Free Vibration of Functionally Graded Beams with Piezoelectric Layers Subjected to Axial Load
الموضوعات :
M Karami Khorramabadi
1
(Faculty of Engineering, Islamic Azad University, Khorramabad Branch)
الکلمات المفتاحية: Free vibration, Functionally graded beam, Piezoelectric layer,
ملخص المقالة :
This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers subjected to axial compressive loads. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing equation is established. Resulting equation is solved using the Euler’s Equation. The effects of the constituent volume fractions, the influences of applied voltage and axial compressive loads on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.
[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.
