An analytical study of the piezothermoelastic behavior of a functionally graded material (FGM) hollow sphere with integrated piezoelectric layers as a sensor and actuator under the effect of radially symmetric thermo-electro-mechanical loading is carried out. The material properties of the FGM layer are assumed to be graded in the radial direction according to a power law function. Governing differential equations are developed in terms of the components of the displacement field, the electric potential and the temperature of each layer of the smart FGM hollow sphere. The resulting differential equations are solved analytically. Numerical examples are given and discussed to show the significant influence of grading index of material properties and feedback gain on the mechanical–electrical responses. This will be useful for modern engineering design.
Issue Section:
Design and Analysis
Keywords:
High pressure engineering
References
1.
Qin
, Q.-H.
, 2001
, Fracture Mechanics of Piezoelectric Materials
,WIT
, Southampton, UK
.2.
Lutz
, M. P.
, and Zimmerman
, R. W.
, 1996
, “Thermal Stresses and Effective Thermal Expansion Coefficient of a Functionally Graded Sphere
,” J. Therm. Stress
, 19
(1
), pp. 39
–54
.10.1080/014957396089461593.
Zimmerman
, R. W.
, and Lutz
, M. P.
, 1999
, “Thermal Stress and Thermal Expansion in a Uniformly Heated Functionally Graded Cylinder
,” J. Therm. Stress
, 22
(2
), pp. 177
–188
.10.1080/0149573992809594.
Obata
, Y.
, and Noda
, N.
, 1994
, “Steady Thermal Stresses in a Hollow Circular Cylinder and a Hollow Sphere of a Functionally Gradient Material
,” J. Therm. Stresses
, 17
(3
), pp. 471
–487
.10.1080/014957394089462735.
Jabbari
, M.
, Sohrabpour
, S.
, and Eslami
, M. R.
, 2002
, “Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads
,” Int. J. Pressure Vessels Piping
, 79
(7
), pp. 493
–497
.10.1016/S0308-0161(02)00043-16.
Poultangari
, R.
, Jabbari
, M.
, and Eslami
, M. R.
, 2008
, “Functionally Graded Hollow Spheres Under Non-Axisymmetric Thermo-Mechanical Loads
,” Int. J. Pressure Vessels Piping
, 85
(5
), pp. 295
–305
.10.1016/j.ijpvp.2008.01.0027.
Shao
, Z. S.
, and Wang
, T. J.
, 2006
, “Three-Dimensional Solutions for the Stress fields in Functionally Graded Cylindrical Panel With Finite Length and Subjected to Thermal/Mechanical Loads
,” Int. J. Solids Struct.
, 43
(13
), pp. 3856
–3874
.10.1016/j.ijsolstr.2005.04.0438.
Takeuti
, Y.
, and Tanigawa
, Y.
, 1982
, “Transient Thermal Stresses of a Hollow Sphere Due to Rotating Heat Source
,” J. Therm. Stresses
, 5
(3–4
), pp. 283
–298
.10.1080/014957382089421519.
Tiersten
, H. F.
, 1969
, Linear Piezoelectric Plate Vibrations
, Plenum Press
, New York
.10.
Berlincourt
, D. A.
, 1971
, “Piezoelectric Crystals and Ceramics
,” Ultrasonic Transducer Materials
, O. E.
Mattiat
, ed., Plenum
, New York
, pp. 63
–124
.11.
Berlincourt
, D. A.
, Curran
, D. R.
, and Jaffe
, H.
, 1964
, “Piezoelectric and Piezomagnetic Materials and Their Function in Transducers
,” Physical Acoustics: Principles and Methods
, W. P.
Mason
, ed., Academic
, New York
, pp. 169
–270
.12.
Adelman
, N. T.
, Stavsky
, Y.
, and Segal
, E.
, 1975
, “Axisymmetric Vibrations of Radially Polarized Piezoelectric Ceramic Cylinders
,” J. Sound Vib.
, 38
(2
), pp. 245
–254
.10.1016/S0022-460X(75)80008-313.
Ootao
, Y.
, and Tanigawa
, Y.
, 2001
, “Control of Transient Thermoelastic Displacement of a Two-Layered Composite Plate Constructed of Isotropic Elastic and Piezoelectric Layers Due to Nonuniform Heating
,” Arch. Appl. Mech.
, 71
(4–5
), pp. 207
–220
.10.1007/s00419000013614.
Ashida
, F.
, and Tauchert
, T. R.
, 2001
, “A General Plane-Stress Solution in Cylindrical Coordinates for a Piezothermoelastic Plate
,” Int. J. Solids Struct.
, 38
(28–29
), pp. 4969
–4985
.10.1016/S0020-7683(00)00321-815.
Qin
, Q. H.
, and Mai
, Y. W.
, 1998
, “Thermoelectroelastic Green's function and Its application for Bimaterial of Piezoelectric Materials
,” Arch. Appl. Mech.
, 68
(6
), pp. 433
–444
.10.1007/s00419005017716.
Shul'ga
, N. A.
, 1990
, “Radial Electro-Elastic Vibrations of a Hollow Piezoceramic Sphere
,” Sov. Appl. Mech.
, 26
(8
), pp. 731
–734
.10.1007/BF0089178717.
Ding
, H. J.
, Wang
, H. M.
, and Chen
, W. Q.
, 2003
, “Analytical Solution for a Non-Homogeneous Isotropic Piezoelectric Hollow Sphere
,” Arch. Appl. Mech.
, 73
(1–2
), pp. 49
–62
.10.1007/s00419-002-0244-718.
Chen
, W. Q.
, and Shioya
, T.
, 2001
, “Piezothermoelastic Behavior of a Pyroelectric Spherical Shell
,” J. Therm. Stress
, 24
(2
), pp. 105
–120
.10.1080/0149573015050042419.
Chen
, W. Q.
, Lu
, Y.
, Ye
, G. R.
, and Cai
, J. B.
, 2002
, “3D Electroelastic fields in a Functionally Graded Piezoceramic Hollow Sphere Under Mechanical and Electric Loadings
,” Arch. Appl. Mech.
, 72
(1
), pp. 39
–51
.10.1007/s00419010018420.
Dai
, H. L.
, and Wang
, X.
, 2005
, “Thermo-Electro-Elastic Transient Responses in Piezoelectric Hollow Structures
,” Int. J. Solids Struct.
, 42
(3–4
), pp. 1151
–1171
.10.1016/j.ijsolstr.2004.06.06121.
Ootao
, Y.
, and Tanigawa
, Y.
, 2007
, “Transient Piezothermoelastic Analysis for a Functionally Graded Thermopiezo-Electric Hollow Sphere
,” Compos. Struct.
, 81
(4
), pp. 540
–549
.10.1016/j.compstruct.2006.10.00222.
Wang
, H. M.
, Ding
, H. J.
, and Chen
, Y. M.
, 2005
, “Transient Responses of a Multilayered Spherically Isotropic Piezoelectric Hollow Sphere
,” Arch. Appl. Mech.
, 74
(9
), pp. 581
–599
.10.1007/s00419-005-0374-923.
Wang
, H. M.
, and Xu
, Z. X.
, 2010
, “Effect of Material Inhomogeneity on Electromechanical Behaviors of Functionally Graded Piezoelectric Spherical Structures
,” Comput. Mater. Sci.
, 48
(2
), pp. 440
–445
.10.1016/j.commatsci.2010.02.00424.
Sabzikar Boroujerdy
, M.
, and Eslami
, M. R.
, 2013
, “Nonlinear Axisymmetric Thermomechanical Response of Piezo-FGM Shallow Spherical Shells
,” Arch. Appl. Mech.
, 83
(12
), pp. 1681
–1693
.10.1007/s00419-013-0769-yCopyright © 2015 by ASME
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