Intelligent Computational Framework for Thermo-Vibrational Response and Critical Speed Prediction in Rotating Functionally Graded Annular Disks
Keywords:
Machine Learning, Computational Intelligence, Functionally Graded Materials, Thermo-vibrational Analysis, Critical SpeedAbstract
This study presents a numerical and machine-learning-assisted framework for investigating the thermo-vibration characteristics of a rotating functionally graded Al–SiC annular disk. The aluminium and silicon-carbide volume fractions vary continuously in the radial direction according to a power-law distribution. The governing thermoelastic and transverse-vibration equations are solved using the Chebyshev spectral collocation method. The formulation incorporates a non-uniform radial temperature field, radially graded and temperature-dependent material properties, centrifugal prestress, thermal membrane forces, and rotation-induced splitting of travelling-wave frequencies. Numerical convergence is examined by progressively increasing the collocation order. The generated database is used to train multilayer perceptron, gradient-boosting, and Gaussian-process regression models. For the baseline disk, the first natural frequency in the rotating frame is 1500.23 Hz, while the forward- and backward-travelling wave frequencies are 1579.81 and 1420.65 Hz, respectively. Gradient boosting provides the best overall test performance (R² = 0.8661), whereas critical-speed prediction remains less accurate (R² = 0.5770). The framework provides an efficient computational tool for thermo-vibrational assessment and preliminary design of functionally graded rotating annular disks.
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Eraslan, A. N. (2003). Elastic-plastic deformations of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions. International Journal of Mechanical Sciences, 45(4), 643–667. https://doi.org/10.1016/S0020-7403(03)00112-7
Nie, G. J., & Batra, R. C. (2010). Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness. Composite Structures, 92(3), 720–729. https://doi.org/10.1016/j.compstruct.2009.08.052
Mahamood, R. M., Akinlabi, E. T., Shukla, M., & Pityana, S. (2012). Functionally graded material: An overview. In Proceedings of the World Congress on Engineering (Vol. III). London, UK. https://hdl.handle.net/10204/8551
Reddy, J. N., & Chin, C. D. (1998). Thermomechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses, 21(6), 593–626. https://doi.org/10.1080/01495739808956165
Bayat, M., Saleem, M., Sahari, B. B., Hamouda, A. M. S., & Mahdi, E. (2008). Analysis of functionally graded rotating disks with variable thickness. Mechanics Research Communications, 35(5), 283–309. https://doi.org/10.1016/j.mechrescom.2008.02.007
Asghari, M., & Ghafoori, E. (2010). A three-dimensional elasticity solution for functionally graded rotating disks. Composite Structures, 92(5), 1092–1099. https://doi.org/10.1016/j.compstruct.2009.09.055
Çallıoğlu, H., Bektaş, N. B., & Sayer, M. (2011). Stress analysis of functionally graded rotating discs: Analytical and numerical solutions. Acta Mechanica Sinica, 27(6), 950–955. https://doi.org/10.1007/s10409-011-0499-8
Zafarmand, H., & Hassani, B. (2014). Analysis of two-dimensional functionally graded rotating thick disks with variable thickness. Acta Mechanica, 225(2), 453–464. https://doi.org/10.1007/s00707-013-0966-3
Hassani, A., Hojjati, M. H., Mahdavi, E., Alashti, R. A., & Farrahi, G. (2012). Thermo-mechanical analysis of rotating disks with non-uniform thickness and material properties. International Journal of Pressure Vessels and Piping, 98, 95–101. https://doi.org/10.1016/j.ijpvp.2012.07.010
Jalali, M. H., & Shahriari, B. (2018). Elastic stress analysis of rotating functionally graded annular disk of variable thickness using finite difference method. Mathematical Problems in Engineering, 2018, 1-11. https://doi.org/10.1155/2018/1871674
Hosseini Kordkheili, S. A., & Naghdabadi, R. (2007). Thermoelastic analysis of a functionally graded rotating disk. Composite Structures, 79(4), 508–516. https://doi.org/10.1016/j.compstruct.2006.02.010
Dai, T., & Dai, H. L. (2016). Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed. Applied Mathematical Modelling, 40, 7689–7707. https://doi.org/10.1016/j.apm.2016.03.025
Carrera, E., Entezari, A., Filippi, M., & Kouchakzadeh, M. A. (2016). 3D thermoelastic analysis of rotating disks having arbitrary profile based on a variable kinematic 1D finite element method. Journal of Thermal Stresses, 39(12), 1572–1587. https://doi.org/10.1080/01495739.2016.1207119
Kouchakzadeh, M. A., & Entezari, A. (2015). Analytical solution of classic coupled thermoelasticity problem in a rotating disk. Journal of Thermal Stresses, 38(11), 1267–1289. https://doi.org/10.1080/01495739.2015.1073529
Entezari, A., & Kouchakzadeh, M. A. (2016). Analytical solution of generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads. Journal of Thermal Stresses, 39(12), 1588–1609. https://doi.org/10.1080/01495739.2016.1221329
Peng, X. L., & Li, X. F. (2012). Elastic analysis of rotating functionally graded polar orthotropic disks. International Journal of Mechanical Sciences, 60(1), 84–91. https://doi.org/10.1016/j.ijmecsci.2012.04.014
Jalali, M. H., & Jalali, M. R. (2020). Stress analysis of rotating functionally graded polar orthotropic disk under thermomechanical loading. Journal of Vibroengineering, 22(3), 640–656. https://doi.org/10.21595/jve.2019.20575
Afzal, A., & Mujeebu, M. A. (2019). Thermo-mechanical and structural performances of automobile disc brakes: A review of numerical and experimental studies. Archives of Computational Methods in Engineering, 26(5), 1489–1513. https://doi.org/10.1007/s11831-018-9279-y
Belhocine, A., & Bouchetara, M. (2013). Investigation of temperature and thermal stress in ventilated disc brake based on 3D thermomechanical coupling model. Ain Shams Engineering Journal, 4(3), 475–483. https://doi.org/10.1016/j.asej.2012.08.005
Jiregna, I. T., & Lemu, H. G. (2021). Thermal stress analysis of disc brake using analytical and numerical methods. IOP Conference Series: Materials Science and Engineering, 1201(1), Article 012033. https://doi.org/10.1088/1757-899X/1201/1/012033
Farooq, D., Moslem, S., Hussan, S., Riaz, M. A., Esztergár-Kiss, D., & Martinez-Pastor, B. (2026). Spherical fuzzy analytic hierarchy process approach to evaluate the effect of significant factors on drivers' perceived risk related to road safety: A case study. Discover Civil Engineering, 3(1), Article 167. https://doi.org/10.1007/s44290-026-00557-0
Kayiran, H. F. (2026a). Sustainable engineering design: Accelerating thermoelastic stress prediction in hybrid SiC–Ti6Al4V components via machine learning. International Journal of Sustainable Development Goals, 2, 655–667. https://doi.org/10.59543/dbs4d790
Kayiran, H. F. (2026b). Explainable physics-informed deep learning framework for thermoelastic analysis of rotating Ti-6Al-4V disks. Applied Expert Systems and Knowledge Management, 1, 1–15. https://doi.org/10.59543/qhn3ek50
Kayiran, F. (2026c). Physics-informed machine learning for predicting thermomechanical stress in rotating carbon-aramid hybrid composites. Knowledge and Decision Systems with Applications, 2, 408–421. https://doi.org/10.59543/rpwq1n92
Shen, H.-S. (2009). Functionally graded materials: Nonlinear analysis of plates and shells. CRC Press. https://doi.org/10.1201/9781420092578
Timoshenko, S. P., & Goodier, J. N. (1970). Theory of elasticity (3rd ed.). McGraw-Hill.
Trefethen, L. N. (2000). Spectral methods in MATLAB. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9780898719598
Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.
Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The Annals of Statistics, 29(5), 1189–1232. https://doi.org/10.1214/aos/1013203451
Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press. https://doi.org/10.7551/mitpress/3206.001.0001
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