Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30309
Vibration Analysis of Functionally Graded Engesser- Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation

Authors: A. R. Nezamabadi, M. Karami Khorramabadi


This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. 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 and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: free vibration, functionally graded beam, Engesser-Timoshenko beam theory, Elastic Foundation

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1528


[1] PJC. Branco, JA. Dente, “On the electromechanics of a piezoelectric transducer using a bimorph cantilever undergoing asymmetric sensing and actuation”, Smart Mater Struct 2004, pp.631–42.
[2] M. Sitti, “Piezoelectrically actuated four-bar mechanism with two flexible links for micromechanical flying insect thorax”, Trans Mechatronics, 2003, pp.26–36.
[3] R. Fung, S. Chao, “Dynamic analysis of an optical beam deflector”, Sensors Actuators, 2000, pp.1–6.
[4] A. Kruusing, “Analysis and optimization of loaded cantilever beam microactuators”, Smart Mater Struct, 2000, pp.186–96.
[5] TT. Liu, ZF. Shi, “Bending behavior of functionally gradient piezoelectric cantilever”, Ferroelectrics, 2004, pp.43–51.
[6] ZF. Shi, “Bending behavior of piezoelectric curved actuator”, Smart Mater Struct, 2005, pp.35–42.
[7] ZF. Shi, HJ. Xiang, “Spencer BFJ. Exact analysis of multi-layer piezoelectric/composite cantilevers”, Smart Mater Struct, 2006,pp.47– 58.
[8] TT. Zhang, ZF. Shi, “Two-dimensional exact analyses for piezoelectric curved Actuators”, J Micromech Microeng, 2006, pp.640–7.
[9] DA. Saravanos, PR. Heyliger, DA. Hopkins, “Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates”, Int J Solids Struct, 1997, pp. 359–78.
[10] S. Kapuria, N. Alam, “Efficient layerwise finite element model for dynamic analysis of laminated piezoelectric beams”, Comput Methods Appl Mech Eng, 2006, pp. 2742–60.
[11] W.Q. Chen, X. Wang, H.J. Ding, “Free vibration of a fluid-filled hollow sphere of a functionally graded material with spherical isotropy”, Journal of the Acoustical Society of America, 1999, pp.2588-2594.
[12] W.Q. Chen, “Vibration theory of non-homogeneous, spherically isotropic piezoelastic bodies”, Journal of Sound and vibration, 2000, pp. 833-860.
[13] Y. Ootao, Y. Tanigawa, “Three-dimensional transient piezothermoelasticity in functionally graded rectangular plate bonded to a piezoelectric plate”, International Journal of Solids and Structures, 2000, pp. 4377-4401.
[14] B.L. Wang, J.C. Han, S.Y. Du, “Functionally graded penny-shaped cracks under dynamic loading”, Theoretical and Applied Fracture Mechanics, 1999, pp.165-175.
[15] W.Q. Chen, J. Liang, H.J. Ding, “Three dimensional analysis of bending problems of thick piezoelectric composite rectangular plates (in Chinese)”, Acta Materiae Compositae Sinica, 1997, pp.108-115.
[16] W.Q. Chen, R.Q. Xu, H.J. Ding, “On free vibration of a piezoelectric composite rectangular plate”, Journal of Sound and vibration, 1998, pp.741-748.
[17] H.J. Ding, R.Q. Xu, F.L. Guo, “Exact axisymmetric solution of laminated transversely isotropic piezoelectric circular plates (I) exact solutions for piezoelectric circular plate”, Science in China, 1999, pp.388-395.
[18] J.N. Reddy, G.N. Praveen, “Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates”, International Journal of. Solids and Structures, 1998, pp.4467-4476.
[19] V.V. Bolotin, “The dynamic Stability of Elastic Systems”, Holden Day, San Francisco,1964.