Uncoupled vibrations in cracked functionally graded beams with temperature-dependent properties
Author affiliations
DOI:
https://doi.org/10.15625/0866-7136/24104Keywords:
functionally graded material, cracked beam, thermal effect, uncoupled vibrationAbstract
In the present study, the free vibration of cracked temperature-dependent functionally graded Euler--Bernoulli beams is addressed using the power law of material gradation and double spring model of a transverse open crack. Under the assumptions of ignoring inertia for rotation and axial deformation, discomposed longitudinal and bending vibrations are investigated for temperature-dependent multiple-cracked functionally graded beams. Hence, the effect of the material gradation index, temperature rise distribution, and cracks on the natural frequencies of the decoupled vibration modes is examined. Numerical results show that the longitudinal wave speed and the natural frequencies of both the longitudinal and bending vibrations decrease with an increasing material fraction index and temperature rise. It is also revealed that there is a significant effect of material gradation and temperature on the sensitivity of the beam natural frequencies to crack location and depth.
Downloads
References
Alshorbagy, A. E. (2013). Temperature Effect on the Vibration Characteristics of a Functionally Graded Thick Beam. Ain Shams Engineering Journal, 4(3), 455–464. https://doi.org/10.1016/j.asej.2012.11.001
Aria, A. I., Friswell, M. I., & Rabczuk, T. (2019). Thermal Vibration Analysis of Cracked Nanobeams Embedded in an Elastic Matrix Using Finite Element Analysis. Composite Structures, 212, 118–128. https://doi.org/10.1016/j.compstruct.2019.01.040
Aydin, K. (2013). Free Vibration of Functionally Graded Beams with Arbitrary Number of Surface Cracks. European Journal of Mechanics A/Solids, 42, 112–124. https://doi.org/10.1016/j.euromechsol.2013.05.002
Aydogdu, M., & Taskin, V. (2007). Free Vibration Analysis of Functionally Graded Beams with Simply Supported Edges. Materials and Design, 28(5), 1651–1656. https://doi.org/10.1016/j.matdes.2006.02.007
Birman, V., & Byrd, L. M. (2007). Modeling and Analysis of Functional Graded Materials and Structures. Applied Mechanics Reviews, 60(5), 195–216. https://doi.org/10.1115/1.2777164
Chen, J., Fang, H., Liu, W., Zhu, L., Zhuang, Y., Wang, J., & Han, J. (2018). Thermal Vibration of FGM Beams with General Boundary Conditions Using a Higher-order Shear Deformation Theory. Composites Part B: Engineering, 153, 376–386. https://doi.org/10.1016/j.compositesb.2018.08.122
Chen, W. R., & Chang, H. (2017). Closed-form Solution for Free Vibration Frequencies of Functionally Graded Euler-Bernoulli Beams. Mechanics of Composite Materials, 53(1), 79–98. https://doi.org/10.1007/s11029-017-9642-3
Chondros, T. G., Dimarogonas, A. D., & Yao, J. (1998a). A Continuous Cracked Beam Vibration Theory. Journal of Sound and Vibration, 215(1), 17–34. https://doi.org/10.1006/jsvi.1998.1640
Chondros, T. G., Dimarogonas, A. D., & Yao, J. (1998b). Longitudinal Vibration of a Continuous Cracked Bar. Engineering Fracture Mechanics, 61(5–6), 593–606. https://doi.org/10.1016/s0013-7944(98)00071-x
Elaikh, T. E., & Agboola, O. O. O. (2022). Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam under Thermal Load. Trends in Sciences, 19(23), 1349. https://doi.org/10.48048/tis.2022.1349
Esen, I., Özarpa, C., & Eltaher, M. A. (2021). Free Vibration of a Cracked FG Microbeam Embedded in an Elastic Matrix and Exposed to Magnetic Field in a Thermal Environment. Composite Structures, 261, 113552. https://doi.org/10.1016/j.compstruct.2021.113552
Gayen, D. (2024). Thermo-elastic Buckling and Free Vibration Behavior of Functionally Graded Beams with Various Materials Gradation Laws. International Journal on Interactive Design and Manufacturing, 19(7), 5397–5416. https://doi.org/10.1007/s12008-024-02141-1
Gayen, D., Tiwari, R., & Chakraborty, D. (2019). Static and Dynamic Analyses of Cracked Functionally Graded Structural Components: A Review. Composites Part B: Engineering, 173, 106982. https://doi.org/10.1016/j.compositesb.2019.106982
Gupta, M., & Talha, M. (2015). Recent Development in Modeling and Analysis of Functionally Graded Materials and Structures. Progress in Aerospace Sciences, 79, 1–14. https://doi.org/10.1016/j.paerosci.2015.07.001
Hai, T. T., Hang, P. T., Botyan, S., & Khiem, N. T. (2025). The Effect of Neutral Axis Position on Fundamental Frequency of Functionally Graded Timoshenko Beams in Nonlinear Temperature Rise Environment. Journal of Thermal Stresses, 48(4), 376–399. https://doi.org/10.1080/01495739.2025.2461521
Huyen, N. N., & Khiem, N. T. (2017). Modal Analysis of Functionally Graded Timoshenko Beam. Vietnam Journal of Mechanics, 39(1), 31–50. https://doi.org/10.15625/0866-7136/7582
Huyen, N. N. & others. (2025). Coupled Effect of Crack and Temperature on Free Vibration of Functionally Graded Beams. Journal of the Brazilian Society of Mechanical Sciences and Engineering.
Jin, C., & Wang, X. (2015). Accurate Free Vibration Analysis of Euler Functionally Graded Beams by the Weak Form Quadrature Element Method. Composite Structures, 125, 41–50. https://doi.org/10.1016/j.compstruct.2015.01.039
Khiem, N. T. (2022). Vibration of Cracked Functionally Graded Beams: General Solution and Application—A Review. Vietnam Journal of Mechanics, 44(4), 317–347. https://doi.org/10.15625/0866-7136/17986
Khiem, N. T., Huyen, N. N., & Long, N. T. (2017). Vibration of Cracked Timoshenko Beam Made of Functionally Graded Material. In Shock & Vibration, Aircraft/Aerospace, Energy Harvesting, Acoustics & Optics, Volume 9 (pp. 133–143). River Publishers. https://doi.org/10.1007/978-3-319-54735-0_15
Khiem, N. T., & Lien, T. V. (2001). A Simplified Method for Natural Frequencies of Multiple Cracked Beams. Journal of Sound and Vibration, 245(4), 737–751. https://doi.org/10.1006/jsvi.2001.3585
Li, X. F. (2008). A Unified Approach for Analyzing Static and Dynamic Behaviors of Functionally Graded Timoshenko and Euler-Bernoulli Beams. Journal of Sound and Vibration, 318(4–5), 1210–1229. https://doi.org/10.1016/j.jsv.2008.04.056
Mahi, A., Adda Bedia, E. A., Tounsi, A., & Mechab, I. (2010). An Analytical Method for Temperature-dependent Free Vibration Analysis of Functionally Graded Beams with General Boundary Conditions. Composite Structures, 92(8), 1877–1887. https://doi.org/10.1016/j.compstruct.2010.01.010
Minh, P. P., & Duc, N. D. (2021). The Effect of Cracks and Thermal Environment on Free Vibration of FGM Plates. Thin-Walled Structures, 159, 107291. https://doi.org/10.1016/j.tws.2020.107291
Natarajan, S. & others. (2011). Linear Free Flexural Vibration of Cracked Functionally Graded Plates in Thermal Environment. Computers & Structures, 89, 1535–1546. https://doi.org/10.1016/j.compstruc.2011.04.002
Pradhan, K. K., & Chakraverty, S. (2013). Free Vibration of Euler and Timoshenko Functionally Graded Beams by Rayleigh-Ritz Method. Composites Part B: Engineering, 51, 175–184. https://doi.org/10.1016/j.compositesb.2013.02.027
Sherafatnia, K., Farrahi, G. H., & Faghidian, S. A. (2014). Analytic Approach to Free Vibration and Buckling Analysis of Functionally Graded Beams with Edge Cracks Using Four Engineering Beam Theories. International Journal of Engineering, 27(6 (C)), 979–990. https://doi.org/10.5829/idosi.ije.2014.27.06c.17
Singh, R., & Sharma, P. (2019). A Review on Modal Characteristics of FGM Structures. 1st International Conference on Advances in Mechanical Engineering and Nanotechnology (ICAMEN 2019), 2148(1), 030037. https://doi.org/10.1063/1.5123959
Su, H., & Banerjee, J. R. (2015). Development of Dynamic Stiffness Method for Free Vibration of Functionally Graded Timoshenko Beams. Computers and Structures, 147, 107–116. https://doi.org/10.1016/j.compstruc.2014.10.001
Trinh, L. C., Vo, T. P., Thai, H.-T., & Nguyen, T.-K. (2016). An Analytical Method for the Vibration and Buckling of Functionally Graded Beams under Mechanical and Thermal Loads. Composites Part B: Engineering, 100, 152–163. https://doi.org/10.1016/j.compositesb.2016.06.067
Yang, J., & Chen, Y. (2008). Free Vibration and Buckling Analyses of Functionally Graded Beams with Edge Cracks. Composite Structures, 83(1), 48–60. https://doi.org/10.1016/j.compstruct.2007.03.006
Zahedinejad, P., Zhang, C., Zhang, H., & Ju, S. (2020). A Comprehensive Review on Vibration Analysis of Functionally Graded Beams. International Journal of Structural Stability and Dynamics, 20(04), 2030002. https://doi.org/10.1142/s0219455420300025
Downloads
Published
How to Cite
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Funding data
-
National Foundation for Science and Technology Development
Grant numbers 107.01-2025.20
