Modal analysis of cracked beam with a piezoelectric layer

Author affiliations




cracked beam, piezoelectric layer, modal analysis, structural health monitoring


Piezoelectric material was employed first as sensor/actuator for structural control and then it has got an effective use for structural health monitoring and repairing damaged structures. In this report, modal analysis of cracked beam with piezoelectric layer is carried out to investigate effect of crack and piezoelectric layer thickness on natural frequencies of the structure and output charge generated in the piezoelectric layer by vibration modes. Governing equations of the coupled structure are established using the double beam model and two-spring (translational and rotational) representation of crack and solved to obtain the modal parameters including the output charge associated with natural modes acknowledged as modal piezoelectric charge (MPC). Numerical examples have been examined for validation and illustration of the developed theory.


Download data is not yet available.


E. F. Crawley and J. de Luis. Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal, 25, (1987), pp. 1373–1385. DOI:

C.-K. Lee and F. C. Moon. Modal sensors/actuators. Journal of Applied Mechanics, 57, (1990), pp. 434–441. DOI:

H. S. Tzou and C. I. Tseng. Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach. Journal of Sound and Vibration, 138, (1990), pp. 17–34. DOI:

S. S. Rao and M. Sunar. Piezoelectricity and its use in disturbance sensing and control of flexible structures: A survey. Applied Mechanics Reviews, 47, (1994), pp. 113–123. DOI:

A. S. Islam and K. C. Craig. Damage detection in composite structures using piezoelectric materials (and neural net). Smart Materials and Structures, 3, (1994), pp. 318–328. DOI:

X. H. Jian, H. S. Tzou, C. J. Lissenden, and L. S. Penn. Damage detection by piezoelectric patches in a free vibration method. Journal of Composite Materials, 31, (1997), pp. 345–359. DOI:

S. Bhalla and C. K. Soh. Progress in structural health monitoring and non-destructive evaluation using piezo-impedance transducers. In Smart Materials and Structures: New Research, Nova Science Publishers, (2006), pp. 177–228.

W. H. Duan, Q. Wang, and S. T. Quek. Applications of piezoelectric materials in structural health monitoring and repair: Selected research examples. Materials, 3, (2010), pp. 5169–5194. DOI:

H. A. Winston, F. Sun, and B. S. Annigeri. Structural health monitoring with piezoelectric active sensors. In Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education, American Society of Mechanical Engineers, (2000). DOI:

X. L. Liu, Z. W. Jiang, and L. Ji. Investigation on the design of piezoelectric actuator/sensor for damage detection in beam with lamb waves. Experimental Mechanics, 53, (2012), pp. 485–492. DOI:

D. Mateescu, Y. Han, and A. Misra. Dynamics of structures with piezoelectric sensors and actuators for structural health monitoring. Key Engineering Materials, 347, (2007), pp. 493–498. DOI:

A. Abuzaid, M. Hrairi, and M. S. I. Dawood. Survey of active structural control and repair using piezoelectric patches. Actuators, 4, (2015), pp. 77–98. DOI:

W. H. Duan, S. T. Quek, and Q. Wang. Finite element analysis of the piezoelectric-based repair of a delaminated beam. Smart Materials and Structures, 17, (2007). DOI:

R. Kumar, H. Pathak, A. Singh, and M. Tiwari. Modeling of crack repair using piezoelectric material: XFEM approach. Engineering Computations, 38, (2020), pp. 586–617. DOI:

A. Ariaei, S. Ziaei-Rad, and M. Ghayour. Repair of a cracked Timoshenko beam subjected to a moving mass using piezoelectric patches. International Journal of Mechanical Sciences, 52, (2010), pp. 1074–1091. DOI:

Q. Wang, W. H. Duan, and S. T. Quek. Repair of notched beam under dynamic load using piezoelectric patch. International Journal of Mechanical Sciences, 46, (2004), pp. 1517–1533. DOI:

W. Al-Ashtari. A novel analytical model to design piezoelectric patches used to repair cracked beams. Journal of Engineering, 22, (6), (2016), pp. 117–136.

U. Lee and J. Kim. Dynamics of elastic-piezoelectric two-layer beams using spectral element method. International Journal of Solids and Structures, 37, (2000), pp. 4403–4417. DOI:

H. W. Park, E. J. Kim, K. L. Lim, and H. Sohn. Spectral element formulation for dynamic analysis of a coupled piezoelectric wafer and beam system. Computers&Structures, 88, (2010), pp. 567–580. DOI:

U. Lee, D. Kim, and I. Park. Dynamic modeling and analysis of the PZT-bonded composite Timoshenko beams: Spectral element method. Journal of Sound and Vibration, 332, (2013), pp. 1585–1609. DOI:

S. M. Yang and Y. J. Lee. Modal analysis of stepped beams with piezoelectric materials. Journal of Sound and Vibration, 176, (1994), pp. 289–300. DOI:

C. Maurini, M. Porfiri, and J. Pouget. Numerical methods for modal analysis of stepped piezoelectric beams. Journal of Sound and Vibration, 298, (2006), pp. 918–933. DOI:

Q. Wang and S. T. Quek. Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator. Smart Materials and Structures, 9, (2000), pp. 103–109. DOI:

N. T. Khiem, T. T. Hai, and L. Q. Huong. Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material. Materials Research Express, 7, (2020). DOI:

D.Wang, H. Song, and H. Zhu. Electromechanical impedance analysis on piezoelectric smart beam with a crack based on spectral element method. Mathematical Problems in Engineering, 2015, (2015), pp. 1–13. DOI:

L. J. Jiang, J. Tang, and K. W. Wang. An enhanced frequency-shift-based damage identification method using tunable piezoelectric transducer circuitry. Smart Materials and Structures, 15, (2006), pp. 799–808. DOI:

S. Zhao, N. Wu, and Q. Wang. Crack identification through scan-tuning of vibration characteristics using piezoelectric materials. Smart Materials and Structures, 26, (2016). DOI:

T. G. Chondros, A. D. Dimarogonas, and J. Yao. A continuous cracked beam theory. Journal of Sound and Vibration, 215, (1998), pp. 17–34. DOI:

T. G. Chondros, A. D. Dimarogonas, and J. Yao. Longitudinal vibration of a continuous cracked bar. Engineering Fracture Mechanics, 61, (1998), pp. 593–606. DOI:






Research Article

Funding data

Most read articles by the same author(s)

1 2 3 4 > >> 

Similar Articles

You may also start an advanced similarity search for this article.