Finite element formulation and free vibration analyses of rotating functionally graded blades
More details
Hide details
Istanbul Technical University, Faculty of Aeronautics and Astronautics, Maslak, Istanbul, Turkey
Submission date: 2019-08-11
Final revision date: 2020-02-22
Acceptance date: 2020-04-16
Online publication date: 2020-11-06
Publication date: 2021-01-15
Corresponding author
Özge Özdemir   

Aeronautical Engineering Department, Istanbul Technical University, Turkey
Journal of Theoretical and Applied Mechanics 2021;59(1):3-15
In this study, free vibration characteristics of functionally graded (FG) blades whose material properties change through the blade thickness are inspected. Finite Element Method (FEM) is used to create blade models and to calculate natural frequencies. The blade formulations are derived for both Euler-Bernoulli and Timoshenko beams to inspect the effect of different parameters on vibration characteristics. For each beam, stiffness and mass matrices are derived from energy expressions. In the solution part, effects of several parameters, i.e. rotational speed, material properties, power law index parameter, different boundary conditions and slenderness ratio are investigated. The calculated results are compared with those in open literature and a very good agreement between them is confirmed, which reveals the correctness and accuracy of the finite element formulation developed in this study. Formulations are carried out in great detail and additionally, the results are displayed in several figures and tables, which can be a significant source of information for authors working in this area.
Alshorbagy A.E., Eltaher M.A., Mahmoud F.F., 2011, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35, 412-425.
Giunta G., Crisafulli D., Belouettar S., Carrera E., 2011, Hierarchical theories for the free vibration analysis of functionally graded beams, Composite Structures, 94, 68-74.
Han S.M., Benaroya H., Wei T., 1999, Dynamics of transversely vibrating beams using four engineering theories, Journal of Sound and Vibration, 225, 5, 935-988.
Hartmann F., Katz C., 2004, Structural Analysis with Finite Elements, Springer.
Huang Y., Li X.F., 2010, A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, Journal of Sound and Vibration, 329, 2291-2303.
Lai S.K., Harrington J., Xiang Y., Chow K.W., 2012, Accurate analytical perturbation approach for large amplitude vibration of functionally graded beams, International Journal of Non-Linear Mechanics, 47, 473-480.
Latalski J., Warminski J., Rega G., 2017, Bending-twisting vibrations of a rotating hub-thin-walled composite beam system, Mathematics and Mechanics of Solids, 22, 6.
Lee J.W., Lee J.Y., 2017, Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, International Journal of Mechanical Sciences, 122, 1-17.
Loja M.A.R., Barbosa J.I., Mota Soares C.M., 2012, A study on the modelling of sandwich functionally graded particulate composite, Composite Structures, 94, 2209-2217.
Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Science, 41, 309-324.
Nguyen T.K., Nguyen T.T.P., Vo T.P., Thai H.T., 2015, Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory, Composites, Part B: Engineering, 76, 273-285.
Özdemir Ö., 2019, Vibration analysis of rotating Timoshenko beams with different material distribution properties, Selcuk University, Journal of Science, Engineering and Technology, 7, 2, 272-286.
Şimşek M., 2010, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nuclear Engineering and Design, 240, 4, 697-705.
Thai H.T., Vo T.P., 2012, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, International Journal of Mechanical Sciences, 62, 57-66.
Wattanasakulpong N., Prusty B.G., Kelly D.W., Hoffman M., 2012, Free vibration analysis of layered functionally graded beams with experimental validation, Materials and Design, 36, 182-190.
Journals System - logo
Scroll to top