Abstract
The present study focuses on the free vibration behavior of functionally graded (FG) rotating disk under thermal and centrifugal load, up to the limit elastic state of stress. Power law variation across the radial direction is assumed for the material properties of the FG disks. Variational principles are used to obtain the governing equations, and energy principles are used for the analysis method. The solution algorithm is executed by utilizing MATLABĀ® computational simulation software. For various combinations of rotational speed and thermal load up to the limit elastic state as predicted by von Mises criteria, the dynamic characteristics of the FG disk are presented in a non-dimensional plane. Some parametric studies are carried out to explore the impacts of the disk geometries and material gradients on the in-plane natural and forced frequencies of the FG disks.
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References
Weisensel GN (1989) Natural frequency information for circular and annular plates. J Sound Vib 133(1):129ā137
Bauer HF, Eidel W (2007) Transverse vibration and stability of spinning circular plates of constant thickness and different boundary conditions. J Sound Vib 300:877ā895
Mazzei AJ (2012) On the effect of functionally graded materials on resonances of rotating beams. Shock Vib 19:707ā718
Ramu I, Mohanty SC (2017) Free vibration analysis of rotating plates in high thermal environments using the finite element method. Int J Acoust Vib 22:58ā67
Nayak P, Saha KN (2012) Thermo mechanical analysis and design of rotating disks. In: Emerging trends in science, engineering and technology, proceedings of international conference, INCOSET 2012. Springer, India, pp 473ā484
Barasch S, Chen Y (1972) On the vibration of a rotating disk. J Appl Mech 39:1143ā1144
Irie T, Yamada G, Kanda R (1979) Free vibration of rotating non-uniform discs: spline interpolation technique calculations. J Sound Vib 66:13ā23
Shahab AAS (1993) Finite element analysis for the vibration of variable thickness discs. J Sound Vib 162:67ā88
Tomioka T, Kobayashi Y, Yamada G (1996) Analysis of free vibration of rotating disk-blade coupled systems by using artificial springs and orthogonal polynomials. J Sound Vib 191:53ā73
Luo ACJ (2000) An approximate theory for geometrically-nonlinear thin plates. Int J Solids Struct 37:7655ā7670
Luo ACJ, Mote CD (2003) Asymmetric responses of rotating, thin disks experiencing large deflections. Comput Math Appl 45:217ā228
Tornabene F (2009) Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Comput Methods Appl Mech Eng 198(37ā40):2911ā2935
Kermani ID, Ghayour M, Mirdamadi HR (2012) Free vibration analysis of multi-directional functionally graded circular and annular plates. J Mech Sci Technol 26(11):3399ā3410
Nie GJ, Zhong Z (2007) Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Comput Methods Appl Mech Eng 196:4901ā4910
Dong CY (2008) Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev-Ritz method. Mater Des 29:1518ā1525
Malekzadeh P, Shahpari SA, Ziaee HR (2010) Three-dimensional free vibration of thick functionally graded annular plates in thermal environment. J Sound Vib 329:425ā442
Yang Y, Lam CC, Kou KP (2016) Forced vibration analysis of functionally graded beams by the meshfree boundary-domain integral equation method. Eng Anal Boundary Elem 72:100ā110
Das D, Sahoo P, Saha K (2009) Free vibration analysis of a rotating annular disc under uniform pressure loading. Proc Inst Mech Eng Part C J Mech Eng Sci 224:615ā634
Vel SS, Batra RC (2004) Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J Sound Vib 272:703ā730
Peng XL, Li XF (2010) Thermal stress in rotating functionally graded hollow circular disks. Compos Struct 92:1896ā1904
Narender K, Rao ASM, Rao KGK, Krishna NG (2013) Temperature dependence of density and thermal expansion of wrought aluminum alloys 7041, 7075 and 7095 by gamma ray attenuation method. J Mod Phys 4:331ā336
Acknowledgements
The first author gratefully acknowledges support from the Council of Scientific and Industrial Research (CSIR) funded by the Government of India for the financial grant.
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Nayak, P., Saha, K. (2021). Dynamic Analysis of Thermo-Mechanically Loaded Functionally Graded Disks by an Iterative Variational Method. In: Rao, J.S., Arun Kumar, V., Jana, S. (eds) Proceedings of the 6th National Symposium on Rotor Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5701-9_46
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DOI: https://doi.org/10.1007/978-981-15-5701-9_46
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