Abstract
A comprehensive study on frequency responses of beams made of functionally graded materials (FGM) is presented in this work. A power-law distribution is used to describe the continuous variation of the volumes fractions of the material constituents. The beam is made metal and ceramic portions in its lower and upper surfaces, respectively with a gradually variation of its material properties. A high-order beam theory (HSBDT) is adopted to describe the kinematic of the beam where membrane, bending and shear effects are taken into account in the model. The equilibrium equations are derived from the variational principle in conjunction with the finite element procedure. The discretization of the displacement and strain components is achieved using a two nodes finite beam element with four degrees of freedom. The influence of the gradient index and the slenderness geometrical ratio is investigated via some numerical tests. A comparison of the natural frequencies is first carried out with results from the literature in order to outline the effectives and robustness of the proposed numerical model. Then, tabular and graphical results are presented with the emphasis of the effects of gradient index and length-to-thickness ratio on natural frequencies of FGM beams. It is shown that the material and geometrical parameters are essential factors that should be considered in the control of vibrations.
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References
Koizumi, M.: FGM activities in Japan. Compos. B 28, 1–4 (1997)
Simsek, M.: Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method. Int. J. Eng. Appl. Sci. 1(3), 1–11 (2009)
Simsek, M.: Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl. Eng. Des. 240, 697–705 (2010a)
Simsek, M.: Vibration analysis of a functionally graded beam under a moving mass by using different beam theories. Compos. Struct. 92(4), 904–917 (2010b)
Thai, H.T., Vo, T.P.: Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. Int. J. Mech. Sci. 62(1), 57–66 (2012)
Vo, T.P., Thai, H.T., Nguyen, T.K., Inman, F.: A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Compos. Strcut. 119, 1–12 (2015)
Jing, L.I., Ming, P.J., Zhang, W.P., Fu, L.R., Cao, Y.P.: Static and free vibration analysis of functionally graded beams by combination Timoshenko theory and finite volume method. Compos. Strcut. 138, 192–213 (2016)
Zghal, S., Frikha, A., Dammak, F.: Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures. Appl. Math. Model. 53, 132–155 (2018)
Zghal, S., Frikha, A., Dammak, F.: Large deflection responses-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes. Appl. Math. Mech. 41, 1227–1250 (2020a)
Zghal, S., Dammak, F.: Vibrational behavior of beams made of functionally graded materials by using a mixed formulation. Proc. Inst. Mech. Eng., Part C: J. Mech. 234(18), 3650–3666 (2020b)
Zghal, S., Trabelsi, S., Dammak, F.: Post-buckling behavior of functionally graded and carbon-nanotubes based structures with different mechanical loadings. Mech. Based Des. Struct. Mach. (2020c). https://doi.org/10.1080/15397734.2020.1790387
Trabelsi, S., Zghal, S., Dammak, F.: Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures. J. Braz. Soc. Mech. Sci. Eng. 42(5), 1–22 (2020). https://doi.org/10.1007/s40430-020-02314-5
Zghal, S., Trabelsi, S., Frikha, A., Dammak, F.: Thermal free vibration analysis of functionally graded plates and panels with an improved finite shell element. J. Therm. Stress 44(3), 315–341 (2021a)
Zghal, S., Dammak, F.: Buckling responses of porous structural components with gradient power-based and sigmoid material variations under different types of compression loads. Compos. Struct. 273(2), 114313 (2021b)
Zghal, S., Dammak, F.: Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element. Comput. Math. Appl. 99(18), 52–72 (2021c)
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Zghal, S., Trabelsi, S., Dammak, F. (2022). Frequency Response of FGM Beams. In: Bouraoui, T., et al. Advances in Mechanical Engineering and Mechanics II. CoTuMe 2021. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-86446-0_39
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DOI: https://doi.org/10.1007/978-3-030-86446-0_39
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