Summary
On the basis of three-dimensional theory equations of transversely isotropic piezoelasticity, two independent state equations with variable coefficients are derived. To this end, separation formulae for displacements and shear stresses are employed. A laminated approximation is used to transform the state equations to the ones with constant coefficients in each layer. The free vibration problem of a piezoelectric rectangular plate with a functionally graded property is then investigated. Discussion on the boundary conditions is presented.
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References
Tanigawa, Y.: Some basic thermoelastic problems for nonhomogeneous structural materials. Appl. Mech. Reviews48, 287–300 (1995).
Reddy, J. N., Chin, K.: Thermomechanical behavior of functionally graded cylinders and plates. J. Thermal Stresses26, 593–626 (1998).
Reddy, J. N., Wang, C. M., Kitipornchai, S.: Axisymmetric bending of functionally graded circular and annular plates. Europ. Mechanics A/Solids18, 185–199 (1999).
Loy, C. T., Lam, K. Y., Reddy, J. N.: Vibration of functionally graded cylindrical shells. Int. J. Mech. Sci.41, 309–324 (1999).
Cheng, Z. Q., Batra, R. C.: Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates. J. Sound Vibrat.229, 879–895 (2000).
Chen, W. Q., Wang, X., Ding, H. J.: Free vibration of a fluid-filled hollow sphere of a functionally graded material with spherical isotropy. J. Acoust. Soc. America106, 2588–2594 (1999).
Chen, W. Q.: Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy. J. Strain Anal. Eng. Design35, 13–20 (2000).
Liu, G. R., Tani, T.: Characteristics of wave propagation in functionally gradient piezoelectric material plates and its response analysis (Part 1 and 2). Trans. Japan Soc. Mech. EngineersA57, 2212–2217 (1991). (In Japanese with English abtract.)
Liu, G. R., Tani, T.: SH surface waves in functionally gradient piezoelectric material plates. Trans. Japan Soc. Mech. EngineersA58, 504–507 (1992). (In Japanese with English abstract.)
Bufler, H.: Planar elastic laminates and their homogenization. Acta Mech.141, 21–36 (2000).
Sosa, H. A., Castro, M. A.: Electroelastic analysis of piezoelectric laminated structures. Appl. Mech. Reviews46, s21–s28 (1993).
Lee, J. S., Jiang, L. Z.: Exact electroelastic analysis of piezoelectric laminae via state space approach. Int. J. Solids Struct.33, 977–990 (1996).
Chen, W. Q., Xu, R. Q., Ding, H. J.: On free vibration of a piezoelectric composite rectangular plate. J. Sound Vibrat.218, 741–748 (1998).
Ding, H. J., Xu, R. Q., Chi, Y. W., Chen, W. Q.: Free axisymmetric vibration of transversely isotropic piezoelectric circular plates. Int. J. Solids Struct.36, 4629–4652 (1999).
Ding, H. J., Chen, B., Liang, J.: General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct.33, 2283–2298 (1996).
Tang, Y. Y., Xu, K.: Exact solutions of piezoelectric materials with moving screw and edge dislocation. Int. J. Eng. Sci.32, 1579–1591 (1994).
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Chen, W.Q., Ding, H.J. On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mechanica 153, 207–216 (2002). https://doi.org/10.1007/BF01177452
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DOI: https://doi.org/10.1007/BF01177452