Energy Harvesting from Smart Nanocomposite Microbeam Using Piezoelectric Materials

Document Type : Original Article

Author

Department of Mecahnical Engineering, University of Ayatollah Boroujerdi

Abstract

This paper deals with the energy harvesting of microbeam reinforced with functionally graded carbon nanotubes. The microbeam is intended to place a harmonic position. The effects of size are assumed using strain gradient theory. The effective modulus of the nanocomposite beam is obtained using the principle of porosity. Based on the theory of sine theory, the final relations of motion are calculated. Using the differential square solution and Newmark methods, the energy harvesting and dynamic instability region of the microbeam is calculated. The effects of boundary conditions, volume fraction and distribution of carbon nanotubes, size, temperature and length-to-thickness ratio of microbeam on the dynamic instability curve are shown. Numerical results show that the dynamic instability region occurred at higher resonant frequencies and with increasing volume fraction of carbon nanotubes. In addition, the resonant frequency is higher for functionally graded carbon nanotubes with X-shaped distribution compared to the uniform state. In addition, the electric power produced increases with the increase in the thickness of the piezoelectric layer.

Keywords


[1] Virgin, L.N., Plaut, R.H., "Influence of axial load on forced vibrations of beams", Journal of Sound and Vibration, Vol. 168, pp.395-405, 1993. https://doi.org/10.1006/jsvi.1993.1382
[2] Orhan, S., "Analysis of free and forced vibration of a cracked cantilever beam", NDT & E International, Vol. 40, pp. 443-450, 2007. https://doi.org/10.1016/j.ndteint.2007.01.010
[3] Repetto, C.E., Roatta, A., Welti, R.J., "Forced vibrations of a cantilever beam", European Journal of Physics, Vol. 33, pp. 345-366, 2012. 10.1088/0143-0807/33/5/1187
[4] Simsek, M., "Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory", Steel Composite Structures, Vol. 11, pp. 59-76, 2012. 10.12989/scs.2011.11.1.059
[5] Uymaz, B., "Forced vibration analysis of functionally graded beams using nonlocal elasticity", Composite Structures, Vol. 105, pp. 227-239, 2013. https://doi.org/10.1016/j.compstruct.2013.05.006
[6] Bhushan, A., Inamdar, M.M., Pawaskar, D.N., “Simultaneous planar free and forced vibrations analysis of an electrostatically actuated beam oscillator”, International Journal of Mechanical Science, Vol. 23, pp. 8290-99, 2014. https://doi.org/10.1016/j.ijmecsci.2014.03.003
[7] Ghulghazaryan, L.G., "Forced vibrations of orthotropic shells when there is viscous resistance", Journal of Appllied Mathematical Mechanics, Vol. 79, pp. 281-292, 2015. https://doi.org/10.1016/j.jappmathmech.2015.09.008
[8] Chen, D., Yang, J., Kitipornchai, S., "Free and forced vibrations of shear deformable functionally graded porous beams", International Journal of Mechanical Science, Vol. 108–109, pp. 14-22, 2018. https://doi.org/10.1016/j.ijmecsci.2016.01.025
[9] Dai, H.L., Zhao, D.M., Zou, J.J., Wang, L., "Surface influence on the nonlinear forced vibration of cantilevered nanobeams", Physica E, Vol. 80, pp. 25-30, 2016. https://doi.org/10.1016/j.physe.2016.01.008
[10] Chen, L., "Forced vibration of surface foundation on multi-layered half space", Structural Engineering and Mechanics, Vol. 54, pp. 623-648, 2015. https://doi.org/10.12989/sem.2015.54.4.623
[11] Akbarov, S.D., Mehdiyev, M.A., "Forced vibration of the elastic system consisting of the hollow cylinder and surrounding elastic medium under perfect and imperfect contact", Structural Engineering and Mechanics, Vol. 62, pp. 113-123, 2017. https://doi.org/10.12989/sem.2017.62.1.113
[12] Li, Y.H., Dong, Y.H., Qin, Y., Lv, H.W., "Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam", International Journal of Mechanical Science, Vol. 138–139, pp. 131-145, 2018. https://doi.org/10.1016/j.ijmecsci.2018.01.041
[13] Mirzaee, M., Bagheri, A., "Employing dynamic line rating in unit commitment problem in the presence of wind power generation units under uncertainty condition", Energy Engineering and Management, 2023. https://doi.org/10.22052/jeem.2023.113712
[14] Mohammadimehr, M., Farsi, A.A., Eslami Farsani, R., Dashti Gohari, P., Yousefi Ramandi, M., "The surface stress effects on linear vibration of nonlocal triple-walled boron nitride nano tube conveying viscose fluid flow using DQM", Journal of Modeling in Engineering, Vol. 43, pp. 47-66, 2016. https://doi.org/10.22075/jme.2017.1739
[15] Rostami, H., Jedari Salami, S., "Large amplitude free vibration of sandwich beams with flexible core and FG Graphene Platelet Reinforced Composite (FG-GPLRC) face sheets based on extended higher-order sandwich panel theory", Thin-Walled Structures, Vol. 180, pp. 109999, 2022. https://doi.org/10.1016/j.tws.2022.109999
[16] Kumar Kar, U., Srinivas, J., "Vibration analysis of Bi-directional FG-GNPs reinforced rotating micro-beam under Thermo-mechanical loading", Materials Today: Proceedings, Vol. 78, pp. 752-759, 2023. https://doi.org/10.1016/j.matpr.2022.10.227
 [17] Duc, N.D., Hadavinia, H., Van Thu, P., Quan, T.Q., "Vibration and nonlinear dynamic response of imperfect three-phase polymer nanocomposite panel resting on elastic foundations under hydrodynamic loads", Composite Structures, Vol. 131, pp. 229-237, 2015. https://doi.org/10.1016/j.compstruct.2015.05.009
[18] He, X.Q., Rafiee, M., Liew, K.M., "Large amplitude vibration of fractionally damped viscoelastic CNTs/fiber/polymer multiscale composite beams", Composite Structures, Vol. 131, pp. 1111-1123, 2015. https://doi.org/10.1016/j.compstruct.2015.06.038
[19] Pan, Zh., Liew, K.M., "Predicting vibration characteristics of rotating composite blades containing CNT-reinforced composite laminae and damaged fiber-reinforced composite laminae", Composite Structures, Vol. 250, pp. 112580, 2020. https://doi.org/10.1016/j.compstruct.2020.112580
[20] Talebi, M., "Analysis of unsteady fluid induced vibration forces on a nuclear fuel rod bundle in turbulent axial flow", Energy Engineering and Management, Vol. 12, No. 1, pp. 158-169, 2022. (In Persian) https://doi.org/10.22052/12.1.158
 [21] Wu, H., Li, Y., Yang, J., "Free vibration analysis of functionally graded graphene nanocomposite beams partially in contact with fluid", Composite Structures, Vol. 291, pp. 115609, 2023. https://doi.org/10.1016/j.compstruct.2022.115609
[22] Ma, Zh., Arvin, H., "Nonlinear thermo-electro-mechanical free vibrations of sandwich nanocomposite beams bonded with sensor layers considering pyroelectricity", Engineering Analysis with Boundary Elements, Vol. 148, pp. 90-103, 2023. https://doi.org/10.1016/j.enganabound.2022.12.019
[23] Şimşek, M., Reddy, J.N., "Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory", International Journal of Engineering Science, Vol. 64, pp. 37-53, 2013. https://doi.org/10.1016/j.ijengsci.2012.12.002
[24] Lei, J., He, Y., Zhang, B., Gan, Z., Zeng, P., "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", International Journal of Engineering Science, Vol. 72, pp. 36-52, 2013. https://doi.org/10.1016/j.ijengsci.2013.06.012
[25] Liew, K.M., Lei, Z.X., Yu, J.L., Zhang, L.W., "Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Computer Methods in Applied Mechanics and Engineering, Vol. 268, pp. 1-17, 2014. https://doi.org/10.1016/j.cma.2013.09.001
[26] Rajora, A., Dwivedi, A., Vyas, A., Gupta, S., Tyagi, A., "Energy harvesting estimation from the vibration of a simply supported beam", International Journal of Acoustics and Vibration, Vol. 22, pp. 186-193, 2017. https://doi.org/10.20855/ijav.2017.22.2463
[27] Al-Furjan, M.S.H., Yin, C., Shen, X., Kolahchi, R., Zarei, M.S., Hajmohammad, M.H., "Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate", Mechanical Systems and Signal Processing Vol. 178, pp. 109269, 2022. https://doi.org/10.1016/j.ymssp.2022.109269
 [28] Simsek, M., Kocatu¨rk, T., "Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load", Journal of Sound and Vibration, Vol. 320, pp. 235–253, 2009. https://doi.org/10.1016/j.jsv.2008.07.012