Vibration Characteristics of a Laminated Composite Plate with a Surface-Bonded PZT Patch under Classical Boundary Conditions: A Finite Element Study

Abstract:

This study presents a finite element investigation of the vibration characteristics of a laminated carbon fiber reinforced polymer (CFRP) composite plate with a centrally surface-bonded piezoelectric (PZT-5H) patch under classical boundary conditions. A square CFRP plate of dimensions 300 × 300 × 3 mm with a [0/90/0/90] layup is analyzed with and without an active piezoelectric patch, considering clamped–clamped–clamped–clamped (CCCC), clamped–free–clamped–free (CFCF), clamped–free–free–free (CFFF), and simply supported–simply supported–simply supported–simply supported (SSSS) boundary conditions. Linear piezoelectric theory and steady-state harmonic excitation are employed using Abaqus/CAE 2025 Learning Edition. Modal characteristics are obtained from the first six natural frequencies, while harmonic response is evaluated in terms of peak out-of-plane displacement at the plate center under combined mechanical loading and open-loop electrical actuation. The results demonstrate that the presence of the PZT patch induces boundary-condition-dependent modifications in both natural frequencies and harmonic response amplitudes. For highly constrained configurations (CCCC and SSSS), the active PZT patch leads to a reduction in peak harmonic displacement, whereas for less constrained cases (CFCF and CFFF), a slight amplification of the response is observed. These findings highlight the strong coupling between structural boundary conditions and piezoelectric actuation effectiveness, and they establish a validated baseline for future investigations involving closed-loop control, multi-patch configurations, and data-driven optimization strategies.

• Periodical: Materials Science Forum (Volume 1194)
• Pages: 53-66
• DOI: https://doi.org/10.4028/p-MBP4iJ
• Online since: June 2026
• Authors: Dhruv Bagai*, Abhishek Roy, Supen Kumar Sah, Narayan Sharma
• Keywords: Boundary Conditions, Finite Element Method, Harmonic Response, Laminated Composite Plate, Modal Analysis, Piezoelectric Actuator, PZT-5H, Vibration Characteristics

References

[1] Crawley, E.F., de Luis, J., "Use of piezoelectric actuators as elements of intelligent structures," AIAA Journal, 25(10), 1373–1385 (1987)

DOI: 10.2514/3.9792

[2] Chopra, I., "Review of state of art of smart structures and integrated systems," AIAA Journal, 40(11), 2145–2187 (2002)

DOI: 10.2514/2.1561

[3] ANSI/IEEE Std 176-1987, IEEE Standard on Piezoelectricity, IEEE, New York (1987).

[4] PZT-5H Piezoelectric Ceramics Datasheet, APC International / PI Ceramics.

[5] Kapania, R.K., Raciti, S., "Recent advances in analysis of laminated beams and plates," AIAA Journal, 27(7), 923–934 (1989)

DOI: 10.2514/3.10148

[6] Reddy, J.N., Mechanics of Laminated Composite Plates and Shells, 2nd ed., CRC Press, Boca Raton (2004).

[7] Benjeddou, A., "Advances in piezoelectric finite element modeling of adaptive structural elements," Smart Materials and Structures, 9(6), 805–823 (2000)

DOI: 10.1088/0964-1726/9/6/303

[8] Tzou, H.S., Piezoelectric Shells: Distributed Sensing and Control of Continua, Kluwer Academic Publishers, Dordrecht (1993).

[9] Li, S., Wang, K., Zhou, S., "Active vibration control of composite plates with piezoelectric actuators," Journal of Sound and Vibration, 260(2), 317–335 (2003)

[10] Narayanan, S., Balamurugan, V., "Finite element modeling of piezolaminated smart structures for vibration control," Journal of Sound and Vibration, 262(2), 529–562 (2003)

DOI: 10.1016/s0022-460x(03)00110-x

[11] Gözüm, S., Tarakçıoğlu, N., "Vibration analysis of laminated composite plates with piezoelectric layers under different boundary conditions," Journal of the Indian Institute of Science, 98(3), 425–438 (2018)

[12] Sun, D., Tong, L., "Active vibration control of composite structures with piezoelectric materials," Smart Materials and Structures, 21(10), 105012 (2012)

DOI: 10.1088/0964-1726/21/10/105012

[13] Zhang, Y., Li, X., Chen, Y., "Dynamic response of piezoelectric composite plates under harmonic excitation," Composite Structures, 220, 758–770 (2019)

DOI: 10.1016/j.compstruct.2019.04.045

[14] Wang, L., Liu, Y., Zhao, X., "Vibration characteristics of laminated composite plates integrated with piezoelectric layers," Materials, 13(9), 2035 (2020)

DOI: 10.3390/ma13092035

[15] Liu, Z., Huang, Y., Zhang, J., "Numerical investigation of piezoelectric composite plates subjected to harmonic loading," Sensors, 21(6), 2154 (2021)

DOI: 10.3390/s21062154

[16] Kumar, R., Singh, B.N., "Finite element analysis of smart composite plates with piezoelectric actuators," Engineering Structures, 252, 113596 (2022). https://doi.org/10.1016/j.engstruct. 2021.113596

[17] Zhao, H., Chen, X., Li, J., "Harmonic response analysis of piezoelectric laminated plates," Applied Sciences, 12(3), 1187 (2022)

DOI: 10.3390/app12031187

[18] Rahman, M., Hossain, M., Islam, M., "Vibration analysis of smart composite plates with surface-bonded piezoelectric actuators," Structures, 48, 763–775 (2023)

DOI: 10.1016/j.istruc.2023.01.045

[19] Chen, Y., Zhang, H., Wang, P., "Numerical investigation of vibration control in piezoelectric laminated composite plates," Composite Structures, 332, 116217 (2024)

[20] Sah, S.K., Ghosh, A., "Influence of porosity distribution on free vibration and buckling analysis of multi-directional functionally graded sandwich composite plates," Composite Structures, 279, 114795 (2022)

DOI: 10.1016/j.compstruct.2021.114795

[21] Sah, S.K., Ghosh, A., "Free vibration and buckling analysis of functionally graded composite plates using inverse trigonometric shear deformation theory," Aircraft Engineering and Aerospace Technology, 93(2), 298–310 (2021)

DOI: 10.1108/AEAT-01-2020-0001

[22] Vidja, C., Sah, S.K., "Behaviour analysis of functionally graded sandwich composite plates for free vibration using finite element method," in Advances in Materials Engineering, Springer Nature, Singapore, p.275–290 (2025)

DOI: 10.1007/978-981-97-7114-1_23