Mechanics and computational models for laminated piezoelectric beams, plates, and shells

Applied Mechanics Reviews

Volumn 52, Issue 10, 1999, Pages 305-320

  Saravanos, Dimitris A ^a   Heyliger, Paul R ^b  

^a UNIVERSITY OF PATRAS   (Greece)

^b Engineering Research Center and Hydraulics Laboratory   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; INTELLIGENT STRUCTURES; MATHEMATICAL MODELS; PIEZOELECTRIC MATERIALS; PLATES (STRUCTURAL COMPONENTS); SHELLS (STRUCTURES); STRUCTURAL ANALYSIS;

PIEZOELECTRIC ACTUATORS; PIEZOELECTRIC SENSORS;

LAMINATED COMPOSITES;

EID: 0033204901     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3098918     Document Type: Article

References (103)

1. Allik H and Hughes TJR (1970), Finite element for piezoelectric vibration, Int 7 Num Methods Eng 2(2) 151-157.
2. Adelman NT and Stavsky Y (1975a), Axisymmetric vibrations of radially polarized piezoelectric ceramic cylinders, JAcoust Soc Am 38, 245-254.
3. Adelman NT and Stavsky Y (1975b), Vibrations of radially polarized composite cylinders and discs, J Sound Vib 43, 37-44.
4. Bailey T and Hubbard E (1985), Distributed piezoelectric-polymer active vibration control of a cantilever beam, J Guidance Control Dyn 8(5) 605-611.
5. Batra RC, Liang XQ, and Yang JS (1996), The vibration of a simply supported rectangular elastic plate due to piezoelectric actuators, Int J Solids Struct 33(11)1597-1618.
6. Baz A and Poh S (1988), Performance of an active control system with piezoelectric actuators, J Sound Vib 126(2) 327-343.
7. Bisegna P and Maceri F (1996), An exact 3-dimensional solution for simply supported rectangular piezoelectric plates, J Appl Mech 63(3) 628-638.
8. Brooks SP and Heyliger PR (1994), Static behavior of piezoelectric laminates with distributed and patched electrodes, J Intelligent Mat Syst Struct 5(5) 635-646.
9. Cady WG (1964), Piezoelectricity, rev Ed, 1-2, Dover, New York.
10. Chandra R, and Chopra I (1993), Structural modeling of composite beams with induced-strain actuators, AIAA 731(9) 1692-1701.
11. Chandrashekhara K and Agarwal AN (1993), Active vibration control of laminated composite plates using piezoelectric devices: A finite element approach, J Intelligent Mat Syst Struct 4(4) 496-508.
12. Chandrashekhara K and Koli M (1995), Thermally induced vibration of adaptive doubly curved composite shells with piezoelectric devices, AIAA/ASME/-ASCE/AHS/ASC 36th Structures, Structural Dyn and Mat Conf, New Orleans LA, 1628-1629.
13. Chandrashekhara K and Varadarajan S (1997), Adaptive shape control of composite beams with piezoelectric actuators, J Intelligent Mat Syst Struct 8(2) Feb, 112-124.
14. Chattopadhyay A, Gu H, and Dragomir-Daescu D (1999), Dynamics of delaminated composite plates with piezoelectric actuators, AIAA 737(2) 248-254.
15. Choi JS, Ashida HF, and Noda N (1997), Control of thermally induced elastic displacement of an isotropic structural plate bonded to a piezoelectric ceramic plate, Acta Mech 122(1-4) 49-63.
16. Chopra I (1996), State-of-the-art of smart structures and integrated systems, SPIE Smart Struct and Mat Conf, SP1E 2717, 20-62.
17. Crawley EF, and de Luis J (1987), Use of piezoelectric actuators as elements of intelligent structures, AIAA 725(10) 1373-1385.
18. Crawley EF and Lazarus KB (1991), Induced strain actuation of isotropic and anisotropic plates, AIAA 7 29(6) 944-951.
19. Debus JC, Dubus B, and Coutte J (1998), Finite-element modeling of lead magnesium niobate electrostrictive materials-static analysis, J. Acoust Soc Am 103(6) 3336-3343.
20. Detwiler DT, Shen MH, and Venkaya VB (1995), Finite element analysis of laminated composite structures containing distributed piezoelectric actuators and sensors, FE Anal Des 20(2) 87-100.
21. Dimitriadis EK, Fuller CR, and Rogers CA (1991), Piezoelectric actuators for distributed vibration excitation of thin plates, J. Vib Acoust 113(1) 100-107.
22. Dokmeci MC (1978), Theory of vibrations of coated, thermopiezoelectric laminae, J Math Phys 19, Jan, 109-126.
23. Dokmeci MC (1990), Shell theory for vibrations of piezoceramics under a bias, IEEE Trans Ultrasonics, Ferroelectrics, and Frequency Control, 37(5) 369-385.
24. Drumheller DS and Kalnins A (1970), Dynamic shell theory for ferroelectric ceramics, J Acoust Soc Am 47, 1343-1348.
25. Dube GP, Kapuria S, and Dumir PC (1996a), Exact piezothermoelastic solution of simply-supported orthotropic flat-panel in cylindrical bending, Int 7 Mech Sci 38(11) 1161-1177.
26. Dube GP, Kapuria S, and Dumir PC (1996b), Exact piezothermoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending, Arch Appl Mech 66(8) 537-554.
27. Fripp MLR and Hagood NW (1997), Distributed structural actuation with electrostrictors, J Sound Vib 203(1) 11-40.
28. Ha SK, Keilers C, and Chang FK (1992), Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators, AIAA 730(3) 772-780.
29. Hagood NW, Chang WH, and Von Flotow A (1990), Modelling of piezoelectric actuator dynamics for active structural control, AIAA/ASME/ASCE/AHS/ASC 31st Structures, Structural Dyn and Mat Conf, Long Beach CA, 2242-2256.
30. Haskins DS and Kalnins A (1970), Dynamic shell theory for ferroelectric ce-ramies, JAcoust Soc Am 47, 1343-1353.
31. Heyliger P (1994), Static behavior of laminated elastic piezoelectric plates, AIAA 732,2481-2484.
32. Heyliger PR (1997a), Planar free vibrations of off-axis piezoelectric laminates, J Eng Mech 123(6) 604-610.
33. Heyliger PR (1997b), Exact solutions for simply-supported laminated piezoelectric plates, J Appl Mech 64(2) 299-306.
34. Heyliger PR (1997c), A note on the static behavior of simply-supported laminated piezoelectric cylinders, Int J Solids Struct 34(29) 3781-3794.
35. Heyliger PR, Ramirez G, and Saravanos DA (1994), Coupled discrete-layer finite-element models for laminated piezoelectric plates, Commun Numer Methods Eng 10, 971-981.
36. Heyliger P, and Brooks S (1995), Free-vibration of piezoelectric laminates in cylindrical bending, Int J Solids Struct 32(20) 2945-2960.
37. Heyliger PR and Brooks SP (1996), Exact solutions for piezoelectric laminates in cylindrical bending, J Appl Mech 63(4) 903-910.
38. Heyliger P, Pei KC, and Saravanos DA (1996), Layerwise mechanics and finite element model for laminated piezoelectric shells, AIAA 734(11) 2353-2360.
39. Heyliger P and Saravanos DA (1995), Exact free-vibration analysis of laminated plates with embedded piezoelectric layers, J Acoust Soc Am 98(3) 15471557.
40. Hoffman KH, and Botkin ND (1998), Oscillations of nonlinear thin plates excited by piezoelectric patches, Z Angew Math Mech 78(7) 495-503.
41. Hwang WS and Park HC (1993), Finite-element modeling of piezoelectric sensors and actuators, AIAA 731(5) 930-937.
42. Im S and Atluri SN (1989), Effects of a piezo-actuator on a finitely deformed beam subject to general loading, AIAA 7, 27, 1801-1807.
43. Karlash VL (1987), Dynamic stresses in a compound piezoceramic hollow cylinder, Prikl Mekh 23, 49-54.
44. Kim J, Varadan W, and Varadan VK (1997), Finite element modeling of structures including piezoelectric active devices, Int 7 Num Methods Eng 40(5)817-832.
45. Koconis DB, Kollar LP, and Springer GS (1994), Shape control of composite plates and shells with embedded actuators. I. Voltages specified, 7 Composite Mat 28(5)415-458.
46. Lalande F, Chaudhry Z, and Rogers CA (1997), Impedance-based modeling of induced strain actuators bonded on ring structures, J Sound Vib 201(2) 169-187.
47. Lammering R (1991), The application of a shell finite element for composites containing piezoelectric polymers in vibration control, Comput Struct 41(5) 1101-1109.
48. Lee CK and Moon FC (1989), Laminated piezopolymer plates for torsion and bending sensors and actuators, J Acoust Soc Am 85(6) 2432-2439.
49. Lee CK (1990), Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships, J Acoust Soc Am 87(3) 1144-1158.
50. Lee PCY, Syngellakis S, and Hou JP (1987), A two-dimensional theory for high frequency vibrations of piezoelectric crystal plates with or without electrodes, J ApplPhys 61 1249-1262.
51. Lee HJ and Saravanos DA (1996), Coupled layerwise analysis of thermopiezoelectric composite beams, AIAAJ 34(6) 1231-1237.
52. Lee HJ and Saravanos DA (1997), Generalized finite element formulation for smart multilayered thermal piezoelectric composite plates, IntJ Solids Struct 34(26)3355-3371.
53. Lee HJ and Saravanos DA (1998), The effect of temperature dependent material nonlinearities on the response of piezoelectric composite plates, J Intelligent Mat Syst Struct 9(7) 503-508.
54. Lee JS and Jiang LZ (1996), Exact electroelastic analysts of piezoelectric laminae via state-space approach, Int J Solids Struct 33(7) 977-990.
55. Librescu L, Meirovich L, and Na SS (1997), Control of a cantilever vibration via structural tailoring and adaptive materials, AIAA J 35(8) 1309-1315.
56. Mitchell JA and Reddy JN (1995a), A refined hybrid plate-theoiy for composite laminates with piezoelectric laminae, IntJ Solids Struct 32(16) 2345-2367.
57. Mitchell JA and Reddy JN (1995b), A study of embedded piezoelectric layers in composite cylinders, J Appl Mech 62(1) 166-173.
58. Naillon M, Coursant RH, and Besnier F (1983), Analysis of piezoelectric structures by a finite element method, Acta Electrónica 25(4) 341-362.
59. Nye NY (1972), Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford Univ Press, UK.
60. Pai PF, Nayfeh AH, Oh KY, and Mook DT (1993), A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors, Int J Solids Struct 30(12) 1603-1630.
61. Parton VZ and Kudryavtsev BA (1988), Electromagnetoelasticity: Piezoelectrics and Electrically Conductive Solids, Gordon and Breach Sci Publ, New York.
62. Paul HS, Nelson VK, and Vazhapadi K (1996), Flexural vibration of piezoelectric composite cylinder, J Acoust Soc Am 99(1) 309-313.
63. Paul HS and Vankatesan M (1986), Axisymmetric vibration of a piezoelectric solid cylinder guided by a thin film, J Acoust Soc Am 80, 1091 -1096
64. Pauley KE (1974), Analysis of plane waves in infinite laminated, piezoelectric plates, PhD Dissertation, Engineering, UCLA.
65. Rao SS and Sunar M (1993), Analysis of distributed thertnopiezoelectric sensors and actuators in advanced intelligent structures, AIAA J 31(7) 1280-1286.
66. Rao SS and Sunar M (1994), Piezoelectricity and its use in disturbance sensing and control of flexible structures: A survey, Appl Mech Rev 47(4) 113-123.
67. Ray MC, Rao KM, and Samanta B (1992), Exact analysis of coupled electroelastic behavior of a piezoelectric plate under cylindrical bending, Comput Struct 45(4) 667-677.
68. Ray MC, Bhattacharya R, and Samanta B (1993), Exact-solutions for static analysis of intelligent structures, AIAA J 31(9) 1684-1691.
69. Ray MC, Bhattacharya R, and Samanta B (1994), Static analysis of an intelligent structure by the finite element method, Comput Struct 52(4) 617-631.
70. Robbins DH and Reddy JN (1991), Analysis of piezoelectrically actuated beams using a layerwise displacement theory, Comput Struct 41(2) 265-279.
71. Saravanos DA (1997), Coupled mixed-field laminate theory and finite element for smart piezoelectric composite shell structures, AIAA J 35(8) 1327-1333.
72. Saravanos DA and Heyliger PR (1995), Coupled electromechanical response of composite beams with embedded piezoelectric sensors and actuators, J Intelligent Mat Syst Struct 6(3) 350-363.
73. Saravanos DA, Heyliger PR, and Hopkins DA (1997), Layerwise mechanics and finite element model for the dynamic analysis of piezoelectric composite plates, Int J Solids Struct 34(3) 359-378.
74. Siao JCT, Dong SB, and Song J (1994), Frequency spectra of laminated piezoelectric cylinders, J Vib Acoust 116(3) 364-370.
75. Sonti VR and Jones JD (1996), Curved piezoactuator model for active vibration control of cylindrical-shells, AIAA J 34(5) 1034-1040.
76. Stam M and Carman G (1996) Electrothermoelastic behavior of piezoelectric coupled cylinders, AIAA 734(8) 1612-1618.
77. Suleman A and Venkaya VB (1995), A simple finite element formulation for a laminated composite plate with piezoelectric layers, J Intelligent Mat Syst Struct, 6(6), 776.
78. Sun CT and Cheng NC (1974), Piezoelectric waves on a layered cylinder, J Appl Phys 45,4288-4294.
79. Sunar M and Rao SS (1999), Recent advances in sensing and control of flexible structures via piezoelectric materials technology, Appl Mech Rev 52(1) 1-16.
80. Tani J, Takagi T, and Qiu J (1998), Intelligent material systems: application of functional materials, Appl Mech Rev 51(8) 505-521.
81. Tauchert TR (1992), Piezothermoelastic behavior of a laminated plate, J Thermal Stresses 15(1) 25-37.
82. Tiersten HF (1969), Linear Piezoelectric Plate Vibrations, Plenum, New York.
83. Toupin RA (1959), Piezoelectric relations and the radial deformation of polarized spherical shell, J Acoust Soc Am 31, 315-318.
84. Tzou HS (1993), Piezoelectric Shells: Distributed Sensing and Control of Continua, Kluwer Acad Publ, Norwell MA.
85. Tzou HS and Bao Y (1995), Theory on anisotropic piezothermoelastic shell laminates with sensor/actuator applications, J Sound Vib 184(3) 453-473.
86. Tzou HS, and Bao, Y (1997a), Nonlinear piezothermoelasticity and multi-field actuations, Part 1: Nonlinear anisotropic piezothermoelastic shell laminates, J Vib Acoust 119(3) 374-381.
87. Tzou HS, and Bao, Y (1997b), Nonlinear piezothermoelasticity and multi-field actuations, Part 2: Control of nonlinear deflection, buckling and dynamics, J Vib Acoust 119(3) 382-389.
88. Tzou HS and Howard RV (1994), A piezothermoelastic thin shell theory applied to active structures, J Vib Acoust 116(3) 295-302.
89. Tzou HS and Garde M (1989), Theoretical analysis of a multi-layered thin shellcoupled with piezoelectric shell actuators for distributed vibration controls, J Sound Vib 132(3) 433-450.
90. Tzou HS and Ye R (1994), Piezothermoelasticity and precision control of piezoelectric systems: Theory and finite element analysis, J Vib Acoust 116(4) 489-495.
91. Tzou HS and Ye R (1996), Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements, AIAA 734(1) 110-115.
92. Tzou HS and Zhong JP (1993), Electromechanics and vibrations of piezoelectric shell distributed systems, 7 Dyn Syst Meas Control 115(3) 506-517.
93. Vatal’yan AO, Getman IP, and Lapitskaya NB (1992), Flexure of a piezoelectric bimorphic plate, Prikl Mekh 27(10) 101-105.
94. Xu KM and Noor AK (1996), 3-Dimensional analytical solutions for coupled thermoelectroelastic response of multilayered cylindrical-shells, AIAA J. 34(4) 802-812.
95. Xu KM, Noor AK, and Tang YY (1995), 3-Dimensional solutions for coupled thermoelectroelastic response of multilayered plates, Comput Methods in Appl Mech Eng 126(3-4) 355-371.
96. Xu KM, Noor AK, and Tang YY (1997), Three-dimensional solutions for free vibrations of initially-stressed thermoelectroelastic multilayered plates, Comput Methods in Appl Mech Eng 141(1-2) 125-139.
97. Yang JS and Yu JD (1993), Equations for a laminated piezoelectric plate, Arch Mech 45, 653.
98. Yong YK, Stewart JT, and Ballato A (1993), A laminated plate theory for high frequency, piezoelectric thin-film resonators, J Appl Phys 74(5) 3028-3046.
99. Yu JW, Kang WY, and Kim SJ (1995), Elastic tailoring of laminated composite plate by anisotropic piezoelectric polymers - Theory, computation, and experiment, J. Composite Mat 29(9) 1201.
100. Wang BT and Rogers CA (1991a), Modeling of finite-length spatially-distributed induced strain actuators for laminate beams and plates, J. Intelligent Mat Syst Struct 2(1) 38-58.
101. Wang BT and Rogers CA (1991b), Laminate plate theoiy for spatially distributed induced strain actuators, 7 Composite Mat 25(4) 433-452.
102. Wang J, Yong YK, and Imai T, (1999), Finite element analysis of the piezoelectric vibrations of quartz plate resonators with higher-order plate theory, Int J Solids Struct 36(15) 2303-2319.
103. Zhang Z and Yong YK (1995), Numerical analysis of thickness shear film piezoelectric resonators using a laminated plate theory, IEEE Trans Ultrasonics, Ferroelectrics, and Frequency Control 42(4) 734-746