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Free Vibration of Cross Ply Laminated Beams with Multiple Distributed Piezoelectric Actuators

Published online by Cambridge University Press:  22 March 2012

A. A. Khdeir ,
E. Darraj  and
O. J. Aldraihem
A. A. Khdeir*
Affiliation:
Mechanical Engineering Department, King Saud University, Riyadh 11421, Kingdom of Saudi Arabia
E. Darraj
Affiliation:
Mechanical Engineering Department, King Saud University, Riyadh 11421, Kingdom of Saudi Arabia
O. J. Aldraihem
Affiliation:
Mechanical Engineering Department, King Saud University, Riyadh 11421, Kingdom of Saudi Arabia
*
*Corresponding author (khdeir@ksu.edu.sa)
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Abstract

Analytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

Keywords

Free vibrationSmart beamsMultiple piezoelectric patchesAnalytical solutionsArbitrary boundary conditions
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 217 - 227
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1. Lee, C. K., “Piezoelectric Laminates for Torsional and Bending Modal Control: Theory and Experiment,” Ph.D. Dissertation, Cornell University (1987).Google Scholar
2. Crawley, E. F. and Lazarus, K. B., “Induced Strain Actuation of Isotropic and Anisotropic Plates,” AIAA Journal, 29, pp. 944–951 (1991).CrossRefGoogle Scholar
3. Rao, S. S. and Sunar, M., “Piezoelectricity and Its Use in Disturbance Sensing and Control of Flexible Strucures: A Survey,” Applied Mechanics Reviews, 47, pp. 113–123 (1994).CrossRefGoogle Scholar
4. Crawley, E. F. and De Luis, J., “Use of Piezoelectric Actuators as Elements of Intelligent Structures,” AIAA Journal, 25, pp. 1373–1385 (1987).CrossRefGoogle Scholar
5. Crawley, E. F. and Anderson, E. H, “Detailed Models of Piezoelectric Actuation of Beam,” Journal of Intelligent Material Systems and Structures, 1, pp. 4–25 (1990).CrossRefGoogle Scholar
6. Yang, S. M. and Lee, Y. J., “Modal Analysis of Stepped Beams with Piezoelectric Materials,” Journal of Sound and Vibration, 176, pp. 289–300 (1994).CrossRefGoogle Scholar
7. Bhattacharya, P., Suhail, H. and Sinha, P. K., “Finite Element Free Vibration Analysis of Smart Laminated Composite Beams and Plates,” Journal of Intelligent Material Systems and Structures, 9, pp. 20–28 (1998).CrossRefGoogle Scholar
8. Aldraheim, O. J., Singh, T. and Wetherhold, R. C., “Optimal Size and Location of Piezoelectric Actuator/Sensors: Practical Considerations,” Journal of Guidance, Control and Dynamics, 23, pp. 509–515 (2000).CrossRefGoogle Scholar
9. Khdeir, A. A. and Aldraihem, O. J., “Deflection Analysis of Beams with Extension and Shear Piezoelectric Patches Using Discontinuity Functions,” Smart Materials and Structures, 10, pp. 212–220 (2001).CrossRefGoogle Scholar
10. Aldraihem, O. J. and Khdeir, A. A., “Precise Deflection Analysis of Beams with Piezoelectric Patches,” Composite Structures, 60, pp. 135–143 (2003).CrossRefGoogle Scholar
11. Kapuria, S., Dumir, P. C. and Ahmed, A., “An Efficient Coupled Layerwise Theory for Dynamic Analysis of Piezoelectric Composite Beams,” Journal of Sound and Vibration, 261, pp. 927–944 (2003).CrossRefGoogle Scholar
12. Maxwell, N. D. and Asokanthan, S. F., “Modal Characteristics of a Flexible Beam with Multiple Distributed Actuators,” Journal of Sound and Vibration, 269, pp. 19–31 (2004).CrossRefGoogle Scholar
13. Kusculuoglu, Z. K., Fallahi, B. and Royston, T. J., “Finite Element Model of a Beam with a Piezoceramic Patch Actuator,” Journal of Sound and Vibration, 276, pp. 27–44 (2004).CrossRefGoogle Scholar
14. Maurini, C., Porfiri, M. and Pouget J., “Numerical Methods for Modal Analysis of Stepped Piezoelectric Beams,” Journal of Sound and Vibration, 298, pp. 918–933 (2006).CrossRefGoogle Scholar
15. Kekana, M., “Calculation of Eigenvalues of a Piezoelectric Beam Using the Pseudospectral Method,” Smart Materials and Structures, 15, p. 1079 (2006).CrossRefGoogle Scholar
16. Wang, Y. and Xu, R. Q., “A Model for Flrexural Vibration of Laminated Beams Embedded with Piezoelectric Layers Including Shear Deformation,” Technology and Innovation Conference, Hangzhou, China, pp. 2249–2252 (2006).Google Scholar
17. Christian, N. Della and Dongwei, Shu, “Vibration of Beams with Embedded Piezoelectric Sensors and Actuators,” Smart Materials and Structures, 15, p. 529 (2006).Google Scholar
18. Wang, R.-T., “Structural Responses of Surface-Mounted Piezoelectric Beams,” Journal of Mechanics, 26, pp. 47–59 (2010).CrossRefGoogle Scholar
19. Subramaniam, M. K., Liang, C. and Rogers, C. A., “A Computer Implementation of the Static and Dynamic Analysis of Induced Strain Actuated Beam,” Proceedings of the Second Conference on Recent Advances in Active Control of Sound and Vibration, Virginia Polytechnic Institute and State University, Blacksburg, VA (1993).Google Scholar
20. Lin, M. W., Abatan, A. O. and Rogers, C. A., “Application of Commercial Finite Element Codes for the Analysis of Induced Strain-Actuated Structures,” Second International Conference on Intelligent Materials, Lancaster, PA, Technomic, pp. 846–855 (1994).Google Scholar