Energy harvesting from large amplitude vibrations of pipes conveying fluid using piezoelectric layers with varying spanning angle
Source abstract
Abstract
Abstract This study analytically investigates the large-amplitude vibrations of a fluid-conveying piezoelectric pipe supported at both ends and resting on a nonlinear viscoelastic foundation. To enable energy harvesting, two piezoelectric layers with varying spanning angles are placed on the upper and lower surfaces of the pipe, which is subjected to external harmonic excitation near primary resonance. The modeling framework is based on Euler-Bernoulli beam theory combined with von Kármán nonlinear strain-displacement relations. Hamilton’s principle is employed to derive the governing equations of motion, which are subsequently reduced to a set of ordinary differential equations using the Galerkin method. The harmonic balance method is then utilized to derive analytical expressions for the amplitude–frequency response, voltage output, harvested power, and force–response behavior. The influence of damping coefficient, excitation force, excitation frequency and load resistance on the system’s response is examined in detail. The findings highlight the existence of optimal values for load resistance and spanning angle that maximize the electrical output.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Innovative Energy Harvesting Technologies · Vibration and Dynamic Analysis · Acoustic Wave Phenomena Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (48)
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1. Bibo, A., Abdelkefi, A., Daqaq, M.F.: Modeling and characterization of a piezoelectric energy harvester under combined aerodynamic and base excitations. J. Vib. Acoust. 137(3), 031017 (2015)10.1115/1.4029611 ↗
2. Cao, Y., Cao, D., He, G., Ge, X., Hao, Y.: Vibration analysis and distributed piezoelectric energy harvester design for the L-shaped beam. Eur. J. Mech. –a Solids 87, 104214 (2021)10.1016/j.euromechsol.2021.104214 ↗
3. Chiba, M., Shimazaki, N., Ichinohe, K.: Dynamic stability of a slender beam under horizontal–vertical excitations. J. Sound Vib. 333(5), 1442–1472 (2014)10.1016/j.jsv.2013.10.022 ↗
4. Daqaq, M.F., Stabler, C., Qaroush, Y., Seuaciuc-Osório, T.: Investigation of power harvesting via parametric excitations. J. Intell. Mater. Syst. Struct. 20(5), 545–557 (2009)10.1177/1045389X08100978 ↗
5. Dehrouyeh-Semnani, A.M., Nikkhah-Bahrami, M., Yazdi, M.R.H.: On nonlinear vibrations of micropipes conveying fluid. Int. J. Eng. Sci. 117, 20–33 (2017)
6. Ebrahimi, R., Ziaei-Rad, S.: Nonplanar vibration and flutter analysis of vertically spinning cantilevered piezoelectric pipes conveying fluid. Ocean Eng. 261, 112180 (2022)10.1016/j.oceaneng.2022.112180 ↗
7. Erturk, A., Inman, D. J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. (2008)10.1115/1.2890402 ↗
8. Fang, F., Xia, G., Wang, J.: Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations. Acta Mech. Sin. 34, 561–577 (2018)10.1007/s10409-017-0743-y ↗
9. Ghayesh, M.H., Païdoussis, M.P., Amabili, M.: Nonlinear dynamics of cantilevered extensible pipes conveying fluid. J. Sound Vib. 332(24), 6405–6418 (2013)10.1016/j.jsv.2013.06.026 ↗
10. Hassannejad, R., Alizadeh-Hamidi, B.: Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects. Int. J. Mech. Mater. des. 20(6), 1147–1162 (2024)10.1007/s10999-024-09720-w ↗
11. Iqbal, M., et al.: Vibration-based piezoelectric, electromagnetic, and hybrid energy harvesters for microsystems applications: a contributed review. Int. J. Energy Res. 45(1), 65–102 (2021)10.1002/er.5643 ↗
12. Javadi, M., Rahmanian, M.: Nonlinear vibration of fractional Kelvin-Voigt viscoelastic beam on nonlinear elastic foundation. Commun. Nonlinear Sci. Numer. Simul. 98, 105784 (2021)10.1016/j.cnsns.2021.105784 ↗
13. Kheiri, M., Païdoussis, M., Del Pozo, G.C., Amabili, M.: Dynamics of a pipe conveying fluid flexibly restrained at the ends. J. Fluids Struct. 49, 360–385 (2014)10.1016/j.jfluidstructs.2013.11.023 ↗
14. Khodabakhsh, R., Saidi, A.R., Bahaadini, R.: An analytical solution for nonlinear vibration and post-buckling of functionally graded pipes conveying fluid considering the rotary inertia and shear deformation effects. Appl. Ocean Res. 101, 102277 (2020)10.1016/j.apor.2020.102277 ↗
15. Khodabakhsh, R., Saidi, A.R., Bahaadini, R.: Homotopy solution for nonlinear vibration analysis of multilayer graphene platelets-reinforced thin-walled pipes conveying fluid with rectangular cross-section. Acta Mech. 234(2), 577–598 (2023)10.1007/s00707-022-03389-y ↗
16. Ma, X., Zhou, S.: A review of flow-induced vibration energy harvesters. Energy Convers. Manag. 254, 115223 (2022)10.1016/j.enconman.2022.115223 ↗
17. Ma, Y., Wang, Z., Fan, B., Yong, X.: Vibration characteristics of functionally graded fractional derivative viscoelastic fluid–conveying pipe with initial geometric defects. J. Eng. Mech. 150(5), 04024014 (2024)
18. Mao, X.-Y., Gao, S.-Y., Ding, H., Chen, L.-Q.: Static bifurcation and nonlinear vibration of pipes conveying fluid in thermal environment. Ocean Eng. 278, 114418 (2023)10.1016/j.oceaneng.2023.114418 ↗
19. Oyelade, A.O., Oyediran, A.A.: Nonlinear dynamics of horizontal pipes conveying two phase flow. Eur. J. Mech. a. Solids 90, 104367 (2021)10.1016/j.euromechsol.2021.104367 ↗
20. Paidoussis, M. P.: Flow-induced instabilities of cylindrical structures. (1987)10.1115/1.3149530 ↗
21. Paidoussis, M.P., Issid, N.: Dynamic stability of pipes conveying fluid. J. Sound Vib. 33(3), 267–294 (1974)10.1016/S0022-460X(74)80002-7 ↗
22. Pasharavesh, A., Ahmadian, M., Zohoor, H.: Electromechanical modeling and analytical investigation of nonlinearities in energy harvesting piezoelectric beams. Int. J. Mech. Mater. des. 13(4), 499–514 (2017)10.1007/s10999-016-9353-2 ↗
23. Rahmani Naeim Abadi, M., Saidi, A.R., Askari Farsangi, M.A.: Piezoelectric energy harvesting via thin annular sectorial plates: an analytical approach. Arch. Appl. Mech. 91(7), 3365–3382 (2021)10.1007/s00419-021-01971-9 ↗
24. Rezaei, M., Khadem, S.E., Friswell, M.: Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation. Meccanica 55, 1463–1479 (2020)10.1007/s11012-020-01187-1 ↗
25. Saadatnia, Z., Esmailzadeh, E.: Nonlinear harmonic vibration analysis of fluid-conveying piezoelectric-layered nanotubes. Compos. Part B Eng. 123, 193–209 (2017)10.1016/j.compositesb.2017.05.012 ↗
26. Sabahi, M.A., Saidi, A.R.: An analytical investigation on nonlinear vibrations and stability of Timoshenko pipes conveying two-phase flow. Thin Walled Struct. 198, 111749 (2024)10.1016/j.tws.2024.111749 ↗
27. Sabahi, M.A., Saidi, A.R.: On nonlinear vibrations of Timoshenko FG porous micropipes in thermal environment: analysis and optimization. Int. J. Mech. Mater. des. 21(4), 799–821 (2025). https://doi.org/10.1007/s10999-025-09764-610.1007/s10999-025-09764-6 ↗
28. Sabahi, M.A., Saidi, A.R., Khodabakhsh, R.: An analytical solution for nonlinear vibration of functionally graded porous micropipes conveying fluid in damping medium. Ocean Eng. 245, 110482 (2022)10.1016/j.oceaneng.2021.110482 ↗
29. Sabahi, M.A., Saidi, A.R., Bahaadini, R.: Nonlinear vibrations and stability analysis of GPL reinforced pipes conveying fluid excited by arbitrary initial conditions: an optimized analytical solution. Int. J. Struct. Stab. Dyn. (2023). https://doi.org/10.1142/S021945542450210910.1142/S0219455424502109 ↗
30. Safaei, M., Sodano, H.A., Anton, S.R.: A review of energy harvesting using piezoelectric materials: state-of-the-art a decade later (2008–2018). Smart Mater. Struct. 28(11), 113001 (2019)10.1088/1361-665X/ab36e4 ↗
31. Setoodeh, A., Rezaei, M., Zendehdel Shahri, M.: Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory. Appl. Math. Mech. 37, 725–740 (2016)10.1007/s10483-016-2085-6 ↗
32. Sodano, H.A., Inman, D.J., Park, G.: A review of power harvesting from vibration using piezoelectric materials. Shock Vib. Dig. 36(3), 197–206 (2004)10.1177/0583102404043275 ↗
33. Sun, W., et al.: Navigating the future of flow-induced vibration-based piezoelectric energy harvesting. Renew. Sustain. Energy Rev. 201, 114624 (2024)10.1016/j.rser.2024.114624 ↗
34. Tan, T., Yan, Z., Ma, K., Liu, F., Zhao, L., Zhang, W.: Nonlinear characterization and performance optimization for broadband bistable energy harvester. Acta Mech. Sin. 36, 578–591 (2020)10.1007/s10409-020-00946-3 ↗
35. Tang, Y., Yang, T.: Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material. Compos. Struct. 185, 393–400 (2018)10.1016/j.compstruct.2017.11.032 ↗
36. Tang, Y., Wang, G., Yang, T., Ding, Q.: Nonlinear dynamics of three-directional functional graded pipes conveying fluid with the integration of piezoelectric attachment and nonlinear energy sink. Nonlinear Dyn. 111(3), 2415–2442 (2023)10.1007/s11071-022-07971-w ↗
37. Tuo, Y.-h, Fu, G.-m, Sun, B.-j, Lou, M., Su, J.: Stability of axially functionally graded pipe conveying fluid: generalized integral transform solution. Appl. Ocean Res. 125, 103218 (2022)10.1016/j.apor.2022.103218 ↗
38. Wang, G.: Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler-Bernoulli beam theory. J. Intell. Mater. Syst. Struct. 24(2), 226–239 (2013)10.1177/1045389X12461080 ↗
39. Wang, G., Shen, J.: Flutter instabilities of cantilevered piezoelectric pipe conveying fluid. J. Intell. Mater. Syst. Struct. 30(4), 606–617 (2019)10.1177/1045389X18818774 ↗
40. Wei, C., Jing, X.: A comprehensive review on vibration energy harvesting: modelling and realization. Renew. Sustain. Energy Rev. 74, 1–18 (2017)10.1016/j.rser.2017.01.073 ↗
41. Xie, W., Gao, X., Xu, W.: Stability and nonlinear vibrations of a flexible pipe parametrically excited by an internal varying flow density. Acta Mech. Sin. 36, 206–219 (2020)10.1007/s10409-019-00910-w ↗
42. Zhen, Y., Gong, Y., Tang, Y.: Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature. Compos. Struct. 268, 113980 (2021)10.1016/j.compstruct.2021.113980 ↗
43. Zhou, M., Al-Furjan, M.S.H., Wang, B.: Modeling and efficiency analysis of a piezoelectric energy harvester based on the flow induced vibration of a piezoelectric composite pipe. Sensors 18(12), 4277 (2018)10.3390/s18124277 ↗
44. Zhou, J., Chang, X., Li, Y.: Nonlinear vibration analysis of functionally graded flow pipelines under generalized boundary conditions based on homotopy analysis. Acta Mech. 233(12), 5447–5463 (2022a)10.1007/s00707-022-03391-4 ↗
45. Zhou, J., Chang, X., Xiong, Z., Li, Y.: Stability and nonlinear vibration analysis of fluid-conveying composite pipes with elastic boundary conditions. Thin Walled Struct. 179, 109597 (2022b)10.1016/j.tws.2022.109597 ↗
46. Zhou, W., Du, D., Cui, Q., Lu, C., Wang, Y., He, Q.: Recent research progress in piezoelectric vibration energy harvesting technology. Energies 15(3), 947 (2022c)10.3390/en15030947 ↗
47. Zhu, B., Xu, Q., Li, M., Li, Y.: Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation. Compos. Struct. 252, 112672 (2020)10.1016/j.compstruct.2020.112672 ↗
48. Zhu, H., Tang, T., Yang, H., Wang, J., Song, J., Peng, G.: The state-of-the-art brief review on piezoelectric energy harvesting from flow-induced vibration. Shock. Vib. 2021(1), 8861821 (2021)10.1155/2021/8861821 ↗