The geometry uniformity parameters effect on the dynamic behaviour of trapezoidal beam


  • Mohamed Bouamama
  • Mohamed Bouamama
  • Zouaoui Satla
  • Azzeddine Belaziz
  • Lakhdar Boumia



active control, trapezoidal beam, piezoelectric materials, finite element model, fundamental frequency


Understanding the delicate interplay between geometric design principles and dynamic responses is vital for numerous engineering applications because it allows optimization of structural integrity and performance for manufacturing and special use of this structures. In this study, a complete numerical analysis is undertaken to investigate how differences in geometric parameters impact the structural behaviour of a cantilever smart trapezoidal beam, giving useful insights for engineering applications. The beam consists of a host structure made of aluminum couple with two piezoelectric layers on its top and bottom surface. For such purpose, the study a 3D finite element model has been implemented in ANSY APDL and applied by Matlab we used the interfaces between the two software, considering that the beam changes its form in the axial direction following polynomial based function. The function takes two geometric parameters as an input which are the tapering ratios and the degree of non-uniformity. The beam is then subjected to a harmonic based excitation and the effect of changing tapering ratios and the degree of non-uniformity is analyzed., allowing analysis of the effects of altering tapering ratios and the degree of non-uniformity The results led to a conclusion that just by manipulating the mentioned parameters a considerable changing in the fundamental frequency and the amplitude has been noticed. Addition our numerical analysis shows that small changes to the tapering ratios and degree of non-uniformity have a considerable influence on the behavior of cantilever smart trapezoidal beams. These discoveries add to continuing research in smart materials, paving the road for creative engineering solutions.


Bendine, K., & Wankhade, R. L. (2017). Optimal shape control of piezolaminated beams with different boundary condition and loading using genetic algorithm. International Journal of Advanced Structural Engineering, 9(4), 375–384.

Bendine, K., Boukhoulda, F. B., Nouari, M., & Satla, Z. (2016). Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory. Earthquake Engineering and Engineering Vibration, 15(4), 611–620.

Bendine, K., Hamdaoui, M., & Boukhoulda, B. F. (2019). Piezoelectric energy harvesting from a bridge subjected to time-dependent moving loads using finite elements. Arabian Journal for Science and Engineering, 44(6), 5743–5763.

Bendine, K., Junho Pereira, J. L., & Ferreira Gomes, G. (2023). Energy harvesting enhancement of nonuniform functionally graded piezoelectric beam using artificial neural networks and Lichtenberg algorithm. Structures, 57, 105271.

Bendine, K., Satla, Z., Boukhoulda, F. B., & Nouari, M. (2018). Active vibration damping of smart composite beams based on system identification technique. Curved and Layered Structures, 5(1), 43–48.

Bendine, K., Wei, Y.-J., Wang, X., Chen, M., & Zhang, S.-Q. (2023). An improved active damping of Fan Blade using piezoelectric MFC actuators and PSO Optimization. Mechanics of Advanced Materials and Structures, 1–10.

Birgin, H. B., D’Alessandro, A., & Ubertini, F. (2023a). Dynamic behavior of structural beams made of innovative smart concrete. Procedia Structural Integrity, 44, 1624–1631.

Cacciola, P., & Tombari, A. (2015). Vibrating barrier: A novel device for the passive control of structures under ground motion. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2179), 20150075.

El Harti, K., Saadani, R., & Rahmoune, M. (2022). Active vibration control of Timoshenko sigmoid functionally graded porous composite beam with distributed piezoelectric sensor/actuator in a thermal environment. Designs, 7(1), 2.

Elmeiche, A., Bouamama, M., Elhannani, A., Belaziz, A., & Hammoudi, A. (2022). Dynamic Modeling of Functionally Graded Beams Undergoing Mobile Mass. Materials Physics & Mechanics, 48(01), 091–105.

Ghadiri, M., Shafiei, N., & Alireza Mousavi, S. (2016). Vibration analysis of a rotating functionally graded tapered microbeam based on the modified couple stress theory by DQEM. Applied Physics A, 122(9).

Huang, Z., Huang, F., Wang, X., & Chu, F. (2022a). Active vibration control of composite cantilever beams. Materials, 16(1), 95.

Huang, Z., Peng, H., Wang, X., & Chu, F. (2023). Finite Element Modeling and vibration control of plates with active constrained layer damping treatment. Materials, 16(4), 1652.

Jang, T. S. (2019). Correction to: A general method for analyzing moderately large deflections of a non-uniform beam: An infinite bernoulli–euler–von kármán beam on a nonlinear Elastic Foundation. Acta Mechanica, 230(9), 3431–3438.

Kambampati, S., & Ganguli, R. (2014). Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings. Acta Mechanica, 226(4), 1227–1239.

Li, C., Shen, L., Shao, J., & Fang, J. (2023). Simulation and experiment of active vibration control based on flexible piezoelectric MFC composed of PZT and Pi Layer. Polymers, 15(8), 1819.

Li, F.-M., Kishimoto, K., Wang, Y.-S., Chen, Z.-B., & Huang, W.-H. (2008). Vibration control of beams with active constrained layer damping. Smart Materials and Structures, 17(6), 065036.

Liu, Q., Shi, R., & Lu, L. (2024). Existing vibration control techniques applied in construction and Mechanical Engineering. Advances in Transdisciplinary Engineering.

Mayer, D., & Herold, S. (2017). Passive, Adaptive, Active Vibration Control, and Integrated Approaches. Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems.

Moheimani, S. O., Halim, D., & Fleming, A. J. (2003). Spatial control of vibration - theory and experiments. Series on Stability Vibration and Control of Systems, Series A.

Praisach, Z. I., Pîrșan, D. A., Harea, I., & Stan, P. T. (2023). An analytical method for evaluating the dynamic behavior of a soft clamped-type support. Vibroengineering Procedia, 52, 1–6.

Rahimi, F., Aghayari, R., & Samali, B. (2020). Application of tuned mass dampers for structural vibration control: A state-of-the-art review. Civil Engineering Journal, 6(8), 1622–1651.

Salah, M., Boukhoulda, F. B., Nouari, M., & Bendine, K. (2020). Temperature variation effect on the active vibration control of smart composite beam. Acta Mechanica et Automatica, 14(3), 166–174.

SATLA, Z., Boumia, L., & Kherrab, M. (2024). Vibration control of FGM plate using optimally placed piezoelectric patches. Revista Mexicana de Física, 70(1 Jan-Feb).

Serhane, H., Bendine, K., Boukhoulda, F. B., & Lousdad, A. (2020). Numerical analysis based on finite element method of active vibration control of a sandwich plate using piezoelectric patches. Mechanics and Mechanical Engineering, 24(1), 7–16.

Singh, K., Sharma, S., Kumar, R., & Talha, M. (2021). Vibration control of cantilever beam using poling tuned piezoelectric actuator. Mechanics Based Design of Structures and Machines, 51(4), 2217–2240.

Waqar, A., Othman, I., Shafiq, N., Altan, H., & Ozarisoy, B. (2023). Modeling the effect of overcoming the barriers to passive design implementation on Project Sustainability Building Success: A structural equation modeling perspective. Sustainability, 15(11), 8954.

Yang, Z.-X., He, X.-T., Peng, D.-D., & Sun, J.-Y. (2019). Free damping vibration of piezoelectric cantilever beams: A biparametric perturbation solution and its experimental verification. Applied Sciences, 10(1), 215.

Yu, Y., Zhang, X. N., & Xie, S. L. (2009). Optimal shape control of a beam using piezoelectric actuators with low control voltage. Smart Materials and Structures, 18(9), 095006.

Zhao, Y., Du, J., Chen, Y., & Liu, Y. (2022). Nonlinear dynamic behavior of a generally restrained pre-pressure beam with a partial non-uniform foundation of nonlinear stiffness. International Journal of Structural Stability and Dynamics, 23(03).




How to Cite

Bouamama, M., Bouamama, M., Satla, Z., Belaziz, A., & Boumia, L. (2024). The geometry uniformity parameters effect on the dynamic behaviour of trapezoidal beam. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 1530–1547.