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Introduction

  • Hornsen (HS) Tzou
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 247)

Abstract

In this book, generic double-curvature piezoelectric shell theories are derived; generic distributed structural sensing, identification, energy harvesting and vibration control theories of a generic deep shell continuum are presented. Open and closed-loop dynamic system equations and state equations of piezoelectric structronic systems are formulated. Simple reduction procedures are proposed and applications to other common geometries and structures are demonstrated in case studies. The revised book not only corrected typos and minor mistakes, but also added new chapters on optimal control of parabolic shells and energy harvesting of shells, including both theoretical and experimental aspects. Furthermore, laboratory and experimental components are added to, almost, all chapters on distributed sensing, energy harvesting and control of shell and non-shell structures and structronic systems. Note that performances of piezoelectric sensors/harvesters/actuators are restricted by breakdown voltages, hysteresis effects, limited strain rates, etc. These material properties need to be further improved in order to enhance the sensor/actuator performance and efficiency. Also, laboratory experiments were carried out over time; different materials with various dielectric constants from different venders were used in various studies presented in newly added Chaps.  10 12. Extreme care should be taken when repeating those studies. It should be pointed out that all piezoelectric shell theories and distributed sensing/control and energy harvesting theories are based on a symmetrical hexagonal piezoelectric structure—class C6v = 6 mm. Extension of these theories to more generic piezoelectric materials, such as a triclinic structure, would make them even more comprehensive and versatile. Besides, the temperature effect, e.g., the pyroelectricity and thermal induced stress/strains, is not considered in all studies; it should be considered when a working environment has significant temperature variations.

References

  1. Adelman, N.T. and Stavsky, Y., 1975a, “Axisymmetric Vibrations of Radially Polarized Piezoelectric Ceramic Cylinders,” J. Sound and Vibration, 38(2), pp.245-254.zbMATHCrossRefGoogle Scholar
  2. Adelman, N.T. and Stavsky, Y., 1975b, “Vibrations of Radially Polarized Composite Piezoelectric Cylinders and Disks,” J. Sound and Vibration, 43(1), pp.37-44.Google Scholar
  3. Allik, H. and Hughes, T.J.R., “Finite Element Method for Piezoelectric Vibration”, Int. J. of Numerical Methods Eng., Vol. 2, 1979, pp.151-168.CrossRefGoogle Scholar
  4. Anderson, E.H., Hagood, N.W., and Goodliffe, J.M., 1992, “Self-sensing Piezoelectric Actuation: Analysis and Application to Controlled Structures,” AIAA Paper: AIAA-92-2465-CP at 33 SDM Conference.Google Scholar
  5. Ashley, S., 1995, “Smart Skis and Other Adaptive Structures, Mechanical Engineering, Vol.117, No.11, pp.76-81.Google Scholar
  6. Banks, H.T. and Smith, R.C., 1998, “Numerical Techniques for Simulation, Parameter Estimation, and Noise Control in Structural Acoustic Systems,” in Dynamics and Control of Distributed Systems, Tzou, H.S. and Bergman, L.A., (Ed), Cambridge University Press, New York, pp.202-263. Google Scholar
  7. Baz A. and Poh S., 1988, “Performance of an Active Control System with Piezoelectric Actuators,” Journal of Sound and Vibration, Vol.126, No.2, pp.327-343.CrossRefGoogle Scholar
  8. Baz A. and Ro, J., 1994, “The Concept and Performance of Active Constrained Layer Damping Treatments,” J. of Sound and Vibration, Vol.28, No.3, pp.18-21.Google Scholar
  9. Cady, W.G., Piezoelectricity, Dover Pub., New York, 1964.Google Scholar
  10. Chai, W.K., DeHaven, J.G. and Tzou, H.S., 2005, “Distributed Micro-control Characteristics of Shallow Conical Shell Sections,” Journal of Vibration and Control, Vol.11, No.11, pp.1397-1411.Google Scholar
  11. Chai, W.K., Tzou, H.S., 2007, “Design and Testing of a Hybrid Electrostrictive/Piezoelectric Polymeric Beam with Bang-bang Control,” Mechanical Systems and Signal Processing (Journal of), Vol.21, pp.417-429.CrossRefGoogle Scholar
  12. Chai, W.K., Tzou, H.S., Arnold, S.M. and Lee, H.J., 2008, “Magnetostrictive Micro-actuations and Modal Sensitivities of Thin Cylindrical Magnetoelastic Shells,” ASME Transactions, Journal of Pressure Vessel Technology, Vol.130, pp.011206-011206-5.CrossRefGoogle Scholar
  13. Chai, W.K., Tzou, H.S. and Higuchi, K., 2006, “Micro-actuation Characteristics of Conical Shell Sections,” Journal of Sound & Vibration. Vol.293, No1-2, pp.286-298.Google Scholar
  14. Chau, L.K., 1986, “The Theory of Piezoelectric Shells,” PMM U.S.S.R., 50(1), pp.98-105.Google Scholar
  15. Crawley, E.F. and de Luis, J., 1987, “Use of Piezoelectric Actuator as Elements of Intelligent Structures,” AIAA Journal, 25(10), pp.1373-1385.CrossRefGoogle Scholar
  16. DeHaven, J.G., Han, Y. and Tzou, 2007, “Transition of Membrane/bending Neural Signals on Transforming Adaptive Shells,” Journal of Vibration and Control, Vol.13, No.7, pp.1007-1029.zbMATHCrossRefGoogle Scholar
  17. Dökmeci, M.C., 1978, “Theory of Vibrations of Coated, Thermopiezoelectric Laminae,” J. Math. Phys., 19(1), January.Google Scholar
  18. Dökmeci, M.C., 1980, “Vibrations of Piezoelectric Crystals,” J. Eng. Soc., 18, pp.431-448.zbMATHCrossRefGoogle Scholar
  19. Dökmeci, M.C., 1983, “Dynamic Applications of Piezoelectric Crystals,” The Shock and Vibration Digest, 15(3), pp.9-22.CrossRefGoogle Scholar
  20. Dosch, J.J., Inman, D.J., and Garcia, E., 1992, “A Self-sensing Piezoelectric Actuator for Collocated Control,” J. of Intell. Materl. Systems and Structures, Vol.3, pp.166-185.CrossRefGoogle Scholar
  21. Drumheller, D.S. and Kalnins, A., 1970, “Dynamic Shell Theroy for Ferroelectric Ceramics,” J. Acoust. Soc. Am.,47(5), pp.1343-1349.Google Scholar
  22. Erturk, A. and D. J. Inman, D.J., “A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters,” Journal of Vibration and Acoustics 130 (2008) 0410021-04100215.CrossRefGoogle Scholar
  23. Fason J.L. and Gabra, J.A., 1988, “Experimental Studies of Active Members in Control of Large Space Structures,” AIAA Paper 88-2207.Google Scholar
  24. Gabbert, U. and Tzou, H.S. (Edtr.), 2001, Smart Structures and Structronic Systems, IUTAM Symposium on Smart Structures and Structronic Systems, (ISBN 0-7923-6968-8), Kluwer Academic Publishers, Dordrecht/Boston/London.Google Scholar
  25. Hanagud S. and Obal, M.W., 1988, “Identification of Dynamic Coupling Coefficients in a Structure with Piezoelectric Sensors and Actuators,” AIAA paper No.88-2418.Google Scholar
  26. Haskins, J.F. and Walsh, 1957, “Vibration of Ferroelectric Cylindrical Shells with Transverse Isotropy,” J. Acoust. Soc. Am., 29, pp.729-734.Google Scholar
  27. Howard, R.V., Chai, W.K. and Tzou, H.S., 2001, “Modal Voltages of Linear and Non-Linear Structures Using Distributed Artificial Neurons,” Mechanical Systems and Signal Processing 15, 629-640.CrossRefGoogle Scholar
  28. Hu, S.D., Li, H. and Tzou, H.S., 2013a, “Flexoelectric responses of circular rings,” Journal of Vibration and Acoustics -Transactions of the ASME, 2013, 135(2): 021003.CrossRefGoogle Scholar
  29. Hu, S.D., Li, H. and Tzou, H.S., 2013b, “Distributed Neural Signals on Parabolic Cylindrical Shells,” Journal of Sound and Vibration 332, 2984-3001.CrossRefGoogle Scholar
  30. Hu, S.D., H. Li, H. and Tzou, H.S., 2014, “Comparison of Flexoelectric and Piezoelectric Dynamic Signal Responses on Flexible Rings,” Journal of Intelligent Material Systems and Structures 25, 832-844.CrossRefGoogle Scholar
  31. Hu, S.D., Li, H. and Tzou, H.S., 2015, “Distributed flexoelectric structural sensing: Theory and experiment,” Journal of Sound and Vibration, 2015, 348(2015): 126-136.CrossRefGoogle Scholar
  32. Koppe, H., Gabbert, U., and Tzou, H.S., 1998, “On Three-Dimensional Layered Piezoelectric Shell Elements for Design Simluation of Adaptive Structures, Fortschritt-Berichte VDI, Smart Mechanical Systems – Adaptronics, 1998.Google Scholar
  33. Lee, C.K. and Moon, F., 1988, “Modal Sensors/Actuators,” IBM Report, RJ 6306 (61975), Research Division, IBM.Google Scholar
  34. Lee K.M. and Arjunan, S., 1989, “A Three Degree of Freedom Micro-motion in Parallel Actuated Manipulator,” Proceedings of 1989 IEEE Intl. Conf. on Robotics and Automation, Vol.(3), pp.1698-1703.Google Scholar
  35. Li, H.Y., Li, H. and Tzou, H.S., 2015, “Frequency Control of Beams and Cylinrical Shells with Light-Activated Shape Memory Polymers,” ASME Journal of Vibration and Acoustics, 37, p.011006.Google Scholar
  36. Li, H., Hu, S. D., Tzou, H. S., and Chen, Z. B., 2012, “Optimal Vibration Control of Conical Shells with Collocated Helical Sensor/Actuator Pairs,” Journal of Theoretical and Applied Mechanics, 50(3), pp.769-784.Google Scholar
  37. Lynch, T., 1996, “Piezoelectric Damper Hones Ski Performance,” Reprint from Design News, February 5.Google Scholar
  38. Mason, W. P., 1950, Piezoelectric Crystals and Their Application to Ultrasonics, Nostrand, NY.Google Scholar
  39. Mason, W.P., 1981, “Piezoelectricity, its History and Applications,” J. Acoust. Soc. Am., 70(6), Dec. 1981, pp.1561-1566.Google Scholar
  40. Mindlin, R.D., 1961, “On the Equations of Motion of Piezoelectric Crystals, Problems on Continuum Mechanics, Radok, J., Editor, Soc. Ind. Appl. Math., Philadelphia, pp.282-290.Google Scholar
  41. Mindlin, R.D., 1972, “High Frequency Vibrations of Piezoelectric Crystal Plates,” Inl. J. Solid Struc., Vol.(8), pp.895-906.zbMATHCrossRefGoogle Scholar
  42. Nailon, M., Coursant, R.H., and Besnier, F., 1983, “Analysis of Piezoelectric Structures by a Finite Element Method”, ACTA Electronica, Vol.25, No.4, pp.341-362.Google Scholar
  43. Obal, M.W., 1986, Vibration Control of Flexible Structures Using Piezoelectric Devices as Sensors and Actuators, Ph.D. Thesis, Georgia Institute of Technology.Google Scholar
  44. Palazzolo, A.B., Lin, R.R., Kascak, R.R., and Alexander, R.M., 1989, “Active Control of Transient Rotordynamic Vibration by Optimal Control methods,” ASME Journal of Engineering for Gas Turbines and Power, Vol.(111), p.265.CrossRefGoogle Scholar
  45. Paul, H.S., 1978, “Vibrations of a Hollow Circular Cylinder of Piezoelectric Ceramics,” J. Acoust. Soc. Am., 82(3), pp.952-956.CrossRefGoogle Scholar
  46. Paul, H.S., 1982, “Asymptotic Analysis of the Modes of Wave Propagation in a Piezoelectric Solid Cylinder,” J. Acoust. Soc. Am., 71(2), pp.255-263.zbMATHCrossRefGoogle Scholar
  47. Paul, H.S., 1986, “Axisymmetric Vibration of a Piezoelectric Solid Cylinder Guided by a Thin Film,” J. Acoust. Soc. Am., 80(4), pp.1091-1096.CrossRefGoogle Scholar
  48. Paul, H.S., 1987, “Wave Propagation in a Piezoelectric Solid Cylinder of Arbitrary Cross Section,” J. Acoust. Soc. Am. 82(6), pp.2013-2020.CrossRefGoogle Scholar
  49. Plumb, J.M., Hubbard, J.E., and Bailey, T., 1987, “Nonlinear Control of a Distributed System: Simulation and Experimental Results,” ASME Journal of Dynamic Systems, Measurements, and Control, 109(2), pp.133-139.Google Scholar
  50. Polla, D.L., 1992, “Micromachining of Piezoelectric Microsensors and Microactuators for Robotics applications,” Precision Sensors, Actuators and Systems, Tzou and Fukuda (Ed.), Kluwer Pub., pp.139-174.Google Scholar
  51. Robinson, A.C., 1971, “A Survey of Optimal Control of Distributed Parameter Systems”, Automatica 7, pp.371-388.MathSciNetzbMATHCrossRefGoogle Scholar
  52. Rogacheva, N.N., 1982, “Equations of State of Piezoceramic Shells,” PMM U.S.S.R., 45(5), pp.677-684.zbMATHCrossRefGoogle Scholar
  53. Rogacheva, N.N., 1984, “On Boundary Conditions in the Theory of Piezoceramic Shells Polarized Along Coordinate Lines,” PMM U.S.S.R., 47(2), pp.220-226.MathSciNetzbMATHCrossRefGoogle Scholar
  54. Rogacheva, N.N., 1986, “Classification of Free Piezoceramic Shell Vibrations,” PMM U.S.S.R., 50(1), pp.106-111.MathSciNetzbMATHCrossRefGoogle Scholar
  55. Rogacheva, N.N., 1994, The Theory of Piezoelectric Shells and Plates, CRC Press, Inc.Google Scholar
  56. Sashida, T. and Kenjo, T., 1993, An Introduction to Ultrasonic Motors, Clarendon Press, Oxford.Google Scholar
  57. Senik, N.A. and Kudriavtsev, B.A., 1980, “Equations on the Theory of Piezoceramic Shells,” In: Mechanics of a solid deformable body and related analytical problems. Moscow, Izd. mosk. Inst. Chim. Mashinostroeniia, U.S.S.R.Google Scholar
  58. Sessler, G.M., 1981, “Piezoelectricity in Polyvinylidene Fluoride,” J. Acoust. Soc. Am., 70(6), pp.1596-1608.CrossRefGoogle Scholar
  59. Shih H.R. and Tzou, H.S., 2005, “Structural Vibration Control Using Spatially Configured Opto-electromechanical Actuators,” Journal of Sound & Vibration, Vol.284, pp.361-378.CrossRefGoogle Scholar
  60. Shih H.R. and Tzou, H.S., 2007, Photostrictive actuators for photonic control of shallow spherical shells,” Smart Materials and Structures, Vol.16, 1712–1717.CrossRefGoogle Scholar
  61. Shih, H.R., Watkin. J. and Tzou, H.S., 2005, “Shape and Displacement Control of Beams via Photostrictive Optical Actuators,” Journal of Intelligent Structures and Material Systems. Vol.16, pp.355-363.Google Scholar
  62. Sirlin, S.W., 1987, “Vibration Isolation for Spacecraft Using the Piezoelectric Polymer PVF2,” Proc. of the 114th Meeting of the Acoustic Soc. Am., Nov.Google Scholar
  63. Stavroulakis, P., 1983, Distributed Parameter System Theory, Part 1 _ 2, Hutchinson Ross Pub. Co. Stroudsburg, PA.Google Scholar
  64. Smithmaitrie, P. and Tzou, H.S., 2004, Micro-control actions of actuator patches laminated on hemispherical shells, Journal of Sound and Vibration, 277, 691-710.CrossRefGoogle Scholar
  65. Smithmaitrie, P. and Tzou, H.S., 2005, “Electro-dynamics, Micro-actuation and Design of Ultrasonic Curvilinear Arc Stators,” Journal of Sound & Vibration, Vol.284, pp.635-650.Google Scholar
  66. Tiersten, H.F., 1969, Linear Piezoelectric Plate Vibrations, Plenum, New York.Google Scholar
  67. Toupin, R.A., 1959, “Piezoelectric Relation and the Rachial Deformation of Polarized Spherical Shell,” J. Acoust. Soc. Am., 31(3), pp.315-318.Google Scholar
  68. Tzou, H.S., 1987, “Active Vibration Control of Flexible Structures via Converse Piezoelectricity,” Development in Mechanics, 14(b), 20th Midwest Mechanical Conference, pp.1201-1206.Google Scholar
  69. Tzou, H.S., 1988, “Integrated Sensing and Adaptive Vibration Suppression of Distributed Systems,” Recent Development in Control of Nonlinear and Distributed Parameter Systems, ASME-DSC-Vol.(10), December 1988, 51-58.Google Scholar
  70. Tzou, H.S., 1989a, “Development of a Light-weight Robot End-effector using Polymeric Piezoelectric Bimorph,” Proceedings of 1989 IEEE Intl. Conf. on Robotics and Automation, Vol.(3), pp.1704-1709.Google Scholar
  71. Tzou, H.S., 1989b, “Integrated Distributed Sensing and Active Vibration Suppression of Flexible Manipulators using Distributed Piezoelectrics,” Journal of Robotic Systems, Vol.(6.6), pp.745-767. December 1989.CrossRefGoogle Scholar
  72. Tzou, H.S., 1990, Intelligent Piezoelectric Systems, Industrial Technology Research Institute, Mechanical Industry Research Laboratories, Hsinchu, Taiwan, ROC.Google Scholar
  73. Tzou, H.S., 1991a, “Distributed Modal Identification and Vibration Control of Continua: Theory and Applications,” ASME Journal of Dynamic Systems, Measurements, and Control, 113(3), pp.494-499, September 1991.CrossRefGoogle Scholar
  74. Tzou, H.S., 1991b, “Distributed Piezoelectric Neurons and Muscles for Shell Continua,” Structural Vibration and Acoustics, Ed. Huang, Tzou, et al., ASME-DE-Vol.34, pp.1-6, 1991 ASME 13th Biennial Conference on Mechanical Vibration and Noise, Symposium on Intelligent Structures and Systems, Miami, FL, September 22-25, 1991.Google Scholar
  75. Tzou, H.S., 1992a, “A New Distributed Sensation and Control Theory for “Intelligent” Shells,” Journal of Sound _ Vibration, Vol.(152), No.(3), pp.335-350, March 1992.Google Scholar
  76. Tzou, H.S., 1992b, Distributed Sensors and Actuators, Tutorial Notes (300 pages), 1992 IEEE International Conference on Intelligent Robots and Systems (IROS’92), Raleigh, NC, July 7-10, 1992.Google Scholar
  77. Tzou, H.S., 1993, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer Academic Publishers.Google Scholar
  78. Tzou, H.S. and Anderson, G.L. (Editors), 1992, Intelligent Structural Systems, ISBN No.0-7923-1920-6, 488 pages, Book, Kluwer Academic Publishers, Dordrecht/Boston/London, August 1992.Google Scholar
  79. Tzou, H.S., and Bao, Y., 1998, “Analysis of Nonlinear Piezothermoelastic Laminated Beams with Electric and Temperature Effects,” Journal of Sound & Vibration, Vol.209, No.3, pp.505-518.Google Scholar
  80. Tzou, H.S., Bao, Y., Venkayya, V.B., 1996a, “Study of Segmented Transducers Laminated on Cylindrical Shells, Part 1: Sensor Patches,” Journal of Sound & Vibration, Vol.197, No.2, pp.207 224.Google Scholar
  81. Tzou, H.S., Bao, Y., Venkayya, V.B., 1996b, “Study of Segmented Transducers Laminated on Cylindrical Shells, Part 2: Actuator Patches,” Journal of Sound & Vibration, Vol.197, No.2, pp.225 249, October 1996.Google Scholar
  82. Tzou, H.S., Chai, W.K. and Arnold, S.M., 2004, “Structronics and Actuation of Hybrid Electrostrictive/piezoelectric Thin Shells,” ASME Journal of Vibration and Acoustics. Vol.128, pp.79-87.CrossRefGoogle Scholar
  83. Tzou, H.S., Chai, W.K. and Wang, D.W., 2003, “Modal Voltages and Micro-Signal Analysis of Conical Shells of Revolution,” Journal of Sound and Vibration 260, 589-609.CrossRefGoogle Scholar
  84. Tzou, H. S., Chai, W. K., and Wang, D. W., 2004, “Micro-Control Actions and Location Sensitivity of Actuator Patches Laminated on Toroidal Shells,” Journal of Vibration and Acoustics-Transactions of the ASME, 126(2), pp.284-297.CrossRefGoogle Scholar
  85. Tzou, H.S., Deng, B.L. and Li, H.Y., 2017, “Flexoelectric Actuation and Vibration Control of Ring Shells,” ASME Transactions, Journal of Vibration & Acoustics, Vol.139 -031014.Google Scholar
  86. Tzou, H. S., Ding, J. H., and Hagiwara, I., 2002, “Micro-Control Actions of Segmented Actuator Patches Laminated on Deep Paraboloidal Shells,” JSME International Journal Series C-Mechanical Systems Machine Elements and Manufacturing, 45(1), pp. 8-15.CrossRefGoogle Scholar
  87. Tzou, H. S. and Ding, J. H., 2004, “Optimal Control of Precision Paraboloidal Shell Structronic Systems,” Journal of Sound and Vibration, 276(1-2), pp.273-291.MathSciNetzbMATHCrossRefGoogle Scholar
  88. Tzou, H.S. and Fu, H., 1994, “A Study of Segmentation of Distributed Sensors and Actuators, Part 2, Parametric Study and Vibration Controls,” Journal of Sound & Vibration, Vol.172, No.2, pp.261 276, April 1994.Google Scholar
  89. Tzou, H.S. and Fukuda, T., 1991, Piezoelectric Smart Systems Applied to Robotics, Micro-Systems, Identification, and Control, Workshop Notes, IEEE Robotics and Automation Society, 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, April 7-12, 1991.Google Scholar
  90. Tzou, H.S. and Fukuda, T. (Editors), 1992, Precision Sensors, Actuators, and Systems, Book (470 pages), Kluwer Academic Publishers, December 1992.Google Scholar
  91. Tzou H.S. and Gadre, M., 1988, “Active Vibration Isolation by Piezoelectric Polymer with Variable Feedback Gain,” AIAA Journal, Vol.(26), No.8, 1014-1017.CrossRefGoogle Scholar
  92. Tzou, H.S., and Gadre, M, 1989, “Theoretical Analysis of a Multi-Layered Thin Shell Coupled with Piezoelectric Shell Actuators for Distributed Vibration Control,” Journal of Sound and Vibration, 132(3), pp.433-450.CrossRefGoogle Scholar
  93. Tzou H.S., and Gadre, M., 1990, “Active Vibration Isolation and Excitation by a Piezoelectric Slab with Constant Feedback Gains,” Journal of Sound and Vibration, Vol.136, No.3, pp.477-490.CrossRefGoogle Scholar
  94. Tzou H.S. and Gabbert, U., 1997, STRUCTRONICS - A New Discipline and Its Challenging Issues, Fortschritt-Berichte VDI, Smart Mechanical Systems – Adaptronics, Reihe 11: Schwingungstechnik Nr.244, pp.245-250, Düsseldorf, Germany.Google Scholar
  95. Tzou, H.S., Guran, A. (Editors), Gabbert, U., Tani, J. and Breitbach, A., (Associate Editors), 1998, Structronic Systems - Smart Structures, Devices, and Systems, Volume-2: Systems and Control, World Scientific Publishing Co., New Jersey/Singapore.Google Scholar
  96. Tzou, H.S., Zhu, Y.T. and Hagiwara, I, 2002, “Distributed Precision Control of Structronic Shells and Common Shapes– A New Approach,” Recent Research Developments in Sound & Vibration, ISBN: 81-7895-031-6, Vol.1, Part-2, pp.613-646, TransWorld Research, 2002.Google Scholar
  97. Tzou, H.S. and Hollkamp, J.J., 1994, “Collocated Independent Modal Control with Self Sensing Orthogonal Piezoelectric Actuators (Theory and Experiment),” Journal of Smart Materials and Structures, Vol.3, pp.277 284.CrossRefGoogle Scholar
  98. Tzou, H.S., Johnson, D., and Liu, K.J., 1999, “Damping Behavior of Cantilever Structronic Systems with Boundary Control,” ASME Transactions, Journal of Vibration & Acoustics, pp.402-407, July 1999.Google Scholar
  99. Tzou, H.S., Lee, H.J. and Arnold, S.M., 2004, “Smart Materials, Precision Sensors/Actuators, Smart Structures and Structronic Systems,” Mechanics of Advanced Materials and Structures, Vol.11, pp.367-393.CrossRefGoogle Scholar
  100. Tzou, H. S., Smithmaitrie, P. and Ding, J. H., 2002, “Sensor Electromechanics and Distributed Signal Analysis of Piezo(Electric)-Elastic Spherical Shells,” Mechanical Systems and Signal Processing (Journal of), Vol.16(2-3), pp.185-199.CrossRefGoogle Scholar
  101. Tzou H.S. and Tseng, C.I., 1990, “Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a finite element approach,” Journal of Sound and Vibration, Vol.(138), No.(1), pp.17-34.CrossRefGoogle Scholar
  102. Tzou, H.S., and Tseng, C.I., 1991, “Distributed Modal Identification and Vibration Control of Continua: Piezoelectric Finite Element Formulation and Analysis,” ASME Journal of Dynamic Systems, Measurements, and Control, 113(3), pp.500-505, September 1991.CrossRefGoogle Scholar
  103. Tzou, H.S. and Wang, D.W., 2002, “Micro-Sensing Characteristics and Modal Voltages Of Linear/Non-Linear Toroidal Shells,” Journal of Sound and Vibration, 2002, 254(2): 203-218.CrossRefGoogle Scholar
  104. Tzou, H.S. and Wang, D.W., 2003, “Vibration Control of Toroidal Shells with Parallel Aand Diagonal Piezoelectric Actuators,” Journal of Pressure Vessel Technology -Transactions of the ASME, 2003, 125(2): 171-176.CrossRefGoogle Scholar
  105. Tzou H.S. and Yang, R.J., 2000, “Nonlinear Piezo-thermoelastic Shell Theory applied to Control of Variable-geometry Shells,” Journal of Theoretical and Applied Mechanics, No.3, Vol.38, pp.623-644.Google Scholar
  106. Tzou, H.S. and Ye, R., 1996a, “Analysis of Piezoelastic Systems with Laminated Piezoelectric Triangle Shell Elements,” AIAA Journal, Vol.34, No.1, pp.110 115.zbMATHCrossRefGoogle Scholar
  107. Tzou, H.S. and Ye, R., 1996b, “Pyroelectric and Thermal Strain Effects in Piezoelectric (PVDF and PZT) Devices,” Mechanical Systems and Signal Processing (Journal of), Vol.10, No.4, pp.459 479.CrossRefGoogle Scholar
  108. Tzou, H.S., Ye, R., and J. H. Ding 2001, “A New X-Actuator Design For Controlling Wing Bending And Twisting Modes,” Journal of Sound & Vibration, 241(2), pp.271-281.Google Scholar
  109. Tzou, H.S. and Zhang, X.F., 2016, “A flexoelectric double-curvature nonlinear shell energy harvester,” Journal of Vibration and Acoustics -Transactions of the ASME, 2016, 138(3): 031006.CrossRefGoogle Scholar
  110. Tzou, H.S., and Zhong, J.P., 1990, “Electromechanical Dynamics of Piezoelectric Shell Distributed Systems, Part-1: Theory,” Robotics Research-1990, ASME-DSC-Vol.26, pp.207-211, 1990 ASME Winter Annual Meetings, Dallas, Texas, Nov. 25-30, 1990; “Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems,” ASME Journal of Dynamic Systems, Measurements, and Control, 1993.Google Scholar
  111. Tzou, H.S., and Zhong, J.P., 1991, “Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings,” Structural Vibration and Acoustics, Edrs. Huang, Tzou, et al., ASME-DE-Vol.34, pp.67-74, Symposium on Intelligent Structural Systems, 1991 ASME 13th Biennial Conference on Mechanical Vibration and Noise, Miami, Florida, September 22-25, 1991.Google Scholar
  112. Tzou, H.S. and Zhong, J., 1996, “Spatially Filtered Vibration Control of Cylindrical Shells,” Shock and Vibration Journal, Vol.3, No.4, pp.269 278.CrossRefGoogle Scholar
  113. Tzou, H.S., Zhong, J.P., and Natori, M.C., 1993, “Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings,” ASME Transactions, Journal of Vibration & Acoustics, Vol.115, No.1, pp.40-46.CrossRefGoogle Scholar
  114. Tzou, H.S., Zhong, J.P., and Hollkamp, J.J., 1994, “Spatially Distributed Orthogonal Piezoelectric Shell Actuators: Theory and Applications,” Journal of Sound & Vibration, Vol.177, No.3, pp.363-378.zbMATHCrossRefGoogle Scholar
  115. Tzou, H.S. and Zhou, Y., 1995, “Dynamics and Control of Nonlinear Circular Plates with Piezoelectric Actuators,” Journal of Sound & Vibration, Vol.188, No.2, pp.189-207.CrossRefGoogle Scholar
  116. Tzou, H.S., and Zhou, Y., 1997, “Nonlinear Piezothermoelasticity and Multi field Actuations, Part 2: Control of Nonlinear Buckling and Dynamics,” ASME Transactions, Journal of Vibration & Acoustics, Vol.119, pp.382-389.Google Scholar
  117. Uchino, K., 1997, Piezoelectric Actuators and Ultrasonic Motors, Kluwer Academic Pub., Dordrecht/Boston/London.CrossRefGoogle Scholar
  118. Ueha, S., Tomikawa, Y., Kurosawa, M., and Nakamura, N., 1993, Ultrasonic Motors, Clarendon Press, Oxford.Google Scholar
  119. Wang, P.K.C., 1966, “On the Feedback Control of Distributed Parameter Systems”, Int. J. on Control, Vol. 3, No. 3, pp.255-273.zbMATHCrossRefGoogle Scholar
  120. Wang, D.W., Tzou, H.S., Arnold, S.M. and Lee, H.J., 2006, “Control of Static Shape, Dynamic Oscillation and Thermally Induced Vibration of Nozzles,” ASME Transactions, Journal of Pressure Vessel Technology, Vol.128, pp.357-363.CrossRefGoogle Scholar
  121. Ye, R. and Tzou, H.S., 2000, “Control of Adaptive Shells with Thermal and Mechanical Excitations,” Journal of Sound & Vibration, Vol.231(5), pp.1321-1338.CrossRefGoogle Scholar
  122. Yue, H. H., Deng, Z. Q., and Tzou, H.S., 2008, “Optimal Actuator Locations and Precision Micro-Control Actions on Free Paraboloidal Membrane Shells,” Communications in Nonlinear Science and Numerical Simulation, 13(10), pp.2298-2307.CrossRefGoogle Scholar
  123. Zhou, Y.H., and Tzou, H.S., 2000, “Active Control of Nonlinear Piezoelectric Circular Shallow Spherical Shells,” International Journal of Solids and Structures, 37(12), pp.1663-1677.zbMATHCrossRefGoogle Scholar
  124. Zhang, X.F., Hu, S.D. and Tzou, H.S., 2014, A generic double-curvature piezoelectric shell energy harvester: Linear/nonlinear theory and applications, Journal of Sound and Vibration, 333, 7286-7298CrossRefGoogle Scholar
  125. Zhang, X.F., Li, H.Y., and Tzou, H.S., 2016, “Analytical and Experimental Studies of Flexoelectric Beam Control,” ASME 2016 International Mechanical Engineering Congress & Exposition, IMECE2016, Paper No. IMECE2016-66527, Phoenix, Arizona, USA.Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanics and Control of Mechanical Structures; Interdisciplinary Research Institute, College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

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