Analytical investigation of the free vibration behavior
of circular functionally graded (FG) plates integrated with two
uniformly distributed actuator layers made of piezoelectric (PZT4)
material on the top and bottom surfaces of the circular FG plate
based on the classical plate theory (CPT) is presented in this paper.
The material properties of the functionally graded substrate plate are
assumed to be graded in the thickness direction according to the
power-law distribution in terms of the volume fractions of the
constituents and the distribution of electric potential field along the
thickness direction of piezoelectric layers is simulated by a quadratic
function. The differential equations of motion are solved analytically
for clamped edge boundary condition of the plate. The detailed
mathematical derivations are presented and Numerical investigations
are performed for FG plates with two surface-bonded piezoelectric
layers. Emphasis is placed on investigating the effect of varying the
gradient index of FG plate on the free vibration characteristics of the
structure. The results are verified by those obtained from threedimensional
finite element analyses.
[1] M. Koizumi, concept of FGM, Ceram. Trans., 34, 1993, 3-10.
[2] T. Bailey & J.E. Hubbard, Distributed piezoelectric polymer active
vibration control of a cantilever beam, J. Guidance, Control Dyn. , 8,
1985, 605-11.
[3] S. E. Millerand & J.E. Hubbard, Observability of a Bernoulli-Euler
beam using PVF2 as a distributed sensor, MIT Draper Laboratory
Report, 1987.
[4] F. Peng, A. Ng & Y.R. Hu, Actuator placement optimization and
adaptive vibration control of plate smart structures, J. Intell. Mater. Syst.
Struct., 16 , 2005, 263-71.
[5] Y. Ootao & Y. Tanigawa, Three-dimensional transient piezo-thermoelasticity
in functionally graded rectangular plate bonded to a
piezoelectric plate, Int. J. Solids Struct., 200, 37, 4377-401.
[6] J.N. Reddy & Z.Q. Cheng, Three-dimensional solutions of smart
functionally graded plates, ASME J. Appl. Mech., 68, 2001, 234-41.
[7] B.L. Wang & N. Noda, Design of smart functionally graded thermopiezoelectric
composite structure Smart Mater. Struct. , 10, 2001, 189-
93.
[8] X.Q. He, T.Y. Ng, S. Sivashanker & K.M. Liew, Active control of FGM
plates with integrated piezoelectric sensors and actuators, Int. J. Solids
Struct., 38, 2001 ,1641-55.
[9] J. Yang, S. Kitipornchai & K.M. Liew, Non-linear analysis of thermoelectro-
mechanical behavior of shear deformable FGM plates with
piezoelectric actuators, Int. J. Numer. Methods Eng., 59, 2004 1605-32.
[10] X.L. Huang & H.S. Shen, Vibration and dynamic response of
functionally graded plates with piezoelectric actuators in thermal
environments, J. Sound Vib. , 289, 2006, 25-53.
[11] J.N. Reddy & G.N. Praveen, Nonlinear transient thermoelastic analysis
of functionally graded ceramic-metal plate Int. J. Solids Struct, 35, 1998,
4457-76.
[12] R.C. Wetherhold & S. Wang, The use of FGM to eliminate or thermal
deformation, Composite Sci Tech, 56, 1996, 1099-104.
[13] Q. Wang, S.T. Quek & X. Liu, Analysis of piezoelectric coupled circular
plate, Smart Mater. Struct, 10, 2001, 229-39.
[14] J.N. Reddy, Theory and analysis of elastic plates, Philadelphia, Taylor
and Francis, 1999.
[15] D. Halliday & R. Resniek, Physics, John Wiley and Sons, 1978.
[16] D.O. Brush & B.O. Almroth, Buckling of bars plates and shells, New
York, Mac-hill, 1975.
[17] C.T. Loy ,K.L. Lam and J.N. Reddy, "Vibration of functionally graded
cylindrical shells", Int. J Mech Sciences, 41, 1999, 309-24
[1] M. Koizumi, concept of FGM, Ceram. Trans., 34, 1993, 3-10.
[2] T. Bailey & J.E. Hubbard, Distributed piezoelectric polymer active
vibration control of a cantilever beam, J. Guidance, Control Dyn. , 8,
1985, 605-11.
[3] S. E. Millerand & J.E. Hubbard, Observability of a Bernoulli-Euler
beam using PVF2 as a distributed sensor, MIT Draper Laboratory
Report, 1987.
[4] F. Peng, A. Ng & Y.R. Hu, Actuator placement optimization and
adaptive vibration control of plate smart structures, J. Intell. Mater. Syst.
Struct., 16 , 2005, 263-71.
[5] Y. Ootao & Y. Tanigawa, Three-dimensional transient piezo-thermoelasticity
in functionally graded rectangular plate bonded to a
piezoelectric plate, Int. J. Solids Struct., 200, 37, 4377-401.
[6] J.N. Reddy & Z.Q. Cheng, Three-dimensional solutions of smart
functionally graded plates, ASME J. Appl. Mech., 68, 2001, 234-41.
[7] B.L. Wang & N. Noda, Design of smart functionally graded thermopiezoelectric
composite structure Smart Mater. Struct. , 10, 2001, 189-
93.
[8] X.Q. He, T.Y. Ng, S. Sivashanker & K.M. Liew, Active control of FGM
plates with integrated piezoelectric sensors and actuators, Int. J. Solids
Struct., 38, 2001 ,1641-55.
[9] J. Yang, S. Kitipornchai & K.M. Liew, Non-linear analysis of thermoelectro-
mechanical behavior of shear deformable FGM plates with
piezoelectric actuators, Int. J. Numer. Methods Eng., 59, 2004 1605-32.
[10] X.L. Huang & H.S. Shen, Vibration and dynamic response of
functionally graded plates with piezoelectric actuators in thermal
environments, J. Sound Vib. , 289, 2006, 25-53.
[11] J.N. Reddy & G.N. Praveen, Nonlinear transient thermoelastic analysis
of functionally graded ceramic-metal plate Int. J. Solids Struct, 35, 1998,
4457-76.
[12] R.C. Wetherhold & S. Wang, The use of FGM to eliminate or thermal
deformation, Composite Sci Tech, 56, 1996, 1099-104.
[13] Q. Wang, S.T. Quek & X. Liu, Analysis of piezoelectric coupled circular
plate, Smart Mater. Struct, 10, 2001, 229-39.
[14] J.N. Reddy, Theory and analysis of elastic plates, Philadelphia, Taylor
and Francis, 1999.
[15] D. Halliday & R. Resniek, Physics, John Wiley and Sons, 1978.
[16] D.O. Brush & B.O. Almroth, Buckling of bars plates and shells, New
York, Mac-hill, 1975.
[17] C.T. Loy ,K.L. Lam and J.N. Reddy, "Vibration of functionally graded
cylindrical shells", Int. J Mech Sciences, 41, 1999, 309-24
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56805", author = "F.Ebrahimi and A.Rastgo", title = "Free Vibration Analysis of Smart FGM Plates", abstract = "Analytical investigation of the free vibration behavior
of circular functionally graded (FG) plates integrated with two
uniformly distributed actuator layers made of piezoelectric (PZT4)
material on the top and bottom surfaces of the circular FG plate
based on the classical plate theory (CPT) is presented in this paper.
The material properties of the functionally graded substrate plate are
assumed to be graded in the thickness direction according to the
power-law distribution in terms of the volume fractions of the
constituents and the distribution of electric potential field along the
thickness direction of piezoelectric layers is simulated by a quadratic
function. The differential equations of motion are solved analytically
for clamped edge boundary condition of the plate. The detailed
mathematical derivations are presented and Numerical investigations
are performed for FG plates with two surface-bonded piezoelectric
layers. Emphasis is placed on investigating the effect of varying the
gradient index of FG plate on the free vibration characteristics of the
structure. The results are verified by those obtained from threedimensional
finite element analyses.", keywords = "Circular plate, CPT, Functionally graded,Piezoelectric.", volume = "2", number = "1", pages = "43-6", }