Abstract
In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction, while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach.
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References
M. Koizumi, The concept of FGM, Ceram. Trans. Func. Grad. Mater., 34 (1993) 3–10.
M. Teymur, N. R. Chitkara, K. Yohngjo, J. Aboudi, M. J. Pindera and S. M. Arnold, Thermoelastic Theory for the Response of Materials Functionally Graded in Two Directions, Int. J. Solids Struct., 33 (1996) 931–66.
E. Feldman and J. Aboudi, Buckling analysis of functionally graded plates subjected to uniaxial loading, Compos. Struct., 38 (1997) 29–36.
Yang and H. S. Shen, Dynamic response of initially stressed functionally graded rectangular thin plates, Compos. Struct., 54 (2001) 497–508.
H. S. Shen, Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments, Int. J. Mech. Sci., 44 (2002) 561–584.
T. Bailey and J. E. Hubbard, Distributed piezoelectric polymer active vibration control of a cantilever beam, J. Guidance, Control Dyn., 8 (1985) 605–611.
F. Peng, A. Ng and Y. R., Hu, Actuator placement optimization and adaptive vibration control of plate smart structures, J. Intell Mater Syst Struct., 16 (2005) 263–271.
W. J. Spencer, W. T. Corbett, L. R. Dominguez and B. D. Shafer, An electronically controlled piezoelectric insulin pump and valves, IEEE Trans. Sonics Ultrason., 25 (1978) 153–156.
S. Dong, X. Du, P. Bouchilloux and K. Uchino, Piezoelectric ring-morph actuation for valve application, J. Electroceram., 8 (2002) 155–161.
C. Y. K. Chee, L. Tong and G. P. Steve, A review on the modelling of piezoelectric sensors and actuators incorporated in intelligent structures, J. Intel. Mater. Syst. Str., 9 (1998) 3–19.
L. Cao, S. Mantell and D. Polla, Design and simulation of an implantable medical drug delivery system using microelectromechanical systems technology, Sensors Actuators A, 94 (2001) 117–125.
X. Chen, C. H. J. Fox and S. McWilliam, Optimization of a cantilever microswitch with piezoelectric actuation, J. Intel. Mater. Syst. Str., 15 (2004) 823–834.
Y. Ootao and Y. Tanigawa, Control of transient thermoelastic displacement of a functionally graded rectangular plate bonded to a piezoelectric plate due to nonuniform heating, Acta Mech., 148 (2001) 17–33.
J. N. Reddy and Z. Q. Cheng, Three-dimensional solutions of smart functionally graded plates, ASME J. Appl. Mech., 68 (2001) 234–241.
B. L. Wang and N. Noda, Design of smart functionally graded thermo-piezoelectric composite structure, Smart Mater. Struct., 10 (2001) 189–193.
X. Q. He, T. Y. Ng, S. Sivashanker and K. M. Liew, Active control of FGM plates with integrated piezoelectric sensors and actuators, Int. J. Solids Struct., 38 (2001) 1641–1655.
J. Yang, S. Kitipornchai and K. M. Liew, Nonlinear analysis of thermo-electro-mechanical behavior of shear deformable FGM plates with piezoelectric actuators, Int. J. Numer. Methods Eng., 59 (2004) 1605–1632
J. Yang, S. Kitipornchai and K. M. Liew, Large amplitude vibration of thermo-electric-mechanically stressed FGM laminated plates, Computer Methods in Applied Mechanics and Engineering, 192, (2003) 3861–3885.
X. L. Huang and H. S. Shen, Vibration and dynamic response of functionally graded plates with piezoelectric actuators in thermal environments, J. Sound Vib., 289 (2006) 25–53.
F. Ebrahimi and A. Rastgoo, An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory, Thin-Walled Structures (2008) Article in press DOI: 10.1016/ j.tws.2008.03.008.
F. Ebrahimi and A. Rastgoo, Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers, Smart Mater. Struct., 17 (2008) no. 015044.
A. J. Markworth, K. S. Ramesh and Jr. Parks, Modeling studies applied to functionally graded materials, J. Mater. Sci., 30 (1995) 2183–2193.
J. N. Reddy and G. N. Praveen, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plate, Int. J. Solids Struct., 35 (1998) 4457–4476.
R. C. Wetherhold and S. Wang, The use of functionally graded materials to eliminate or thermal deformation, Composite Sci. Tech., 56 (1996) 1099–1104.
Y. Tanigawa, H. Morishita and S. Ogaki, Derivation of system of fundamental equations for a three dimensional thermoelastic field with nonhomogeneous material properties and its application to a semi infinite body, J. Thermal Stress, 22 (1999) 689–711.
H. F. Tiersten, Linear piezoelectric plate vibrations, plenum press, New York, USA, (1969).
D. O. Brush and B. O. Almroth, Buckling of bars plates and shells, McGraw-Hill, New York, USA, (1975).
Q. Wang, S. T. Quek and X. Liu, Analysis of piezoelectric coupled circular plate, Smart Mater Struct., 10 (2001) 229–239.
R. D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, J. Appl Mech., 18 (1951) 31–38.
J. N. Reddy, Theory and analysis of elastic plates, Taylor and Francis, Philadelphia, USA, (1999).
X. Liu, Q. Wang and S. T. Quek, Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates, Int. J. Solids Struct., 39 (2002) 2129–2151.
D. Halliday and R. Resnick, Physics, John Wiley and Sons, New York, USA, (1978).
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Ebrahimi, F., Rastgoo, A. & Kargarnovin, M.H. Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers. J Mech Sci Technol 22, 1058–1072 (2008). https://doi.org/10.1007/s12206-008-0303-2
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DOI: https://doi.org/10.1007/s12206-008-0303-2