Free Vibration of Functionally Graded Beams with Piezoelectric Layers Subjected to Axial Load

Subject Areas : Engineering

M  Karami Khorramabadi ¹ (Faculty of Engineering, Islamic Azad University, Khorramabad Branch)

Received: 2009-02-21 Accepted : 2009-04-23 Published : 2009-04-30

Keywords:

References:

[1] Bisegna P., Maceri F., 1996, An exact three-dimensional solution for simply supported rectangular piezoelectric plates, ASME Journal of Applied Mechanics 63: 628-638.

[2] Kapuria S., Dumir P.C., Sengupta S., 1996, Exact piezothermoelastic axisymmetric solution of a finite transversely isotropic cylindrical shell, Computers and Structures 61:1085-1099.

[3] Ding H.J., Chen W.Q., Guo Y.M., Yang Q.D., 1997, Free vibrations of piezoelectric cylindrical shells filled with compressible Fluid, International Journal of Solids and Structures 34: 2025-2034.

[4] Shul'ga N.A., 1993, Harmonic electroelastic oscillation of spherical bodies, Soviet Applied Mechanics 29: 812-817.

[5] Chen W.Q., Ding H.J., 1998, Exact static analysis of a rotating piezoelectric spherical shell, Acta Mechanica Sinica 14: 257-265.

[6] Chen W.Q., Ding H.J., Xu R.Q., 2001, Three dimensional free vibration analysis of a fluid-filled piezoceramic hollow sphere, Computers and Structures 79: 653-663.

[7] Tanigawa Y., 1995, Some basic thermo elastic problems for nonhomogeneous structural materials, Applied Mechanics Reviews 48: 287-300.

[8] Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309-324.

[9] Cheng Z.Q., Batra R.C., 2000, Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates, Journal of Sound and Vibration 229: 879-895.

[10] Chen W.Q., Wang X., Ding H.J., 1999, Free vibration of a fluid-filled hollow sphere of a functionally graded material with spherical isotropy, Journal of the Acoustical Society of America 106: 2588-2594.

[11] Chen W.Q., 2000, Vibration theory of non-homogeneous, spherically isotropic piezoelastic bodies, Journal of Sound and Vibration 229: 833-860.

[12] Ootao Y., Tanigawa Y., 2000, Three-dimensional transient piezothermoelasticity in functionally graded rectangular plate bonded to a piezoelectric plate, International Journal of Solids and Structures 37: 4377-4401.

[13] Wang B.L., Han J.C., Du S.Y., 1999, Functionally graded penny-shaped cracks under dynamic loading, Theoretical and Applied Fracture Mechanics 32: 165-175.

[14] Chen W.Q., Liang J., Ding H.J., 1997, Three dimensional analysis of bending problems of thick piezoelectric composite rectangular plates, Acta Materiale Compositae Sinica 14: 108-115 (in Chinese).

[15] Chen W.Q., Xu R.Q., Ding H.J., 1998, On free vibration of a piezoelectric composite rectangular plate, Journal of Sound and Vibration 218: 741-748.

[16] Ding H.J., Xu R.Q., Guo F.L., 1999, Exact axisymmetric solution of laminated transversely isotropic piezoelectric circular plates (I) exact solutions for piezoelectric circular plate, Science in China (E) 42: 388-395.

[17] Wang J.G., 1999, State vector solutions for nonaxisymmetric problem of multilayered half space piezoelectric medium, Science in China (A) 42: 1323-1331.

[18] Reddy J.N., Praveen G.N., 1998, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International Journal of Solids and Structures 35: 4467-4476.

[19] Bolotin V.V., 1964, The dynamic Stability of Elastic Systems, Holden Day, San Francisco.