Free Vibration Analysis of Rotating Functionally Graded Annular Disc of Variable Thickness Using Generalized Differential Quadrature Method

Document Type : Article

Authors

1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

2 Department of Mechanical and Aerospace Engineering,, Malek- Ashtar University of Technology, Isfahan, Iran

3 School of Mechanical Engineering, College of Engineering, University of Tehran

Abstract

In this paper, free vibration analysis of rotating annular disc made of functionally graded material (FGM) with variable thickness is presented. Elasticity modulus, density and thickness of the disc are assumed to vary radially according to a power low function. The natural frequencies and critical speeds of the rotating FG annular disc of variable thickness with two types of boundary conditions are obtained employing the numerical generalized differential quadrature method (GDQM). The boundary conditions considered in the analysis is the both edges clamped (C-C) and the inner edge clamped and the outer edge free (C-F).The influence of the graded index, thickness variation, geometric parameters and angular velocity on the dimensionless natural frequencies and critical speeds are demonstrated. It is shown that using a plate with a convergent thickness profile, we have a higher critical speed and natural frequency and using a divergent thickness profile, we can lower the critical speed. It is found that increase in the ratio of inner-outer radii could increase the critical speed of the FG annular disk. The results of the present work could improve the design of the rotating FG annular disk in order to avoid resonance condition

Keywords

Main Subjects

References

References

1. Sarra , A. and Mao, Z. \Statistical modeling of
wavelet-transform-based features in structural health
monitoring", In Model Validation and Uncertainty
Quanti cation, 3, Springer, pp. 253-262 (2016).
2. Poozesh, P., Baqersad, J., Niezrecki, C., Avitabile, P.,
Harvey, E., and Yarala, R. \Large-area photogrammetry
based testing of wind turbine blades", Mechanical
Systems and Signal Processing, 86, pp. 98-115 (2017).
3. Niezrecki, C., Poozesh, P., Aizawa, K., and Heilmann,
G. \Wind turbine blade health monitoring using acoustic
beamforming techniques", J. Acoust. Soc. Am.,
135, pp. 2392-2393 (2014).
4. Sadeghi, H., Baghani, M., and Naghdabadi, R. \Strain
gradient thermoelasticity of functionally graded cylinders",
Scientia Iranica, Transactions B, Mechanical
Engineering, 21, p. 1415 (2014).
5. Baghani, M. and Fereidoonnezhad, B. \Limit analysis
of FGM circular plates subjected to arbitrary rotational
symmetric loads using von-Mises yield criterion",
Acta Mechanica, 224, p. 1601 (2013).
6. Lamb, H. and Southwell, R. \The vibrations of a spinning
disk", Proceedings of the Royal Society of London
Series A, Containing Papers of a Mathematical and
Physical Character, 99, pp. 272-280 (1921).
7. Southwell, R. \On the free transverse vibrations of a
uniform circular disc clamped at its centre; and on the
e ects of rotation", In Proceedings of the Royal Society
M.H. Jalali et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 728{740 739
of London A: Mathematical, Physical and Engineering
Sciences, The Royal Society, pp. 133-153 (1922).
8. Deshpande, M. and Mote, C. \In-plane vibrations
of a thin rotating disk", Journal of Vibration and
Acoustics, 125, pp. 68-72 (2003).
9. Bauer, H.F. and Eidel, W. \Transverse vibration
and stability of spinning circular plates of constant
thickness and di erent boundary conditions", Journal
of Sound and Vibration, 300, pp. 877-895 (2007).
10. Lee, H. and Ng, T. \Vibration and critical speeds of
a spinning annular disk of varying thickness", Journal
of Sound and Vibration, 187, pp. 39-50 (1995).
11. Singh, B. and Saxena, V. \Axisymmetric vibration of
a circular plate with exponential thickness variation",
Journal of Sound and Vibration, 192, pp. 35-42 (1996).
12. Taher, H.R.D., Omidi, M., Zadpoor, A., and Nikooyan,
A. \Free vibration of circular and annular plates with
variable thickness and di erent combinations of boundary
conditions", Journal of Sound and Vibration, 296,
pp. 1084-1092 (2006).
13. Davoodi Kermani, I., Mirdamadi, H., and Ghayour,
M. \Nonlinear stability analysis of rotational dynamics
and transversal vibrations of annular circular thin
plates functionally graded in radial direction by di erential
quadrature", Journal of Vibration and Control,
22, pp. 2482-2502 (2014).
14. Horgan, C. and Chan, A. \The stress response of
functionally graded isotropic linearly elastic rotating
disks", Journal of Elasticity, 55, pp. 219-230 (1999).
15. Nie, G. and Batra, R. \Stress analysis and material tailoring
in isotropic linear thermoelastic incompressible
functionally graded rotating disks of variable thickness",
Composite Structures, 92, pp. 720-729 (2010).
16. Mohammadsalehi, M., Zargar, O., and Baghani, M.
\Study of non-uniform viscoelastic nanoplates vibration
based on nonlocal rst-order shear deformation
theory", Meccanica, 52 , pp. 1063-1077 (2017).
17. Asghari, M. and Ghafoori, E. \A three-dimensional
elasticity solution for functionally graded rotating
disks", Composite Structures, 92, pp. 1092-1099
(2010).
18. Peng, X.-L. and Li, X.-F. \Elastic analysis of rotating
functionally graded polar orthotropic disks", International
Journal of Mechanical Sciences, 60, pp. 84-91
(2012).
19. Bahaloo, H., Papadopolus, J., Ghosh, R., Mahdi,
E., Vaziri, A., and Nayeb-Hashemi, H. \Transverse
vibration and stability of a functionally graded rotating
annular disk with a circumferential crack",
International Journal of Mechanical Sciences, 113, pp.
26-35 (2016).
20. Khorasany, R.M. and Hutton, S.G. \An analytical
study on the e ect of rigid body translational degree of
freedom on the vibration characteristics of elastically
constrained rotating disks", International Journal of
Mechanical Sciences, 52, pp. 1186-1192 (2010).
21. Guven, U. and C elik, A. \On transverse vibrations of
functionally graded isotropic linearly elastic rotating
solid disks", Mechanics Research Communications, 28,
pp. 271-276 (2001).
22. Wu, T. and Liu, G. \A di erential quadrature as
a numerical method to solve di erential equations",
Computational Mechanics, 24, pp. 197-205 (1999).
23. Wu, T. and Liu, G. \The generalized di erential
quadrature rule for fourth-order di erential equations",
International Journal for Numerical Methods
in Engineering, 50, pp. 1907-1929 (2001).
24. Shahriari, B., Jalali, M., and Karamooz Ravari, M.
\Vibration analysis of a rotating variable thickness
bladed disk for aircraft gas turbine engine using generalized
di erential quadrature method", Proceedings
of the Institution of Mechanical Engineers, Part G:
Journal of Aerospace Engineering, 231, pp. 2739-2749
(2017).
25. Irie, T., Yamada, G., and Kanda, R. \Free vibration of
rotating non-uniform discs: Spline interpolation technique
calculations", Journal of Sound and Vibration,
66, pp. 13-23 (1979).
26. Shu, C., Di erential Quadrature and Its Application
in Engineering, Springer Science & Business Media
(2012).

Scientia Iranica
Volume 25, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2018
Pages 728-740

Files

Share

How to cite

Statistics