Vibration analysis of FGM rings using a newly designed cylindrical superelement

Document Type : Article


Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Azadi Ave, Tehran, Iran


Rings are widely used in mechanical equipment and their fitness may damage under severe vibration. In these structures functionally graded rings can be used to optimize the resistance, energy consumption and better fitness. Due to their complexity, finite element analysis may be implemented using special elements. Enhancement of accuracy and minimization of time consumption play an important role in the analysis of these rings.
In this study a new cylindrical superelement for the FGM rings is designed and implemented for the vibration analysis of the rings. The power-law distribution is used for modeling of the FGM rings in the thickness direction. Natural frequencies and mode shapes are obtained and results are compared with simple cases obtained from analytical solution and conventional elements. Findings indicate with a few newly designed superelements, comparable results for simple cases in the reported literature can be achieved.


Main Subjects

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
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).