IJE TRANSACTIONS C: Aspects Vol. 31, No. 9 (September 2018) 1585-1592    Article in Press

PDF URL: http://www.ije.ir/Vol31/No9/C/15-2896.pdf  
downloaded Downloaded: 18   viewed Viewed: 63

Z. Tadi Beni, S. A. Hosseini Ravandi and Y. Tadi Beni
( Received: October 10, 2017 – Accepted in Revised Form: January 04, 2018 )

Abstract    In this paper, size dependent nano-beam type peizoelectric energy hardvester is investigated. For this goal, first nonlinear formulation of isotropic piezoelectric Euler-Bernoulli nano-beam is developed based on the size-dependent piezoelectricity theory then special nano-beam type piezoelectric energy hardvester is probed for different parameters. Basic nonlinear equations of piezoelectric nano-beam are derived using principle of minimum potential energy and variational method. To evaluate the formulation derived, static deformation and free vibration of the hinged-hinged piezoelectric nano-beam is investigated in the special case. The results of the derived formulation are investigated under different parameters, and particularly, the ability and performance of the beam type piezoelectric low power energy harvesting was evaluated in nanoscale.


Keywords    Piezoelectric, Size Effect, Euler-Bernoulli Nano-beam, Energy Harvesting



در این مقاله نانوتیر وابسته به اندازه پیزوالکتریک به عنوان برداشت‌کننده انرژی مورد بررسی قرار گرفته است. برای این هدف ابتدا فرمول غیرخطی از نانوتیر اویلر برنولی ایزوتروپ بر پایه تئوری وابسته به اندازه پیزوالکتریک به دست آمده و سپس برای نوع خاصی از این نانوتیر پارامترهای مختلف مورد بررسی قرار گرفته است. معادلات غیرخطی پایه با روش کمینه انرژی پتانسیل و وردش‌گیری به دست آمده است. برای ارزیابی معادلات به دست آمده خمش استاتیکی و ارتعاش آزاد نانوتیر پیزوالکتریک دو سر مفصل برای حالت خاصی بررسی گردیده و نتایج برای معادلات مذکور نشان می‌دهد که این تیر قابلیت برداشت کم انرژی را در مقیاس نانو دارد.


1. Qin, Y., Wang, X., Wang, Z.L., “Microfibre–nanowire hybrid structure for energy scavenging”,  Nature, Vol. 451, No.7180, (2008), 809–813.
2. Erturk, A., Inman, D.J., “An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations”, Smart  Materials and  Structures., Vol. 18, No. 2, (2009), 025009.
3. DuToit, N.E., Wardle, B.L., “Experimental verification of models for microfabricated piezoelectric vibration energy harvesters”,  AIAA Journal, Vol. 45, No. 5, (2007) , 1126–1137.
4. Shu, Y.C., Lien, I.C., “Analysis of power output for piezoelectric energy harvesting systems”, Smart  Materials and  Structures., Vol. 15, (2006) ,1499-1512.
5. Karami, M.A., Inman, D.J., “Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems”, Journal of Sound and Vibration, Vol. 330, No. 23, (2011), 5583-5597.
6. Mohammadpour, M., Dardel, M., Ghasemi, M. H., Pashaei, M. H., ”Nonlinear energy harvesting through a multimodal electro-mechanical system”, Journal of Theoretical and Applied Vibration and Acoustics, Vol. 1, No. 2, (2015), 73-84. 
7. Tadi Beni Y., Jafari A., Razavi H. “Size Effect on Free Transverse Vibration of Cracked Nano-beams using Couple Stress Theory”, International Journal of Engineerig- Transactions B: Applications, Vol. 28, No. 2, (2015), 296-304.
8. Fattahian Dehkordi S., Tadi Beni Y.,”Electro-mechanical free vibration of single-walled piezoelectric/flexoelectric nano cones using consistent couple stress theory”, International Journal of Mechanical Sciences, 128–129 (2017), 125–139.
9. Simsek, M., ”Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory”, International Journal of Engineering Science, Vol. 48, (2010), 1721-1732.
10. Bakhshi Khaniki, H., Hosseini Hashemi, S., “Free Vibration Analysis of Nonuniform Microbeams Based on Modified Couple Stress Theory: an Analytical Solution”, International Journal of Engineering-Transactions B: Applications, Vol. 30, No. 2, (2017), 311-320.
11. Akbari, M.R., Nimafar, M., Ganji, D.D., Karimi Chalmiani, H., “Investigation on non-linear vibration in arched beam for bridges construction via AGM method” ,Applied Mathematics and Computation, Vol. 298, (2017), 95-110 , 
12. Hatami, M., Vahdani, S., Ganji, D.D., ”Deflection prediction of a cantilever beam subjected to static co-planar loading by analytical methods”, HBRC Journal, Vol. 10, No. 2, (2014), 191-197.
13. Gürses, M., Civalek,  O., Korkmaz, A., Ersoy, H., “Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first‐order shear deformation theory”, International Journal for Numerical Methods in Engineering, Vol. 79, No.3,( 2009), 290-313.
14. Demir, C, Mercan, K, Civalek, O. “Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel”, Composites Part B, Vol. 94, (2016), 1-10.
15. Mercan, K, Civalek, O., “DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix”, Composite Structures, Vol. 143, (2016), 300–309.
16. Akgoz, B., Civalek, O., “free vibration analysis of axially functionally graded tapered bernoulli-Euler microbeams based on the modified couple stress theory”, Composite Structures, Vol. 98, (2013), 314-322.
17. Mehralian, F., Tadi Beni, Y., Ansari, R., “Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell”, Composite Structures, Vol. 152, ( 2016), 45–61.
18. Baltacıoglu, A., K., Akgoz, B., Civalek, O., “Nonlinear static response of laminated composite plates by discrete singular convolution method”, Composite Structures ,Vol. 93, (2010) ,153–161.
19. Beni, Y. T., Karimipour, I.,  Abadyan, M. “Modeling the effect of intermolecular force on the size-dependent pull-in behavior of beam-type NEMS using modified couple stress theory”, Journal of Mechanical Science and Technology, Vol. 28, No. 9, ( 2014) , 3749-3757.
20. Tadi Beni,Y.,” Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling”, Mechanics Research Communications, Vol. 75, (2016), 67–80.
21. Tadi Beni Y., “Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams”, Journal of Intelligent Material Systems and Structures, , Vol. 27, No. 16,( 2016), 2199–2215.
22. Tadi Beni, Y., “A nonlinear electro-mechanical analysis of nanobeams based on the size-dependent piezoelectricity theory”, Journal of Mechanics, Vol. 65, ( 2016), 1-13.
23. Shah-Mohammadi-Azar, A., Khanchehgardan,  A., Rezazadeh, G., Shabani R., “Mechanical response of a piezoelectrically sandwiched nano-beam based on the nonlocal theory”, International Journal of Engineering-Transactions C: Aspects, Vol. 26, No. 12, (2013), 1515-1524.
24. Wang, K.F., Wang, B.L., “an analytical model for nanoscale unimorph piezoelectric energy harvesters with flexoelectric effect”, Composite Structures, Vol. 153,(2016), 253-261.
25. Liang, Xu., Hu, S., Shen, S.,”size dependent buckling and vibration behaviors of piezoelectric nanostructures due to flexoelectricity”, Smart  Materials and  Structures. , Vol. 24, (2015), 105012. 
26. Shams Nateri, M., Azizollah Ganji, B.,” The Effect of Material Properties on Sensitivity of the Microelectromechanical Systems Piezoelectric Hydrophone”, International Journal of Engineering-Transactions C: Aspects, Vol. 30, No. 12, (2017) 1848-1855.
27. Mehralian, F., Tadi Beni, Y., Ansari, R., “On the size dependent buckling of anisotropic piezoelectric cylindrical shells under combined axial compression and lateral pressure”, International Journal of Mechanical Sciences, Vol. 119, (2016), 155–169.
28. Ebrahimi, N., Tadi Beni, Y., “Electro-mechanical vibration of nanoshells using consistent size-dependent piezoelectric theory”, Steel and Composite Structures, Vol. 22, No. 6, (2016), 1301-1336.
29. Kheibari F., Tadi Beni Y., “Size dependent electro-mechanical vibration of single-walled piezoelectric nanotubes using thin shell model”, Materials & Design,Vol. 114, (2017), 572–583.
30. Alibeigi B., Beni Y.T., Mehralian F.,”On the thermal buckling of magneto-electro-elastic piezoelectric nanobeams” The European Physical Journal Plus Vol.133, No. 3, (2016), 133.
31. Shen, S.P., Hu, S.L”, A theory of flexoelectricity with surface effect for elastic dielectrics”, Journal of the Mechanics and Physics of Solids, Vol. 58, (2010), 665–677.
32. Hadjesfandiary, A.R., “size dependent piezoelectricity”, International Journal of Solids and Structures, Vol. 50, (2013), 2781-2791. 
33. Ghorbanpour Arani, A., Kolahchi, R., Vossough, H.,” Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory”, Physica B, Vol. 407, (2012), 4458–4465. 

Download PDF 

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir