In this study, vibration and buckling of axially functionally graded simply supported beams is analyzed by using the semi-inverse method. Euler—Bernoulli beam theory was used in the analysis. By using a pre-specified frequency and buckling loads, variation of the Young's modulus in the axial direction is obtained in terms of the axial coordinate. It is found that the Young's modulus changes exponentially between the edges of the beam for the vibration and buckling problem.
Loy, C.T. , Lam, K.Y. and Reddy, J.N. (1999). Vibration of Functionally Graded Cylindrical Shells, International Journal of Mechanical Science, 41: 309-324.
2.
Vel, S.S. and Batra, R.C. (2002). Exact Solution for the Cylindrical Bending Vibration of Functionally Graded Plates, In: Proceedings of the American Society of Composites Seventh Technical Conference, October 21-23, Purdue University, West Lafayette, Indiana.
3.
Yang, J. and Shen, H.S. (2001). Dynamic Response of Initially Stressed Functionally Graded Rectangular Thin Plates, Composite Structures, 54: 497-508.
4.
Yang, J. and Shen, H.S. (2003). Free Vibration and Parametric Resonance of Shear Deformable Functionally Graded Cylindrical Panels, Journal of Sound and Vibration, 261: 871-893.
5.
Chen, W.Q. and Ding, H.J. (2002). On the Free Vibration of Functionally Graded Piezoelectric Rectangular Plate, Acta Mechanica, 153: 207-216.
6.
Aydogdu, M. and Taksin, V. (2007). Free Vibration Analysis of Functionally Graded Beams with Simply Supported Edges, Materials and Design, 28: 1651-1656.
7.
Candan, S. and Elishakoff, I. (2001). Apparently First Closed-form Solutions for Vibrating Inhomogeneous Beams, International Journal of Solids and Structures , 38: 3411-3441.
8.
Elishakoff, I. and Candan, S. (2001). Apparently First Closed-form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams, Journal of Applied Mechanics, 68: 176-185.
9.
Guede, Z. and Elishakoff, I. (2001). Apparently First Closed-form Solutions for Inhomogeneous Vibrating Beams under Axial Loading, In: Proceedings of Royal Society of London A, 457: 623-649.
10.
Neuringer, I. and Elishakoff, I. (2001). Inhomogeneous Beams that may Possess a Prescribed Polynomial Second Mode, Chaos Solitons and Fractals, 12: 881-896.
11.
Becquet, R. and Elishakoff, I. (2001). Class of Analytical Closed-Form Polynomial Solutions for Guided-Pinned Inhomogeneous Beams, Chaos, Solitons&Fractals, 12: 1509-1534.
12.
Elishakoff, I. and Guede, Z. (2004). Analytical Polynomial Solutions for Vibrating Axially Graded Beams, Mechanics of Advanced Materials and Structures, 11: 517-533.
13.
Wu, L., Wang, Q. and Elishakoff, I. (2005). Semi-inverse Method for Axially Functionally Graded Beams with an Anti-symmetric Vibration Mode, Journal of Sound and Vibration, 284: 1190-1202.
14.
Elishakoff, I. (2001). Inverse Buckling Problem for Inhomogeneous Columns, International Journal of Solids and Structures, 38: 457-464.
15.
Calio, I. and Elishakoff, I. (2005). Closed-form Solutions for Axially Graded Beam-columns , Journal of Sound and Vibration, 280: 1083-1094.
16.
Meirovitch, L. (2001). Fundamental of Vibrations , McGrawHill, New York.
17.
Timoshenko, S.P. and Gere, J.M. (1961). Theory of Elastic Stability , McGrawHill, New York.
