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Numerical Study on the Linear and Nonlinear Behavior of A Fluid-Filled Piezoelectric Membrane Under Gravity Waves

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Abstract

This study integrated piezoelectric layers in a flexible membrane to form a piezoelectric membrane. A fluid-filled piezoelectric membrane, which can be used as breakwater and wave energy converter simultaneously, was presented. The mathematical models to describe the interactions of the waves with the piezoelectric membrane were given. The dimensionless parameters to control the behavior of the piezoelectric membrane were obtained. The mixed Eulerian-Lagrangian method was employed to simulate the mathematical models. The simulation code was verified. Based on the simulation results, the effects of dimensionless elastic modulus of the membrane E*, tension of the membrane T0* and the resistance of the load R* on the behavior of the piezoelectric membrane were discussed. As E* is small (E*<0.04) and T0* is not too small (T0* >0.0001), the response of the piezoelectric membrane can be considered as linear. For linear response, the minimum transmission coefficient and maximum output electric power of the piezoelectric membrane can be achieved simultaneously by adjusting T0* and R*. For larger E*, nonlinear behavior of the piezoelectric membrane is observed. At some larger values of E*, working frequency of piezoelectric elements can reach eight times the wave frequency. In these cases, higher output electric power can be achieved for smaller strain of the membrane.

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References

  • Bagheri, S., Wu, N. and Filizadeh, S., 2019. Numerical modeling and analysis of self-powered synchronous switching circuit for the study of transient charging behavior of a vibration energy harvester, Smart Materials and Structures, 28(10), 105056.

    Article  Google Scholar 

  • Bagheri, S., Wu, N. and Filizadeh, S., 2020. Application of artificial intelligence and evolutionary algorithms in simulation-based optimal design of a piezoelectric energy harvester, Smart Materials and Structures, 29, 105004.

    Article  Google Scholar 

  • Chen, S.E., Yang, R.Y., Wu, G.K. and Wu, C.C., 2021. A piezoelectric wave-energy converter equipped with a geared-linkage-based frequency up-conversion mechanism, Sensors, 21(1), 204.

    Article  Google Scholar 

  • Cho, K.H., Park, H.Y., Heo, J.S. and Priya, S., 2014. Structure-performance relationships for cantilever-type piezoelectric energy harvesters, Journal of Applied Physics, 115(20), 204108.

    Article  Google Scholar 

  • Das, S. and Cheung, K.F., 2009. Coupled boundary element and finite element model for fluid-filled membrane in gravity waves, Engineering Analysis with Boundary Elements, 33(6), 802–814.

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, S.T., Shi, H.D. and Dong, X.C., 2019. Capture performance of a multi-freedom wave energy converter with different power takeoff systems, China Ocean Engineering, 33(3), 288–296.

    Article  Google Scholar 

  • Hwang, W.S., Ahn, J.H., Jeong, S.Y., Jung, H.J., Hong, S.K., Choi, J. Y., Cho, J.Y., Kim, J.H. and Sung, T.H., 2017. Design of piezoelectric ocean-wave energy harvester using sway movement, Sensors and Actuators A: Physical, 260, 191–197.

    Article  Google Scholar 

  • Ikeda, T., 1990. Fundamentals of Piezoelectricity, Oxford University Press, Oxford, pp. 263.

    Google Scholar 

  • Jella, V., Ippili, S., Eom, J.H., Pammi, S.V.N., Jung, J.S., Tran, V.D., Nguyen, V.H., Kirakosyan, A., Yun, S., Kim, D., Sihn, M.R., Choi, J., Kim, Y.J., Kim, H.J. and Yoon, S.G., 2019. A comprehensive review of flexible piezoelectric generators based on organic-inorganic metal halide perovskites, Nano Energy, 57, 74–93.

    Article  Google Scholar 

  • Li, A.J., Liu, Y., Li, H.J. and Fang, H., 2020. Analysis of water wave interaction with a submerged fluid-filled semi-circular membrane breakwater, Ocean Engineering, 197, 106901.

    Article  Google Scholar 

  • Liu, C.R. and Huang, Z.H., 2019. A mixed Eulerian-Lagrangian simulation of nonlinear wave interaction with a fluid-filled membrane breakwater, Ocean Engineering, 178, 423–434.

    Article  Google Scholar 

  • Liu, C.R. and Huang, Z.H., 2020. A flexible membrane breakwater with a piezoelectric layer for providing harborage and wave-energy conversion, Journal of Coastal Research, 36(1), 148–156.

    Article  Google Scholar 

  • Liu, C.R., Huang, Z.H. and Tan, S.K., 2009. Nonlinear scattering of non-breaking waves by a submerged horizontal plate: Experiments and simulations, Ocean Engineering, 36(17–18), 1332–1345.

    Article  Google Scholar 

  • Longuet-Higgins, M.S. and Cokelet, E., 1976. The deformation of steep surface waves on water I. A numerical method of computation, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 350(1660), 1–26.

    MathSciNet  MATH  Google Scholar 

  • Mutsuda, H., Miyagi, J., Doi, Y., Tanaka, Y., Takao, H. and Sone, Y., 2014. Flexible piezoelectric sheet for wind energy harvesting, International Journal of Energy Engineering, 4(2), 67–75.

    Google Scholar 

  • Mutsuda, H., Tanaka, Y., Patel, R., Doi, Y., Moriyama, Y. and Umino, Y., 2017. A painting type of flexible piezoelectric device for ocean energy harvesting, Applied Ocean Research, 68, 182–193.

    Article  Google Scholar 

  • Nabavi, S.F., Farshidianfar, A. and Afsharfard, A., 2018. Novel piezoelectric-based ocean wave energy harvesting from offshore buoys, Applied Ocean Research, 76, 174–183.

    Article  Google Scholar 

  • Nabavi, S.F., Farshidianfar, A., Afsharfard, A. and Khodaparast, H.H., 2019. An ocean wave-based piezoelectric energy harvesting system using breaking wave force, International Journal of Mechanical Sciences, 151, 498–507.

    Article  Google Scholar 

  • Ohyama, T., Tanaka, M., Kiyokawa, T., Uda, T. and Murai, Y., 1989. Transmission and reflection characteristics of waves over a submerged flexible mound, Coastal Engineering in Japan, 32(1), 53–68.

    Article  Google Scholar 

  • Patel, R., Tanaka, Y., McWilliam, S., Mutsuda, H. and Popov, A.A., 2016. Model refinements and experimental testing of highly flexible piezoelectric energy harvesters, Journal of Sound and Vibration, 368, 87–102.

    Article  Google Scholar 

  • Phadke, A.C. and Cheung, K.F., 1999. Response of bottom-mounted fluid-filled membrane in gravity waves, Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(6), 294–303.

    Article  Google Scholar 

  • Phadke, A.C. and Cheung, K.F., 2001. Resonance and response of fluid-filled membrane in gravity waves, Applied Ocean Research, 23(1), 15–28.

    Article  Google Scholar 

  • Phadke, A.C. and Cheung, K.F., 2003. Nonlinear response of fluid-filled membrane in gravity waves, Journal of Engineering Mechanics, 129(7), 739–750.

    Article  Google Scholar 

  • Priya, S., Song, H.C., Zhou, Y., Varghese, R., Chopra, A., Kim, S.G., Kanno, I., Wu, L., Ha, D.S., Ryu, J. and Polcawich, R.G., 2017. A review on piezoelectric energy harvesting: Materials, methods, and circuits, Energy Harvesting and Systems, 4(1), 3–39.

    Article  Google Scholar 

  • Ramalingam, U., Gandhi, U., Mangalanathan, U. and Choi, S.B., 2018. A new piezoelectric energy harvester using two beams with tapered cavity for high power and wide broadband, International Journal of Mechanical Sciences, 142–143, 224–234.

    Article  Google Scholar 

  • Reddy, A.R., Umapathy, M., Ezhilarasi, D. and Gandhi, U., 2016. Improved energy harvesting from vibration by introducing cavity in a cantilever beam, Journal of Vibration & Control, 22(13), 3057–3066.

    Article  MathSciNet  Google Scholar 

  • Sezer, N. and Koç, M., 2021. A comprehensive review on the state-of-the-art of piezoelectric energy harvesting, Nano Energy, 80, 105567.

    Article  Google Scholar 

  • Tang, W., Wang, L.B., Ren, Y.M., Bao, B. and Cao, J.J., 2018. Design and experimental analysis of self-sensing SSDNC technique for semi-active vibration control, Smart Materials and Structures, 27(8), 085028.

    Article  Google Scholar 

  • Viet, N.V., Carpinteri, A. and Wang, Q., 2019. A novel heaving ocean wave energy harvester with a frequency tuning capability, Arabian Journal for Science and Engineering, 44(6), 5711–5722.

    Article  Google Scholar 

  • Viet, N.V., Xie, X.D., Liew, K.M., Banthia, N. and Wang, Q., 2016. Energy harvesting from ocean waves by a floating energy harvester, Energy, 112, 1219–1226.

    Article  Google Scholar 

  • Wang, Q. and Varadan, V.K., 2003. Transition of the buckling load of beams by the use of piezoelectric layers, Smart Materials and Structures, 12(5), 696–702.

    Article  Google Scholar 

  • Wang, X. and Lin, L.W., 2013. Dimensionless optimization of piezoelectric vibration energy harvesters with different interface circuits, Smart Materials and Structures, 22(8), 085011.

    Article  Google Scholar 

  • Wu, N., Bao, B. and Wang, Q., 2021. Review on engineering structural designs for efficient piezoelectric energy harvesting to obtain high power output, Engineering Structures, 235, 112068.

    Article  Google Scholar 

  • Xie, X.D. and Wang, Q., 2017. A study on an ocean wave energy harvester made of a composite piezoelectric buoy structure, Composite Structures, 178, 447–454.

    Article  Google Scholar 

  • Xie, X.D., Wang, Z.J., Liu, D.Z., Du, G.F. and Zhang, J.F., 2020. An experimental study on a novel cylinder harvester made of L-shaped piezoelectric coupled beams with a high efficiency, Energy, 212, 118752.

    Article  Google Scholar 

  • Yang, J.H., Ryu, T., Lansac, Y., Jang, Y.H. and Lee, B.H., 2016. Shear stress-induced enhancement of the piezoelectric properties of PVDF-TrFE thin films, Organic Electronics, 28, 67–72.

    Article  Google Scholar 

  • Zaarour, B., Zhu, L., Huang, C., Jin, X.Y., Alghafari, H., Fang, J. and Lin, T., 2021. A review on piezoelectric fibers and nanowires for energy harvesting, Journal of Industrial Textiles, 51(2), 297–340.

    Article  Google Scholar 

  • Zhang, X.T., Yang, J.M. and Xiao, L.F., 2016. An oscillating wave energy converter with nonlinear snap-through power-take-off systems in regular waves, China Ocean Engineering, 30(4), 565–580.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Xiamen University of Technology, Xiamen, 361024, China

    Chun-rong Liu & Wen-yu Yang

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  1. Chun-rong Liu
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  2. Wen-yu Yang
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Correspondence to Chun-rong Liu.

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The authors declare no competing interests.

Additional information

Foundation item: This research work was financially supported by the National Natural Science Foundation of China (Grant No. 12072306).

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Liu, Cr., Yang, Wy. Numerical Study on the Linear and Nonlinear Behavior of A Fluid-Filled Piezoelectric Membrane Under Gravity Waves. China Ocean Eng 37, 768–780 (2023). https://doi.org/10.1007/s13344-023-0064-9

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  • DOI: https://doi.org/10.1007/s13344-023-0064-9

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