Numerical analysis of energy harvesting characteristics in axially functionally graded beam structures with different geometric profiles for automotive application
DOI:
https://doi.org/10.15282/ijame.23.3.2026.3.1039Keywords:
Energy harvesting, Geometric profiles, Axially functionally graded beam, Modal analysisAbstract
The present study presents a wide-ranging numerical investigation of the energy-harvesting characteristics of an axially functionally graded beam structure containing different geometric profiles. Axially functionally graded materials (FGMs) offer exceptional advantages in energy harvesting applications because their varying material properties in the length direction can be optimised for energy conversion. The present study uses the finite element method (FEM) not only to compare different beam configurations but also to analyse them under dynamic loading conditions. Three different geometric profiles, namely uniform, linear, and parabolic variations along the length direction, are used in this analysis. Each profile consists of a piezo-electric layer near the fixed end of the functionally graded beam, enabling it to serve as an energy harvesting system. The material properties of the beam follow a distribution function that defines the grading profile. To find key performance parameters such as power generation, voltage output and natural frequencies under various excitation conditions, the MATLAB platform is used. Both geometric taper ratios, namely width taper and height taper, are used for the analysis, and their influence on overall performance is studied. The results obtained through the numerical analysis provide valuable insight for the proper design of an energy-harvesting device that can be used in autonomous micro-electromechanical systems, structural health monitoring and wireless sensor networks. The parabolic profile beam exhibits an approximately 115% higher voltage response compared to the uniform beam, indicating significantly enhanced electromechanical performance.
References
[1] M. Rahmaty, “Energy harvesting technologies in a super-smart city,” in Energy-Efficient Transformative Technologies for Data-Driven Smart Cities, pp. 55–70, 2026, https://doi.org/10.1016/b978-0-443-27618-7.00008-x.
[2] M. Iqbal, MM Nauman, FU Khan et al., “Vibration‐based piezoelectric, electromagnetic, and hybrid energy harvesters for microsystems applications: A contributed review,” International Journal of Energy Research, vol. 45, no. 1, pp. 65–102, 2021, https://doi.org/10.1002/er.5643.
[3] T. Sanislav, G. D. Mois, S. Zeadally, and S. C. Folea, “Energy harvesting techniques for Internet of Things (IoT),” IEEE Access, vol. 9, pp. 39530–39549, 2021. https://doi.org/10.1109/access.2021.3064066.
[4] A. Garg, W. Zheng, R. Raman, and L. Li, “Machine learning in functionally graded materials and nano FGMs: A comprehensive review of predictive modeling for mechanical behavior,” Archives of Computational Methods in Engineering, vol. 33, no. 1, pp. 533–575, 2026, https://doi.org/10.1007/s11831-025-10316-6.
[5] V. Bhavar, P. Kattire, S. Thakare, and R. K. P. Singh, “A review on functionally gradient materials (FGMs) and their applications,” in IOP Conference Series: Materials Science and Engineering, vol. 229, no. 1, p. 12021, 2017, https://doi.org/10.1088/1757-899x/229/1/012021.
[6] M. Kumar, M. Suhaib, N. Sharma, S. Kumar, and S. Choudhary, “Energy harvesting technologies in mechanical systems: A comprehensive review,” International Journal of Research Publication and Reviews, vol. 5, pp. 2782–2787, 2024, https://doi.org/10.55248/gengpi.5.0124.0303.
[7] A. Singh, P. Kumari, and D. Sharma, “Axially functionally graded beams-a review,” in Asian Conference on Mechanics of Functional Materials and Structures, pp. 479–496, 2022, https://doi.org/10.1007/978-981-99-5919-8_43.
[8] P. C. Ramegowda and D. Ishihara, “Accurate finite element modelling of multilayered flexible piezoelectric energy harvesting devices with strong coupling of structure, piezoelectricity, and circuit,” International Journal for Computational Methods in Engineering Science and Mechanics, vol. 25, no. 3, pp. 137–151, 2024, https://doi.org/10.1080/15502287.2023.2291013.
[9] P. Hajheidari, I. Stiharu, and R. Bhat, “Performance of non-uniform functionally graded piezoelectric energy harvester beams,” Journal of Intelligent Material Systems and Structures, vol. 31, no. 13, pp. 1604–1616, 2020, https://doi.org/10.1177/1045389x20930083.
[10] A. R. Biswal and D. R. Biswal, “Vibrational energy harvesting from functionally graded nonprismatic beams” International Journal of Automotive and Mechanical Engineering, vol. 22, no. 2, pp. 12359–12372, 2025, https://doi.org/10.15282 /ijame.22.2.2025.9.0946
[11] S. Pal and D. Das, “Free vibration response of bidirectional functionally graded rotating micro-disk under mechanical and thermal loading,” The Journal of Strain Analysis for Engineering Design, vol. 58, no. 7, pp. 517–537, 2023, https://doi.org/10.1177/03093247231160617.
[12] T. Yu, F. Liang, and H. Yang, “Vibration energy harvesting of a three-directional functionally graded pipe conveying fluids,” Applied Mathematics and Mechanics, vol. 46, no. 5, pp. 795–812, 2025, https://doi.org/10.1007/s10483-025-3249-8.
[13] B. Gupta, P. Sharma, and S. K. Rathore, “A new numerical modelling of an axially functionally graded piezoelectric beam,” Journal of Vibration Engineering & Technologies, vol. 10, no. 8, pp. 3191–3206, 2022, https://doi.org/10.1007/s42417-022-00550-8.
[14] K. Bendine, J. L. J. Pereira, and G. F. Gomes, “Energy harvesting enhancement of nonuniform functionally graded piezoelectric beam using artificial neural networks and Lichtenberg algorithm,” in Structures, vol. 57, p. 105271, 2023, https://doi.org/10.1016/j.istruc.2023.105271.
[15] P. Zhang, Z. Peng, H. Xu, and J. Peng, “Modal Characteristics of axially functionally graded beams carrying additional masses,” Mechanics of Solids, pp. 1–20, 2025, https://doi.org/10.1134/s0025654425600904.
[16] A. A. Daikh et al., “Static analysis of functionally graded plate structures resting on variable elastic foundation under various boundary conditions,” Acta Mechanica, vol. 234, no. 2, pp. 775–806, 2023, https://doi.org/10.1007/s00707-022-03405-1.
[17] N.D. Nguyen, “A new higher-order beam theory for buckling and free vibration responses of laminated composite and functionally graded porous beams,” The Journal of Strain Analysis for Engineering Design, vol. 59, no. 1, pp. 67–81, 2024, https://doi.org/10.1177/03093247231187454.
[18] M. Heshmati, F. Daneshmand, and Y. Amini, “Vibration and stability analysis of functionally graded elliptical pipes conveying fluid with flow velocity profile modification,” Engineering with Computers, pp. 1–16, 2023, https://doi.org/10.1007/s00366-021-01541-1.
[19] B. Wang, X. Luo, Y. Liu, and Z. Yang, “Thickness-variable composite beams for vibration energy harvesting,” Composite Structures, vol. 244, p. 112232, 2020, https://doi.org/10.1016/j.compstruct.2020.112232.
[20] M. Mousavi, S. Ziaei-Rad, and A. H. Karimi, “Piezoelectric-based energy harvesting from bridge vibrations subjected to moving successive vehicles by functionally graded cantilever beams –Theoretical and experimental investigations,” Mechanical Systems and Signal Processing, vol. 188, p. 110015, 2023, https://doi.org/10.1016/j.ymssp.2022.110015.
[21] R. Singh and P. Sharma, “Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in a humid environment,” Journal of Vibration and Control, vol. 28, no. 23–24, pp. 3608–3621, 2022, https://doi.org/10.1177/10775463211037150.
[22] M. H. Mansor, M. S. M. Sani, M. F. Hassan, and L. Tang, “Fully-coupled modelling and experimental validation of quarter wavelength resonator with piezoelectric backplate in vibro-acoustic energy harvesting,” International Journal of Automotive and Mechanical Engineering, vol. 22, no. 2, pp. 12511–12527, 2025, https://doi.org/10.15282/ijame.22.2.2025.19.0956
[23] J. Zhang, Y. Wang, X. Liu, “Significantly enhanced energy harvesting performance in piezoelectric energy harvesters through synergistic structural design,” Materials Horizons, vol. 12, no. 10, pp. 3494-3504, 2025, https://doi.org/10.1039/d4mh01902d.
[24] S. Dao, Nguyen, D. Nguyen, N. Nguyen, D.Thai, “A closed-form solution for harvesting energy from the vibrations of sandwich beams under impact loading,” Buildings, vol. 15, no. 12, p. 2135, 2025, https://doi.org/10.3390/buildings15122135.
[25] M. H. Abdelati, A. H. Matar, M. Mourad, and M. Rabie, “Evaluating sensor placement in vibration-based engine misfire detection using artificial neural networks,” International Journal of Automotive and Mechanical Engineering, vol. 22, no. 3, pp. 12603–12613, 2025. https://doi.org/10.15282/ijame.22.3.2025.5.0962.
[26] MK. Khorramabadi Free vibration of functionally graded beams with piezoelectric layers subjected to axial load. Journal of Solid Mechanics, vol. 1, no. 1, pp. 22-28, 2009, https://doi.org/10.1007/s10483-009-0803-7.
[27] A. Benjeddou, S.R. Mahmoud, M.A. Eltaher, “Active vibration control of functionally graded beams with piezoelectric layers based on higher-order shear deformation theory,” Composite Structures, vol. 152, pp. 391–404, 2016, https://doi.org/10.1007/s11803-016-0352-y.
[28] Z. G. Ruan, Z.-G. Ying, H. Lei, L. Xia, and W. Wang, “Base-excited random vibration of quasi-periodic controllable viscoelastic sandwich plates with distributed supporting masses,” Mechanics of Advanced Materials and Structures, vol. 33, no. 1, p. 2681941, 2026, https://doi.org/10.1080/15376494.2026.2681941.
[29] A. Abdelkefi “Aeroelastic energy harvesting: A review,” International Journal of Engineering Science, vol. 100, pp. 112–135, 2016, https://doi.org/10.1016/j.ijengsci.2015.10.006.
[30] F. Tornabene, N. Fantuzzi, M. Bacciocchi, “Free vibration analysis of functionally graded structures using advanced finite element formulations,” Composite Structures, vol. 132, pp. 385–410, 2015.
[31] A. Erturk, D. J. Inman, Piezoelectric Energy Harvesting. Chichester: John Wiley & Sons; 2011, https://doi.org/10.1002/9781119991151.
[32] L. Guo and Y. Qin, “Modelling and analysis of a bimorph piezoelectric cantilever,” in 2016 13th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), pp. 248–251, 2016, https://doi.org/10.1109/urai.2016.7625748.
[33] A. Khan, M. Q. Nawaz, and L. Xu, “Investigation and numerical simulation of different piezoelectric bimorph cantilever designs for energy harvesting,” International Journal of Electrical, Energy and Power System Engineering, vol. 7, no. 2, pp. 85–99, 2024, https://doi.org/10.31258/ijeepse.7.2.85-99.
[34] A. Erturk and D. J. Inman, “An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations,” Smart Materials and Structures, vol. 18, p. 025009, 2009, https://doi.org/10.1088/0964-1726/18/2/025009.
[35] M. A. Elgamal, H. Elgamal, and S. A. Kouritem, “Optimised multi-frequency nonlinear broadband piezoelectric energy harvester designs,” Scientific Reports, vol. 14, no. 1, p. 11401, 2024. https://doi.org/10.1038/s41598-024-61355-1.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 The Author(s)

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.





