoma, I. Ju., 1981, "On Construction of a General Theory of the PZ Shells," Sov. Appl. Mech., 17(2), pp. 115-118.
59. Khoma, I. Ju., 1983, "On the Build-up of a Generalized Theory of Thermopiezoelastic Materials," Sov. Appl. Mech., 19(12), pp. 65-71.
60. Rudnitskii, S. I., and Shul'ga, N. A., 1986, "On a Variant of an Applied Theory of the Piezoceramic Shells," Sov. Appl. Mech., 22(3), pp. 24-30.
61. Zhen-Qiang-Cheng, Lim, C. W., and Kitiporn, Chai S., 1999, "Three-Dimensional Exact Solution for Inhomogeneous Laminated PZ Plates," Int. J. Eng. Sci., 37(11), pp. 1425-1439.
62. Burke, V., Duffi, R. J., Hazony, D., et al., 1976, "Distortion-less Wave Propagation in Inhomogeneous Media and Transmission Lines," Q. Appl. Math., 34(2), pp. 183-194.
63. Drumheller, D. S., and Kalmins, A., 1970, "Dynamical Shell Theory for Ferroelectric Ceramics," J. Acoust. Soc. Am., 47(5), pp. 1343-1353.
64. Ambartsumian, S. A., and Belubekian, M. V., 1987, "The Bending and Vibration of the PZ Ceramic Plates," Electromagnetomechanical Interactions in Deformahle Solids and Structures, Y. Yamamoto, K. Miya, eds., UITAM Symp. Proc., Oct. 17-24, 1986, Tokyo, Japan, Elsevier, North Holland, Amsterdam, pp. 59-67.
65. Parton, V. Z., and Kudrjavtsev, B. A., 1988, Electromagnetoelasticity of Solids: PZ and Electrically Conductive Materials, Gordon Breach, New York.
66. Butcher, P. N., and Janus, H. M., 1971, "The Effect of the Static Field Distribution on the Behavior of Short Acousto-Electric Oscillator," Phys. Lett. A, 37A(3), pp. 210-220.
67. Butcher, P. N., and Janus, H. M., 1972, "The Linear Theory of Acoustoelectric Oscillators With Arbitrary Static Field Distribution," J. Phys. C, 5(5), pp. 567-581.
68. Hench, L. L., and West, J. K., 1990, Principles of Electronic Ceramics, Wiley, New York.
69. 3 Plates and its Applications to PZ Devices," Proc. Ultrasonic Symposium, 2, OF2, 86CH2375-4, pp. 719-722.
70. Ostrovsky, I. V., and Polovina, A. I., 1978, "Acoustical Correlation in the PZ Plate-Like Resonators," Sov. Phys. Solid State, 20(11), pp. 3430-3432.
71. Ostrovskii, I. V., and Bulakh, G. I., 1980, "Second Harmonics of the Acoustoelectric Current in Piezo Semiconductors," Phys. Status Solidi A, 59, pp. 83-89.
72. Ricketts, D., 1980, "Electroacoustic Sensitivity of Composite PZ Polymer Cylinders," J. Acoust. Soc. Am., 68(4), pp. 1025-1029.
73. Ridley, B. K., 1973, "Parametric Processes in the Acoustoelectric Effect," J. Phys. C, 6(9), pp. 1605-1614.
74. Toda, M., and Tosima, S., 1969, "Surface Charge Wave Propagation and Proposed Devices," Jpn. J. Appl. Phys., 8(2), pp. 207-213.
75. Klotin'sh, E., and Kotleris, J., 1986, "Parametric Instability of the Acoustic Waves in Ferroelectric Ceramics Excited by an Electrical Field," Ferroelectrics, 69, pp. 51-57.
76. Gulayev, Y. V., 1970, "On the Non-Linear Theory of Ultrasound Amplification in Semiconductors," IEEE Trans. Sonics Ultrason., SU-17(2), pp. 111-122.
77. McFee, J. H., 1966, "Transmission and Amplification of Acoustic Waves in PZ Semiconductors," Phys. Acoust., 4, Part A, (pp. 1-47).
78. Pekar, S. I., 1965, "Electron-Phonon Interaction Proportional to External Electrical Field," J. Exp. Theor. Phys., 49, pp. 621-628 (in Russian).
79. Pekar, S. I., 1966, "On the Amplification of the Hypersound on Space-Charge Waves in Semiconductors," J. Phys. Soc. Jpn., 21, pp. 448-452.
80. Pekar, S. I., 1976, "Investigation of the Electrostrictive Constants a First and Second Order With Great Dielectric Permeability," Sov. Phys. J., 230(5), pp. 1089-1091.
81. Silberman, P. E., 1967, "To Nonlinear Theory of the Sound Non-Stability," Sov. Phys. Solid State, 9(1), pp. 309-316.
82. Tien, P. K., 1968, "Nonlinear Theory of Ultrasonics Wave Amplification and Current Saturation in Piezosemiconductors," Phys. Rev., 171(3), pp. 970-986.
83. Timan, B. L., 1971, "The Amplification of the Sound in the Piezodielectrics at Space-Charge-Limited Current," Sov. Phys. Solid State, 5, pp. 1275-1277.
84. Weinreich, G., 1956, "Acoustodynamic Effect in Semiconductors," Phys. Rev., 104(2), pp. 321-324.
85. White, D. L., 1962, "Amplification of Ultrasonics Waves in PZ Semiconductors," J. Appl. Phys., 33(8), pp. 2547-2557.
86. Zaitsev, B. D., and Kuznetsova, I. E., 2001, "Electric Field Influence on the Acoustic Waves." Handbook of Advanced Electronics and Photonics Materials ad Devices, vol. 4, Ferroelectrics and Dielectrics, HS Nalwa, ed., Academ. Press, San Diego, pp. 139-174.
87. Pustovoit, V. I., and Gertsenshtein, M. E., 1964, "On the Possibility of the Bending Waves Amplification," Sov. Phys. Solid State, 6(3), pp. 879-887.
88. Belyi, V. N., and Savruk, B. B., 1987, "Parametrical Electroacoustic Effects in Crystals With of External Field Rotate Acoustical Anisotropy," Sov. Phys. Tech. Phys., 57(2), pp. 336-340.
89. Kittinger, E., Tichy, J., and Friedel, W., 1986, "Nonlinear Piezoelectricity and Electrostriction of Alpha-Quartz," J. Appl. Phys., 60(4), pp. 1465-1471.
90. Bolkisev, A. M., and Shul'ga, N. A., 1985, "Forced Oscillations of the Piezoceramic Cylinders With Radial Polarization," Sov. Appl. Mech., 21(5), pp. 118-121.
91. Ostrovskii, I. V., 1980, "Ultrasonics Injection Charge Carriers From the Metal in Piezoelectric," Sov. Phys. Solid State, 22(11), pp. 3459-3460.
92. Bogomol'nyi, V. M., 1994, "Calculation of Harmonically Driven Piezoceramic Transducers," Meas. Tech., 12, pp. 1412-1416. (translate in English).
93. Kossov, G., 1966, "The Effects of Backing and Matching on the Performance of PZ Ceramic Transducers," IEEE Trans. Sonics Ultrason., SU-13(1), pp. 20-30.
94. Bogomol'nyi, V. M., 2000a, "Resonance Calculation for Electrothermal Damage of Metal-Insulator-Metal (MDM) Structures," Meas. Tech., 43(6), pp. 538-543. (transferred in English).
95. Bogomol'nyi, V. M., 2000b, "Calculation of the Critical Parameters of Selfexiting Processes in the Electrothermal Destruction of Dielectric Diodes," Meas. Tech., 43(11), pp. 973-981. (in English).
96. Bogomol'nyi, V. M., 2001, "To the Theory of Nondestructive Testing in Electrical Degradation of Semiconductor Devices," Meas. Tech., 44(5), pp. 513-516. (in English.).
97. Ivanov, I. V., 1968, "Temperature Automatic Stabilization in Microwave Segnetoelectric Resonators at Super-High Frequency Diapason," J. Commun. Technol. Electron., 13 (7), pp. 1291-1295.
98. Vatulyan, A. O., Kiryutenko, A. Ju., and Nasedkin, A. V., 1996, "Plane Waves and Fundamental Solutions in Linear Thermoelectroelasticity, " J. Appl. Mech. Tech. Phys., 37(5), pp. 135-142. (in Russian).
99. Vatulyan, A. O., and Rynkova, A. A., 2001, "Bending Vibrations of the PZ Bimorphs With Internal Cut Electrode," J. Appl. Mech. Tech. Phys., 42(1), pp. 184-189.
100. Le, K. C., 1982, "Long Wave High Frequency Oscillations of PZ Plates," Sov. Phys. Dokl., 264(3), pp. 581-583.
101. Le, K. C., 1997, "High Frequency Vibrations and Wave Propagation in Elastic Shells: Variational-Asymptotic Approach," Int. J. Solids Struct., 34(10), pp. 3929-3939.
102. Ass, E. I., and Gribov, N. N., 1987, "Estimation of the Elastic Dissipation Length of Current Carriers in Microcontacts," Phys. Low Temperat., 13(6), pp. 645-647. (in Russian).
103. Bogomol'nyi, V. M., 1999, "To Dynamical Theory of Electrothermal Degradation and Nondestructive Testing (NDT) of the Defects in MDM Structures," Proc. SPIE, 3700, pp. 436-444.
104. Itskovich, I. F., Moskaets, M. V., Shekhter, R. I., and Kulik, I. O., 1987, "Thermoelectric Phenomena in Microcontacts in Heating Limit," Phys. Low Temperat, 13(10), pp. 1034-1045 (in Russian).
105. Linford, R. G., and Mitchell, L. A., 1971, "Interplanar Potentials Function for Calculating Surface Energies and Cohesive Stresses," Surf. Sci., 27, pp. 142-146.
106. Mindlin, R. D., 1972, "Elasticity, Piezoelectricity and Crystal Lattice Dynamics," J. Elast., 2(4), pp. 217-282.
107. Bedford, A., and Drumheller, D. S., 1993, Introduction to Elastic Wave Propagation, Wiley, New York.
108. Ambardar, A., and Ferris, C. D., 1978, "Wave Propagation in a PZ Two-Layered Cylindrical Shell With Hexagonal Symmetry (Some Applications to Long Bone)," J. Acoust. Soc. Am., 65(3), pp. 781-792.
109. Adelman, N. T., and Stavsky, Y., 1980, "Flexural-Extensional Behavior of Composite PZ Circular Plates," J. Acoust. Soc. Am., 67(3), pp. 819-822.
110. Dianov, D. B., and Kuz'menko, A. G., 1970, "Calculation of the Cylindrical PZ Transducers at Radial-Symmetrical Radiation," Sov. Acoust. J., 16(1), pp. 42-48.
111. Dianov, D. B., Zadirenko, I. M., and Kuz'menko, A. G., 1973, "Investigation of Frequency Characteristics and Direction of Radiation of Cylindrical Transducers With Soft Screening," Sov. Acoust. J., 19(5), pp. 677-684.
112. Lazutkin, V. N., and Tsyganov, Ju. V., 1971, "Axissymmetrical Oscillation Modes and Electrical Impedance of the Rings With Radial Polarization," Sov. Acoust. J., 17(3), pp. 394-399.
113. Adelman, N. T., Stavsky, Y., and Segal, E., 1975, "Radial Vibrations of the Axially Polarized PZ Ceramic Cylinders," J. Acoust. Soc. Am., 57(2), pp. 356-360.
114. Dökmeci, M. C., 1978, "Theory of Vibrations of Coated Thermopiezoelectric Laminae," J. Math. Phys., 19(1), pp. 109-126.
115. Dökmeci, M. C., 1990, "Shell Theory for Vibrations of Piezoceramics Under Bias," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 37(5), pp. 369-383.
116. Paul, H. S., and Vanntessan, M., 1987, "Vibration of a Hollow Circular Cylinder of Piezoceramics," J. Acoust. Soc. Am., 82(3), pp. 952-956.
117. Matrosov, A. A., and Ustinov, Ju. A., 1984, "Homogeneous Solution of Steady Vibrations of Piezoceramic Cylinder Problem," J. Appl. Math. Mech., 48(6), pp. 1045-1049 (In Russian).
118. Ganapathi, M., and Makhecha, D. P., 2001, "Free Vibration Analysis of the Multilayer Composite Laminates Based on Accurate Higher-Order Theory," Composites, Part B, 32(6), pp. 535-543.
119. Reissner, E., 1979, "Note on the Effect of Transverse Shear Deformations in Laminated Anisotropic Plates," Comput. Methods Appl. Mech. Eng., 20(12), pp. 203-209.
120. Tiersten, H. F., 1993, "Equations for the Extension and Flexure of Thin Electroelastic Plates Under Large Electric Fields," ASM AMD, 161, pp. 21-34.
121. Varadan, V. V., Jeng, J. H., and Varadan, V. K., 1987, "Form Invariant Con-stitutive Relations for Transversaly Isotropic PZ Materials," J. Acoust. Soc., Am., 82, pp. 337-341.
122. Hou-Cheng, H., 1989, Static and Dynamic Analysis of Plates and Shells, Springer, London.
123. Maugin, G. A., and Attou, D., 1990, "An Asymptotic Theory of Thin PZ Plates," Q. J. Mech. Appl. Math., 43(3), pp. 347-363.
124. Rogatcheva, N. N., 1981, "Constitutive Equations of Piezoceramic Shells," J. Appl. Math. Mech., 45(5), pp. 902-911 (in Russian).
125. Berdichevskii, V. L., 1979, "Variational-Asymptotic Method Construction of the Shell Theory," J. Appl. Math. Mech., 43(4), pp. 664-687.
126. Berdichevskii, V. L., 1980, "Variational-Asymptotic Method of Construction the Non-Linear Shell Theory," Theory of Thin Shells, Proc. 3rd UITAM Symposiun, W. T. Koiter and G. K. Mikhailov, eds., Tbilisi, Russia, August 22-28, 1978, North-Holland, Amsterdam, pp. 75-91.
127. Berdichevskii, V. L., and Le, K. C., 1982, "High Frequency Vibrations of Shells," Sov. Phys. Acoust., 27(11), pp. 988-990.
128. Ustinov, Ju. A., 1975, "Axissymmetrical Stress-Strain State of the Nonhomogeneous Thin Cylindrical Shell, Sov. Appl. Mech., 11(7), pp. 35-41.
129. German, I. P., and Ustinov, Ju. A, 1979, 'To Theory of Nonhomogeneous Plates," J. Appl. Math. Mech., 43(5), pp. 923-935.
130. Vatulyan, A. O., Getman, I. P., and Lapitskaya, N. E., 1991, "On Bending of the PZ Bimorph Plate," Sov. Appl. Mech., 27(10), pp. 101-105.
131. Vatuljan, A. O., Nasedkin, A. V., and Skaliuch, A. S., 1993, "Vibration of the Cantilever PZ Plate With Goffered Washer," J. Appl. Mech. Tech. Phys., 4, pp. 118-123.
132. Rasskazov, O. O., Kozlov, V. I., and Karnauchova, T. V., 1999, "Transverse Oscillations and Vibration Heating Rectangular Bimorph Plate of Dissipative Material," Sov. Appl. Mech., 39(9), pp. 85-93.
133. Croitoro, E., and Singh, M., 1987, "Perturbation Torsion About a Finite Ex-tension an Elastic Dielectrics," ZAMP, 38(3), pp. 450-458.
134. Lee, P. C. Y., Kuong-Ming, W., and Wang, Y. S., 1978, "Effect of Accelera-tion on Resonance Frequencies of a Crystal Plates," J. Acoust. Soc. Am., 63(4), pp. 1039-1047.
135. Yang, J. S., Fang, H. Y., and Jiang, Q., 2000, "A Vibrating PZ Ceramic Shell as a Rotation Sensor," Smart Mater. Struct., 9(4), pp. 445-451.
136. Bogomol'nyi, V. M., 1991, "To Calculation of the PZ Transducers, Meas. Tech., 11, pp. 54-56.
137. Bogomol'nyi, V. M., 1981, "To Calculation of the Piezoceramic Shells at Electrostatic Loading, Sov. Phys. Tech. Phys., 51, pp. 1284-1287.
138. Bogomol'nyi, V. M., 1983a, 'To Dynamical Calculation of the Electroelastic Piezoceramic Toroidal Shells," Sov. Appl. Mech., 19(6), pp. 98-101.
139. Bogomol'nyi, V. M., 1983b, "To Calculation of Thin Electroelastic Toroidal Shells," Sov. Appl. Mech., 19(4), pp. 114-117.
140. Bogomol'nyi, V. M., 1988, "Calculation of the Electrostrictive Effect in Prestressed Ferroelectric Shells," Sov. J. Contemp. Eng. Mech., 41, pp. 33-37.
141. Bogomol'nyi, V. M., 1992, "Calculation of the Electrostrictive Effect in Prestressed Ferroelectric Ceramic Shell Under Harmonical Excitation, J. Appl.Mech. Tech. Phys., 2, pp. 150-155.
142. Bogomol'nyi, V. M., 1994, "Calculation of the Harmonically Driven Piezoceramic Transducers, Meas. Tech., 12, pp. 1412-1416.
143. Bogomol'nyi, V. M., 1995d, "Calculation of the PZ Transducers on Base MDM Structures," Meas. Tech., 2, pp. 50-54.
144. Bolkisev, A. M., Rudnitsky, S.I., and Shulga, N. A., 1985, "Comparative Analysis of the Forced Oscillations of the Electroelastic Shells With Engineering and Three-Dimensional Theories," Sov. Appl. Mech., 21(4), pp. 19-24.
145. Boriseiko, V. A., Grinchenko, V. T., and Ulitko, A. F., 1976, "Relations of Electroelasticity for Piezoceramic Shells," Sov. Appl. Mech., 12(2), pp. 26-33.
146. Chang, S. H., Du, B. C., and Lin, J. F., 1999, "Electroelastic Modelling of Annular Piezoceramic Actuating Disk Transducers," J. Intell. Mater. Syst. Struct., 10(5), pp. 410-421.
147. Chen, W. Q., 2001, "Free Vibrations of Laminated PZ Hollow Spheres," J. Acoust. Soc. Am., 109(1), pp. 41-50.
148. Chowdury, K. L., and Glockner, P. G., 1979, "Some Exact Solutions in Elastic Dielectrics," Bull. Int. Acad. Pol. Sci. Ser. Techn., 27(5/6), pp. 181-191.
149. Correia, J. F. P., Soares, C. M. M., Soares, C. A. M., and Herskovits, J., 1999, "Development of Semi-Analytical Axissymmetrical Shell Models With Embedded Sensors and Actuators," Compos. Struct., 47(1-4), pp. 531-543.
150. Duppare, J., Bücker, P., Götz, B., and Mairtin, Th., 2000, "Theoretical and Experimental Investigation of Significant Characteristics Parameters of PZ Actuators," Proc. SPIE, 3985, pp. 672-677.
151. Hayward, G., and Hossak, J., 1990, "Unidimensional Modelling of Composite Transducers," J. Acoust Soc. Am., 88(2), pp. 599-608.
152. Lee, P. C. Y., 1971, "Extensional Flexural and Width Shear Vibration of Thin Rectangular Plates," J. Appl. Phys., 42(11), pp. 4139-4144.
153. Lee, P. C. Y., and Lin, W. S., 1998, "PZ Forced Vibrations of Rectangular SC-Cut Quartz Plates," J. Appl. Phys., 83, pp. 7822-7833.
154. Ren, J. G., 1974, "Exact Solution for Laminated Cylindrical Shells in Bending," IEEE Trans. Sonics Ultrason., 21(4), pp. 257-268.
155. Vekovisheva, I. A., 1971, "Variational Principles in Theory of Electroelasticity," Sov. J. Appl. Phys., 7(9), pp. 129-133.
156. Vekovisheva, I. A., 1973, "Bending of the Rectangular Plate Fast Clamped at its Outline," Sov. J. Contemp. Eng. Mech., 26 (3), pp. 58-64.
157. Vekovisheva, I. A., 1975, "Bending of Thin PZ Plates Under the Action of the Electrical Charges, Sov. J. Appl. Phys., 10, pp. 275-278.
158. Gopinathan, S. V., Varadan, V. V., and Varadan, V. K., 2000, "A Review and Critique of Theories for PZ Laminates," Smart Mater. Struct., 9(1), pp. 24-48.
159. Bogomol'nyi, V. M., and Zhidjaev, N. A., 1990, "The Choice of the Optimal Excitation Frequency of the Piezoceramic Transducers," Izv. Sibirian Dept. Acad. Sci. Sov. Union, 1, pp. 79-81
160. (translated in English Sov. J. Appl. Phys.).
161. Collet, M., 2001, "Shape Optimization of PZ Sensors Dealing With SpillOver Instability," IEEE Trans. Control Syst. Technol., 9(4), pp. 654-662.
162. Francis, D. T., Ahmad, J., Baylis, C., and Coats, R. F., 1994, "Finite and Boundary Element Modelling of Class III Flextensional Transducers for Ocean Tomography," Proc. Second European Conf. Underwater Acoustic, Vol. 1, Brussels, July 4-8, Lyngby, pp. 515-520.
163. Kim, S. I., and Jones, J. D., 1990, "Optimal Design of Piezoactuators for Active Noise and Vibration Control," Paper 13th Aeroacoust Conf. Amer. Inst, of Aeronaut. Astronaut, AIAA Paper No. 90-3925.
164. Ko, S., and Pond, H. L., 1970, "Improved Design of Spherical Multimode Hydrophone, J. Acoust. Soc. Am., 64(5), pp. 1270-1277.
165. Rogers, P. H., 1986, "Mathematical Model for a Free-Flooded PZ Cylinder Transducer," J. Acoust. Soc. Am., 80 (1), pp. 13-18.
166. Soares, C. M., Soares, C. A., and Correia, V. M., 1999, "Optimal Design of Piezolaminated Structures," Compos. Struct., 47(1-4), pp. 625-634.
167. Kepler, R. G., and Anderson, R. A., 1992, "Ferroelectric Polymers," Adv. Phys., 41, pp. 1-57.
168. Lerch, R., 1981, "Electromechanical Properties of Piezopolymer Microphones," J. Acoust. Soc. Am., 69 (6), pp. 1809-1814.
169. Verma, P. D.S., 1988, "Radial Oscillations of an Elastic Semiconductors," Int. J. Eng. Sci., 26(1), pp. 27-36.
170. Emets, Ju. P., 2001, "Electrical Characteristics Three-Component Dielectric Composite With Density Package of the Inclusions," J. Appl. Mech. Tech. Phys., 42, 1(248), pp. 165-176.
171. Kagawa, Y., and Yamabuchi, T., 1977, "Finite Element Simulation of Composite Electrostrictive Resonators," Proc. Ultrasonics International Conference (UI 77), June 28-30, Business Press, Brighton, UK, pp. 138-144.
172. Bisegna, P., and Luciano, R., 1996, "Variational Bounds for the Overall Properties of PZ Composites," J. Mech. Phys. Solids, 44 (4), pp. 573-602.
173. Rjazantseva, M. Ju., 1985, "Bending Oscillations of Three-Layer Plates of the Symmetrical Structure," Mech. Solids, 3, pp. 153-159.
174. Goldenveiser, A. L., 1963, "Constructing of the Approximate Shell Theory by Asymptotic Integration of Elasticity Theory Equations," J. Appl. Math. Mech., 27(4), pp. 593-608.
175. Khudik, B. I., and Chernjavskii, K. E., 1990, "Dispersion Relations of the Electroelastic Oscillations of Thin PZ Plates," Sov. Phys. Solid State, 32(8), pp. 2472-2474.
176. Clark, R. A., 1958, "Asymptotic Solutions of Toroidal Shell Problem," Q. Appl. Math., 16(1), pp. 47-60.
177. Langer, R. E., 1949, "The Asymptotic Solution of Ordinary LinearDifferential Equations of Second Order With Special Reference to a Turning Point," Trans. Am. Math. Soc., 67, pp. 461-490.
178. Tumarkin, S. A., 1959, "Asymptotic Solution of the Linear Nonhomogeneous Differential Equation of Second Order With Turning Point and its Application to Toroidal Shell Calculation," J. Appl. Math. Mech., 23(6), pp. 1083-1094.
179. Sibiya, Y., 1974, "Uniform Simplification in a Full Neighborhood of a Transition Point," Mem. Am. Math. Soc., 149, pp. 106-114.
180. Zhang, R. J., 1991, "Higher Approximations to the Homogeneous Solution for Toroid," Acta Mech. Sin., 4(4), pp. 363-368.
181. Kudrjavtsev, B. A., Parton, V. Z., and Rakitin, V. I., 1975, "Fracture Mechanics of PZ Materials With Straight Line Tunnel Crack on the Conductor Boundary," J. Appl. Math. Mech., 39(1), pp. 149-159.
182. Belokopytova, L. V., and Filshtinskii, L. A., 1979, "Two Dimensional Boundary Problem of the Electroelasticity of the PZ Media With Cuts," J. Appl. Math. Mech., 43(1), pp. 138-143.
183. Filshtinskii, L. A., and Khizhnjak, L. A., 1983, "Reaction of the Piezoceramic Shell Under Concentrated Loading," J. Appl. Math. Mech., 47(3), pp. 478-482.
184. Hao, T. H., Gong, X., and Suo, Z., 1996, "Fracture Mechanics for the Design of Ceramic Multilayer Actuator," J. Mech. Phys. Solids, 44(1), pp. 23-48.
185. Ru, C. Q., Mao, X., and Epstein, M., 1998, "Electric Field Induced Interfacial Cracking in Multilayer Electrostrictive Actuators," J. Mech. Phys. Solids, 46(8), pp. 1301-1318.
186. Kreher, W. S., 2002, "Influence of Domain Switching Zones on the Fracture Toughness of Ferroelectrics," J. Mech. Phys. Solids, 50(5), pp. 1029-1050.
187. Bogomol'nyi, V. M., and Shwetz, A. V., 1985, "To Estimation of PZ Transducers Temperature Under Harmonical Excitation," J. Eng. Phys., 58(1), pp. 86-89.
188. Bogomol'nyi, V. M., and Gidjaev, N. A., 1984, 'The Influence of Harmonical Excitation on PZ Transducers Temperature," Sov. Phys. Tech. Phys., 54(4), pp. 851-853.
189. Bogomol'nyi, V. M., 1997, "Analysis of the Losses, Temperature Behavior and Optimal Excitation Frequency of PZ Transducers," Meas. Tech., 3, pp. 53-58.
190. Bogomol'nyi, V. M., 1998, "Calculation of Dissipation Energy and Heating Temperature of the Piezoelectric MDM Structures," Meas. Tech., 12, pp. 47-50.
191. Erofeev, S. A., 1998, "Nonlinear Problems of Electrothermoelasticity," J. Commun. Technol. Electron., 43(1), pp. 100-111.
192. Linhardt, F., and Oberst, H., 1961, "Uber temperature abhängingkeit schwingungdampfender künststoffe," Akustishe Beihefte, 1, pp. 255-264.
193. Lindefeit, U., 1994, "Heat Generation in Semiconductor Devices," J. Appl. Phys., 75(2), pp. 942-957.
194. Mezheritsky, A. V., 1984, "Energy Losses in Piezoceramics Under Electrical Excitation," Electricity, 10, pp. 65-67.
195. Ter-Martirosian, L. T., 1975, "Parametric Heating of the Acoustical Modes in Non-Linear Dielectrics," J. Commun. Technol. Electron., 20(12), pp. 2592-2598.
196. Holland, R., and Eer, Nisse E., 1968, Design of Resonant PZ Devices, MIT Press, Cambridge, MA.
197. Qin, Q. H., 2000, "General Solutions for Thermoelectroelastics With Various Holes Under Thermal Loading," Int. J. Solids Struct., 37, pp. 5561-5578.
198. Qin, Q. H., 2000, "Thermoelectroelastic Solution on Elliptic Inclusions and its Application to Crack-Inclusion Problems," Appl. Math. Model., 25, pp. 1-23.
199. Kornilov, V. M., and Lachinov, A. N., 1997, "Electrical Conductivity in the Metal-Polymer-Metal System and a Role of Boundary Conditions," J. Exp. Theor. Phys., 84(4), pp. 327-337.
200. Cherepanov, G. P., 1994, "On the Theory of Thermal Stresses in a Thin Film on a Ceramic Substrate," J. Appl. Phys., 75(2), pp. 844-849.
201. Rana, A. P.S., 1986, "Temperature Internal Friction Background in Polycrystals," J. IES, 94(10), pp. 1029-1035.
202. Ames, K. A., and Payne, L. E., 1994, "Uniqueness and Continuous Dependence of Solutions to a Multidimensional Thermoelastic Contact Problem," J. Elast., 2, pp. 139-148.
203. Homberg, D., Khludnev, A. M., and Sokolovsku, J., 1999, "On Equilibrium Problem for a Cracked Body With Electrothermoconductivity," Les. Prepubl. Inst Elie Cartan., 23, pp. 1-16.
204. Wang, B. L., and Mai, Y. W., 2003, "Thermal Shock Fracture of PZ Materials," Philos. Mag., 83(5), pp. 631-657.
205. Gray, E., 1968, "Thermal Effects on Space-Charge-Limited Current Flow in Solids," J. Phys. B, 14(6), pp. 374-377.
206. Young, J. H., 1987, "Quasi-Linear Electrical Potentials in Steady-State Joule Heating," J. Eng. Math., 21(1), pp. 33-40.
207. Chandrasekharajah, D. S., 1988, "A Generalized Thermoelasticity Theory of PZ Media," Acta Mech., 71(1/4),ss pp. 39-49.
208. Nowick, A. S., and Berri, B. S., 1972, An Elastic Relaxation in Crystalline Solids, Academic, New York.
209. Yamauchi, F., and Takahashi, M., 1970, "Internal Friction of Modified Lead-Zirkonate-Titanate Ceramics," J. Phys. Soc. Jpn., 28 Suppl., pp. 313-315.
210. Garcia, J. E., Perez, R., and Albareda, A., 2001, "High Electric Field Measurement of Dielectric Constant and Losses of Ferroelectric Ceramics," J. Phys. D, 34(22), pp. 3279-3284.
211. Qin, Q. H., 2001, Fracture Mechanics of Piezoelectric Materials, WIT Press, Southampton.
212. McMeeking, R. M., 2001, "Towards a Fracture Mechanics for Brittle Piezoelectric and Dielectric Materials," Int. J. Fract., 108(1), pp. 25-41.
213. Robeis, U., and Arlt, G., 1993, "Domain Wall Clamping in Ferroelectric by Orientation of Defects, J. Appl. Phys., 73(7), pp. 3454-3460.
214. Robels, U., Calderwood, J. H., and Arlt, G., 1995, "Shift and
215. Fuling, S., Kuna, M., and Scherzer, M., 2000, "Analytical Solution for Two Penny-Shaped Crack Problem in Thermo-Piezoelectric Materials and Their Finite Element Comparisons," Int. J. Fract., 117(1), pp. 113-121.
216. Singh, R. N., 2001, "Electromechanical Response of Cracks Materials," 25th Annual Conference of Composites. Advanced Ceramics, Materials and Structures: B, Cocoa Beach. FL, Jan. 21-27, 2001, Westerville. Amer. Ceram. Soc., OH, pp. 509-520.
217. Fan, H., Park, G. T., Choi, J. J., Rui, J., and Kun, H. F., 2002, "Preparation and Improvement in the Electrical Properties of Lead-Zinc-Niobate Based Ceramics by Thermal Treatment," J. Mater. Res., 17(1), pp. 180-185.
218. Pak, Y. E., 1992, "Linear Electro-Elastic Fracture Mechanics of Piezoelectric Materials," Int. J. Fract., 54, pp. 79-100.
219. Fantini, E. et al., 2001, "Failure Mechanisms in Compound Semiconductor Electron Devices," Handbook of Advanced Electronic and Photonics Materials, 2, Semiconductor Devices. H. S. Nalwa, ed., Academic, San Diego, pp. 155-157.
220. Markenscoff, X., 1993, "On the Dundur's Correspondence Between Cavities and Rigid Inclusions," Trans. ASME, J. Appl. Mech., 60(2), pp. 260-264.
221. Deeg, W. F., 1980, "The Analysis of Dislocation, Crack and Inclusion Problem in PZ Solids," Ph.D. thesis, Stanford University, Stanford, CA.
222. Wang, B., 1992, "Three Dimensional Analysis of an Ellipsoidal Inclusion in a PZ Material," Int. J. Solids Struct., 29(3), pp. 293-308.
223. Li, Y., Sato, Y., and Watanabe, K., 2002, "Stress Singularity Analysis of Axisymmetric PZ Bonded Structure," JSME Int. J., Ser. A, 45(3), pp. 363-370.
224. Inglis, C. E., 1913, "Stresses in a Plate Due to Presence of Cracks and Sharp Corners," Engineering (London), 95(2462), pp. 415-418
225. (see also Trans. Inst. Naval. Architectes, 55, 219-230).
226. Griffith, A. A., 1970, "The Phenomena of Rupture and Flow in Solids," Philos. Trans. R. Soc. London, Ser. A, 221, pp. 163-198.
227. Shin, C. S., 1986, "A Discussion on Various Estimation of Elastic Stresses Distribution and Stress Concentration Factors for Sharp Edge Notches," Int. J. Fatigue, 8(4), pp. 235-237 (Techn. Notes).
228. Machova, A., 2001, "Stress Calculation on Atomistic Level," Modell. Simul. Mater. Sci. Eng., 9(4), pp. 327-337.
229. Antontsev, S. N., and Chirot, M., 1994, "The Thermistor Problem Existence, Smoothness, Uniquess, Blowup," SIAM J. Math. Anal., 25(4), pp. 1128-1156.
230. Sakagami, T., and Rubo, S., 1999, "Development of a New Crack Identification Method Based on Singular Current Measurement Using Differential Thomography," Proc. SPIE, 3700, pp. 369-376.
231. Endo, M., 1989, "Measurement of Surface Crack Depth by Surface Temperature Difference," Imono (Japan), 6(9), pp. 650-655.
232. Vladimirov, A. F., and Moos, E. N., 1998, "A Parameter of the Electron Working Function in Ion Spectroscopy," Bull. Russ. Acad. Sci. Phys., 62(7), pp. 1445-1450.
233. Govorukha, V. B., and Loboda, V. V., 2000, "Contact Zone Models for an Interface Crack in a Piezoelectric Material," Acta Mech., 140, pp. 233-246.
234. Nishioka, T., and Shen, S., 2001, "Higher Order Asymptotic Solution for an Interfacial Crack in PZ Bimaterials Under Impact," Mater. Sci. Res. Int., 7(3), pp. 157-165.
235. Shirakihara, K., et al., 2002, "Effect of Polarization on Deformation and Fracture of PZ Ceramics," J. Soc. Mater. Sci. Jpn., 51(7), pp. 736-742.
236. Ueda, S., 2002, "The Mode/Crack Problem Layered PZ Plates," Int. J. Fract., 114(1), pp. 63-86.
237. Oates, W. S., and Lynch, C. S., 2003, "New Approach to Solving Crack Tip Stress Fields for PZ Materials," Active Materials: Behavior and Mechanics, San Diego, C. A., Mar. 3-6, 2003, SPIE, Bellingham, WA, pp. pp. 376-386.
238. Arai, M., Sato, Y., and Adachi, T., 2003, "Elastodynamic Crack Analysis by Boundary Element Method Using Inversion Laplace Transformation, " JSME Int. J., Ser. A, 46(2), pp. 131-139.
239. Ricoer, A., and Kuna, M., 2003, "Influence of the Fracture Process Zone in Ferroelectric on the Effective Fracture Toughness," Active Materials: Behavior and Mechanics, San Diego, C. A., Mar. 3-6, 2003, SPIE, Bellingham, WA, pp. 395-404.
240. Yocum, M., Abramovich, H., et al., 2003, "Fully Reversed Electromechanical Fatigue Behavior of Composite Laminate With Embedded PZ Actuator/ Sensor," Smart Mater. Struct., 12(4), pp. 556-564.
241. Mindlin, R. D., 1968, "Polarization Gradient on Elastic Dielectrics," Int. J. Solids Struct., 4, pp. 637-642.
242. Mindlin, R. D., 1969, "Continuum and Lattice Theories of Influence of Electromechanical Coupling on Capacitance of Thin Dielectric Film," Int. J. Solids Struct., 5, pp. 1197-1208.
243. Mindlin, R. D., 1972, "Polarization Gradient in Elastic Dielectrics," Course held at Dept Mechanics Deformable Bodies, Udine CISM Springer, Wien.
244. Mindlin, R. D., and Applied Mechanics, 1974, A Coll. Studies in Development of Applied Mechanics G. Hermann, ed., Pergamon, New York.
245. Deresiewicz, H., et al., eds., 1989, The Collected Papers of Raymond D. Mindlin: The Late James Finch Prof-Emeretus of Appl. Sci. Columbia University, Springer, New York.
246. Shao, J., and Wright, G. T., 1961, "Characteristic of the Space-ChargeLimited Dielectric Diode at Very High Frequencies," Solid-State Electron., 3(13), pp. 291-303.
247. Moriarty, J. A., 1981, "Small-Signal AC Response of Dielectric Materials Containing Static Space-Charge Fields: Applications to Ionic Conductors and MIS Structures," J. Appl. Phys., 52(5), pp. 3413-3427.
248. Strashilov, V. L., and Nadolinskii, M. M., 1989, "Thickness-Shear Approximation for PZ Ceramic Plates," Int. J. Electron., 66(3), pp. 399-408.
249. Williams, W. S., 1983, "Piezoelectricity and lnhomogeneity in Ceramics, Polymer and Bone," Ferroelectrics, 51(1/2), pp. 61-69.
250. Gross, B., von Seggern, H., and Gerhardt-Multhaupt, R., 1985, "Carrier Mobilities in Polyvinylidenefluoride," J. Phys. D, 18(12), pp. 2497-2504.
251. Lang, S. B., and Yin-Qing-Rui, 1987, "Poling Techniques for Producing Non-Uniform Polarization Distribution in PSZT Ceramics," Ferroelectrics, 76(3/4), pp. 443-450.
252. Fowler, R. H., and Nordheim, L., 1928, "Electron Emission in Intense Electric Fields, Proc. R. Soc. London, Ser. A, 119A, pp. 173-181.
253. Skrjabysheva, I. Ju., 1998, "The Calculation of the Radiation-Induced Conductivity Current in Dielectrics Irradiated With High-Energy Electron and Proton for Two-Component Maxwellian Distribution," Meas. Tech., 11, pp. 6-12.
254. Hench, L. L., and Dove, D. B., eds., 1971, Physics of Electronic Ceramics, Part A, Marcel Dekker, New York.
255. Fan, H. Y., 1948, "Theory of Rectification of an Insulating Layer," Phys. Rev., 74(10), pp. 1505-1513.
256. Cohen, J, 1957, "Electrical Conductivity of Fused Quartz," J. Appl. Phys., 28(7), pp. 795-800.
257. Sedov, L. I., 1968, "Models of Solid Media With Internal Freedom Degrees," J. Appl. Math. Mech., 32(5), pp. 771-785 (in Russian).
258. Carrera, E., 2001 "Development, Ideas, and Evolution Based Upon Reissner's Mixed Variational Theorem in the Modelling of Multilayered Plates and Shells," Appl. Mech. Rev., 54(4), pp. 301-329.
259. Kadoli, R., and Ganesan, N., 2004, "Studies on Dynamic Behavior of Composite and Isotropic Cylindrical Shells With PZT Layers Under Axisymmetric Temperature Variation," J. Sound Vib., 271(1-2), pp. 103-130.
260. Nagata, K., Thongrueng, J., and Kato, K., 1997, "Evaluation of the Reliability of Piezoelectric Transformers," Jpn. J. Appl. Phys., Part 1, 36(9b), pp. 6103-6105.
261. Luchaninov, A. G., 2000, "Domain-Wall Contribution to the Piezoeffect in BaTiO3 Ceramics," Proc. SPIE. 7th Int. Symp. on Smart Structures and Materials, March 5-9, Newport Beach, CA, pp. 13-21.
262. 3 Ceramics," J. Phys. D, 34(15), pp. 2353-2358.
263. Sheikh, N. A., Ahmad, J., Upadhyay, C. S., and Venkatesan, C., 2002, "Electro-Thermo-Elastic Formulation and Analysis of PZ Beam," Proc. SPIE, Bellingham, WA, 5062, pp. 225-232.
264. Pamidighatam, S., Puers, R., Baert, K., and Tilmans, H. A. C., 2002, "Pull in Voltage Analysis of Electrostatically Actuated Beam Structures With FixedFixed and Fixed-Free End Conditions," J. Micromechanics Microengineering Structures, Devices and Systems, 12(4), pp. 458-464.
265. Sehr, H., Tomlin, I. S., Huang, B., Beeby, S. P., Evans, A. G. R., Brunnschweiler, A., Ensell, G. J., Schabmueller, C. G. J., and Nibbok, T. E. G., 2002, "Time Constant and Lateral Resonances of Thermal Vertical Bimorph Actuators," J. Micromech. Microeng. Struct. Devices and Systems, 12(4), pp. 410-413.
266. Varadan, V. K., Vinny, K. J., and Jose, K. A., 2003, "RF MEMS and Their Applications," Wiley, Atrium, South Gate, Chichester.
267. Diestelhorst, M., 2003, "What Can Learn About Ferroelectrics Using Methods of Nonlinear Dynamics," Condens. Matter Phys., 6(34), pp. 189-196.
268. Kapsh, R. P., Kantz, H., Hegger, R., and Diestelhorst M., 2001, "Determination of the Dynamical Properties of Ferroelectrics Using Nonlinear Time Series Analysis," Int. J. Bifurcation Chaos Appl. Sci. Eng., 11(3), pp. 1019-1034.
269. Damjanovic, D., 1997, "Stress and Frequency Dependence of the Direct PZ Effect in Ferroelectric Ceramics," J. Appl. Phys., 82, pp. 1788-1797.
270. Silva, E. C., and Kikuchi, N., 1999, "Design of Piezocomposite Materials and Piezoelectric Transducers Using Topology Optimization. Part 1," Comput. Math. Eng., 6(2), pp. 117-182.
271. Jinghua, Zhong, Seeleke, S., et al., 2003, "Optimal Control of PZ Actuators, Modelling, Signal Processing and Control. San Diego, CA. Mar. 3-6, 2003, Bellingham, WA.," Proc. SPIE, 5049, pp. 264-274.
272. Bai, M. R., and Huang, Ch., 2003, "Optimization and Implementation of PZ Radiators Using a Genetic Algorithm," J. Acoust. Soc. Am., 113(11), pp. 3197-3208.
273. Del'Isola, F., Henneke, E. G., and Porfiri, M., 2003, "PiezoelectromechanicalStructures: A Survey of Basic Concepts and Methodologies," Proc. SPlE, 5056, pp. 574-582.
274. Bruch, J. C., Jr., Sloss, J. M., Adali, S., and Sadek, I. S., 2000, "Optimal Piezoactuator Locations/Lengths and Applied Voltage for Shape Control of Beams," Smart Mater. Struct., 9(2), pp. 205-211.
275. Adachi, K., Takahshi, T., and Hasegawa, H., 2004, "Analysis of Screw Pitch Effects on the Performance of Bolt-Clamped Langevin-Type Transducers," J. Acoust. Soc. Am., 116(3), pp. 1544-1548.
276. Maurizio, R., 2004, "Electromagnetoacoustic Surface Waves on Dispersive PZ Layered Media," J. Acoust. Soc. Am., 116(3), pp. 1488-1497.
277. 2 Models With Hydrogenated Impurities and Charges," Appl. Surf. Sci., 216(1-4), pp. 463-470.
278. Ricoeur, A., and Kuna, M., 2003, "A Micromechanical Analysis the Fracture Process Zone in Ferroelectrics, Comput. Mater. Sci., 27(3), pp. 235-239.
279. 2 and Related Dielectrics: Science and Technology, Pbl. Ser. II: Math. Phys. Chemistry. 2000.G. Pacchioni, L. Skuja, and D. L.Griscom, Kluwer Academic, Dordrecht.
280. Stapper, C. H., el al., eds., 1990, Defect and Fault Tolerance in VLSI Systems, Vol. 2, Plenum, New York.
281. Bogomol'nyi, V. M., ed., 2004, "Electrophysical Method for Evaluating the Fracture Surface Energy of Dielectric Materials in Contact With Metal," Meas. Tech., 47(10), pp. 1025-1031.
282. Ray, M. C., 2003, "Optimal Control of Laminated Shells Using PZ Sensor and Actuator Layers," AIAA J., 41(6), pp. 1151-1157.
283. Mallik, N., and Ray, M. C., 2003, "Effective Coefficients of PZ Fiber-Reinforced Composites," AIAA J., 41(4), pp. 704-710.
284. Onoda, J., et al., 2003, "Energy-Recycling Semi-Active Method for Vibration Suppression with PZ Transducers," AIAA J., 41(4), pp. 711-719.
285. Lesieure, G. A., 1998, "Vibration Damping and Control Using Shunted PZ Materials," Shock Vib. Dig., 30(3), pp. 187-195.
286. Heyliger, P. R., 2004, "Static Fields in Magneto-Electro-Elastic Laminates," AIAA J., 42(7), pp. 1435-1444.
287. Pan, E., 2001, "Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates," J. Appl. Mech., 68, pp. 608-618.
288. Pan, E., and Heyliger, P. R., 2002, "Free Vibrations of Simply Supported and Multilayered Magneto-Electro-Elastic Plates," J. Sound Vib., 252, pp. 429-442.
289. Sun, D., and Tong, L., 2003, "Optimum Control Voltage Design for Constrained Static Shape Control of Piezoelectric Structures," AIAA J., 41(12), pp. 2444-2450.
290. Paradies, R., Hertwig, M., and Elspass, W. J., 1996, "Shape Control of an Adaptive Mirror at Different Angles of Inclination," J. Intell. Mater. Syst. Struct., 7(2), pp. 203-210.
291. Irschik, H., 2002, "A Review on Static and Dynamic Shape Control of Structures by PZ Actuation," Eng. Struct., 24(1), pp. 6381-6403.
292. Kapuria, S., Dumir, P. C., and Ahmed, A., 2004, "Efficient Coupled Zigzag Theory for Hybrid PZ Beams for Thermoelectric Load," AIAA J., 42(2), pp. 383-394.
293. Tauchen, T. R., Aschida, F., Noda, N., Adali, S., and Verijenko, V., 2000, "Developments in Thermopiezoelectroelasticity With Relevance to Smart Composite Structures," Compos. Struct., 48, pp. 31-45.
294. Benjeddon, A., 2000, "Advances in PZ Finite Elements Modelling of Adaptive Structural Elements: A Survey," Comput. Struct., 76, pp. 347-363.
295. Gautschi, G., 2002, Piezoelectric Sensors: Force Strain Pressure Acceleration a. Acoustic Emission Sensors Materials and Amplifiers, Springer, Berlin.
296. Kielczynski, P., 2004, "The Analog of the Kanazava-Gordon Formula for Cylindrical Resonators," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 51(11), pp. 1367-1372.
297. Ebeneser, D. D., 2004, "Determination of Complex Coefficients of Radially Polarized PZ Ceramic Cylindrical Shells Using Thin Shell Theory," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 51(10), pp. 1209-1215.
298. Chen, Z., Meng, S. Y., and Lin, Y., 2002, "Effective Properties of Layered Magneto-Electro-Elastic Composites," Compos. Struct., 57(1-4), pp. 177-182.
299. Wang, Zh., Ackaert, J., Kuper, F. G., Tock, M., De Backer, E., Coppens, P., De Semper, L., and Vlachakis, B., 2004, "Plasma-Charging Damage of Floating MIM Capacitors," IEEE Trans. Electron Devices, 51(6), pp. 1017-1024.
300. Li, H. L., Hu, J. H., and Chan, H. L. W., 2004, "Finite Element Analysis on PZ Ring Transformer," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 51(10), pp. 1206-1208.
301. Makino, H., and Kamiya, N., 1998, "Electromechanical Fatigue of Lead Zirconate Titanate Ceramics," Jpn. J. Appl. Phys., Part 1, Part 1; 37(9b), pp. 5301-5305.