Effect of Piezoelectric Patches on the Vibration and Buckling of Euler-Bernoulli Beams under Axial Load

علوم کاربردی و محاسباتی در مکانیک

Article 3, Volume 27, Issue 2 - Serial Number 14, September 2016, Pages 29-40   

Document Type: Original Article

DOI: 10.22067/fum_mech.v27i2.37712

Authors

Hasan Bighlari¹; Vahid Arab Maleke^{* 2}; Nima Jafarzade²

¹دانشگاه تبریز

²Tabriz University

Abstract

Piezoelectric layers have significant effect on the vibration behavior and buckling capacity of the structures. For optimum usage of piezoelectric materials, it is possible to use the piezoelectric patches instead of the piezoelectric layers. In this paper, the effects of piezoelectric patches and boundary conditions on the buckling and vibration behaviors of Euler-Bernoulli beams is investigated. The piezoelectric stress resultants are introduced in terms of Heaviside discontinuity functions and the characteristics equation is obtained via Galerkin method. The effects of variation of location, length of the piezoelectric patches and the applied voltages on the natural frequencies and critical buckling loads of beam with different boundary conditions are investigated. Results show that the natural frequencies and critical buckling load are dependent on the voltage, length and location of the piezoelectric patches and the axial load. Also, patches have a considerable effect if they placed at the beam center.

Keywords

Euler-Bernoulli beam; Natural Frequency; Axial Load; Buckling Load; Piezoelectric Patch

Supplementary Files

EditNoMarkup.EA-3arabmaleki.pdf

References

1. Chopra, I., "Review of state of art of smart structures and integrated systems", AIAA journal, 40(11), pp. 2145-2187, (2002).

2. Zhang, Z., Kan, J., Cheng, G., Jia, Y. and Wang, H., "Influence of multiple piezoelectric effects on sensors and actuators", Mechanical Systems and Signal Processing, 35(1), pp. 95-107, (2013).

3. Waisman, H. and Abramovich, H., "Variation of natural frequencies of beams using the active stiffening effect", Composites Part B: Engineering, 33(6), pp. 415-424, (2002).

4. Asadi, K., Ahmadian, H. and Jalali, H., "Micro/macro slip damping in beams with frictional contact interface", Journal of Sound and Vibration, 331(21), pp. 4704–4712, (2012).

5. Vashist, S.K. and Chhabra, D., "Optimal placement of piezoelectric actuators on plate structures for active vibration control using genetic algorithm", In SPIE Smart Structures and Materials Nondestructive Evaluation and Health Monitoring. International Society for Optics and Photonics, pp. 905720-905732, (2014).

6. Hernandes, J.A., Almeida, S.F.M. and Nabarrete, A., "Stiffening effects on the free vibration behavior of composite plates with PZT actuators", Composite structures, 49(1), pp. 55-63, (2000).

7. Wang, Q. and Quek, S.T., "Enhancing flutter and buckling capacity of column by piezoelectric layers", International journal of solids and structures, 39(16), pp. 4167-4180, (2002).

8. Sadek, I., Kucuk, I., Zeini, E., Adali, S., "Optimal boundary control of dynamics responses of piezo actuating micro-beams", Applied Mathematical Modeling, 33(8), pp. 3343–3353, (2009).

9. Maurini, C., Pouget, J. and Vidoli, S., "Distributed piezoelectric actuation of a bistable buckled beam", European Journal of Mechanics-A/Solids, 26(5), pp. 837-853, (2007).

10. Wang, Q., "On buckling of column structures with a pair of piezoelectric layers", Engineering structures, 24(2), pp. 199-205, (2002).

11. Kayacık. O., et al., "Integral equation approach for piezo patch vibration control of beams with various types of damping", Computers and Structures, 86, pp. 357–366, (2008).

12. Sridharan, S. and Kim, S., "Piezo-electric control of stiffened panels subject to interactive buckling", International Journal of Solids and Structures, 46(6), pp. 1527-1538, (2009).

13. Przybylski, J.,"Stability of an articulated column with two collocated piezoelectric actuators", Engineering Structures, 30(12), pp. 3739-3750, (2008).

14. Wang, Q., Varadan, V.K., "Transition of the buckling load of beams by the use of piezoelectric layers", Smart materials and structures, 12(5), pp. 696-702, (2003).

15. Della, C.N. and Shu, D., "Vibration of beams with piezoelectric inclusions", International journal of solids and structures, 44(7), pp. 2509-2522, (2007).

16. Sloss, J.M., Bruch, J.C., Sadek, I.S. and Adali, S., "Piezo patch sensor/actuator control of the vibrations of a cantilever under axial load", Composite Structures, 62(3), pp. 423-428, (2003).

17. Chhabra, D., Narwal, K. and Singh, P., "Design and Analysis of Piezoelectric Smart Beam for Active Vibration Control", International Journal of Advancements in Research & Technology, 1(1), pp. 1-5, (2012).

18. Aldraihem, 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(3),

pp. 509-515, (2000).

19. 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(2), p. 212, (2001).

20. Aldraihem, O.J. and Khdeir, A.A., "Precise deflection analysis of beams with piezoelectric patches", Composite Structures, 60(2), pp. 135-143, (2003).

21. Nikkhoo, A., "Investigating the behavior of smart thin beams with piezoelectric actuators under dynamic loads", Mechanical Systems and Signal Processing, 45(2), pp. 513-530, (2014).

22. Ducarne, J., Thomas, O. and Deü, J.F., "Placement and dimension optimization of shunted piezoelectric patches for vibration reduction", Journal of Sound and Vibration, 331(14), pp. 3286-3303, (2012).

23. Crawley, E.F. and De Luis, J., "Use of piezoelectric actuators as elements of intelligent structures", AIAA Journal, 25(10), pp. 1373-1385, (1987).

24. Lawrence, N., "Virgin-Vibration of Axially-Loaded Structures", Cambridge University Press, (2007).

25. Wang, Q. and Wang, C.M., "Optimal placement and size of piezoelectric patches on beams from the controllability perspective", Smart Materials and Structures, 9(4), pp. 558–567, (2000).