References
1. Rao, S., Vibration of Continuous Systems, John Wiley
& Sons, New Jersey (2007).
2. Wang, L., Lu, Y., Xiang, Y., Qin, L., and Cai, D.
\Vibration analysis for piezoceramic ring", Ceramics
International, 39(1), pp. 739-742 (2013).
3. Mustapha, K.B. \Modeling of a functionally graded
micro-ring segment for the analysis of coupled
extensional-
exural waves", Composite Structures,
117, pp. 274-287 (2014).
4. Loy, C.T., Larn, K.Y., and Reddy, J.N. \Vibration of
functionally graded cylindrical shells", Int. J. Mech.
Sci., 41(3), pp. 309-324 (1999).
5. Shakeri, M., Akhlaghi, M., and Hoseini, S.M. \Vibration
and radial wave propagation velocity in functionally
graded thick hollow cylinder", Composite Structures,
76(1-2), pp. 174-181 (2006).
6. Asgari, M. and Akhlaghi, M. \Natural frequency analysis
of 2D-FGM thick hollow cylinder based on threedimensional
elasticity equations", European Journal of
Mechanics - A/Solids, 30(2), pp. 72-81 (2011).
7. Yin, S., Yu, T., and Liu, P. \Free vibration analysis
of functionally graded plates using isogeometric nite
element method", Journal of Vibration and Shock, 24,
pp. 180-186 (2013).
8. Yu, T.T., Yin, S., Bui, T.Q., and Hirose, S. \A simple
FSDT-based isogeometric analysis for geometrically
nonlinear analysis of functionally graded plates", Finite
Elem. Anal. Des., 96, pp. 1-10 (2015).
9. Sarvi, M.N. and Ahmadian, M.T. \Design and implementation
of a new spherical super element in
structural analysis", Applied Mathematics and Computation,
218(14), pp. 7546-7561 (2012).
10. Jiang, J. and Olson, M.D. \Nonlinear analysis of
orthogonally sti ened cylindrical shells by a super
element approach", Finite Elem. Anal. Des., 18(1-3),
pp. 99-110 (1994).
11. Koko, T.S. and Olson, M.D. \Vibration analysis of
sti ened plates by super elements", J. Sound Vib.,
158(1), pp. 149-167 (1992).
12. Ju, F. and Choo, Y.S. \Superelement approach to
cable passing through multiple pulleys", Int. J. Solids
Struct., 42, pp. 3533-3547 (2005).
13. Ahmadian, M.T. and Bonakdar, M. \A new cylindrical
element formulation and its application to structural
analysis of laminated hollow cylinders", Finite Elem.
Anal. Des., 44(9-10), pp. 617-630 (2008).
14. Taghvaeipour, A., Bonakdar, M., and Ahmadian, M.T.
\Application of a new cylindrical element formulation
in nite element structural analysis of FGM hollow
cylinders", Finite Elem. Anal. Des., 50, pp. 1-7 (2012).
15. Ghorbani, Sh. and Ahmadian, M.T. \Extend the
cylindrical superelement and its application to vibration
analysis of cylindrical structures", Proceeding of
the Fourth International Conference on Vibration and
Acoustic, Tehran, Iran (2014) (in Persian).
16. Reddy, J.N., Theory and Analysis of Elastic Plates,
Taylor and Francis, PA (1999).
17. Stasa, F.L., Applied Finite Element Analysis for Engineers,
CBS, Japan (1986).
)