Research article Special Issues

Resonant frequency of mass-loaded membranes for vibration energy harvesting applications

  • Received: 13 April 2015 Accepted: 05 August 2015 Published: 13 August 2015
  • Vibration based energy harvesting has been widely investigated to target ambient vibration sources as a means to generate small amounts of electrical energy. While cantilever-based geometries have been pursued frequently in the literature, here membrane-based geometries for the energy harvesting device is considered, with the effects of an added mass and tension on the effective resonant frequency of the membranes studied. An analytical model is developed to describe the vibration response for a circular membrane with added mass structure, with the results closely agreeing with finite element simulation in ANSYS. A complementary study of square membranes loaded with a central mass shows analogous behavior. The analytical model is then used to interpret the experimentally observed shift in resonance frequency of a circular membrane with a proof mass. The impact of membrane tension and central proof mass on the resonant frequency of the membrane suggests that this approach may be used as a tuning method to optimize the response of membrane-based designs for maximum power output for vibration energy harvesting applications.

    Citation: Lin Dong, Michael Grissom, Frank T. Fisher. Resonant frequency of mass-loaded membranes for vibration energy harvesting applications[J]. AIMS Energy, 2015, 3(3): 344-359. doi: 10.3934/energy.2015.3.344

    Related Papers:

    [1] Mengshi Shu, Rui Fu, Wendi Wang . A bacteriophage model based on CRISPR/Cas immune system in a chemostat. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1361-1377. doi: 10.3934/mbe.2017070
    [2] Miller Cerón Gómez, Eduardo Ibarguen Mondragon, Eddy Lopez Molano, Arsenio Hidalgo-Troya, Maria A. Mármol-Martínez, Deisy Lorena Guerrero-Ceballos, Mario A. Pantoja, Camilo Paz-García, Jenny Gómez-Arrieta, Mariela Burbano-Rosero . Mathematical model of interaction Escherichia coli and Coliphages. Mathematical Biosciences and Engineering, 2023, 20(6): 9712-9727. doi: 10.3934/mbe.2023426
    [3] Frédéric Mazenc, Gonzalo Robledo, Daniel Sepúlveda . A stability analysis of a time-varying chemostat with pointwise delay. Mathematical Biosciences and Engineering, 2024, 21(2): 2691-2728. doi: 10.3934/mbe.2024119
    [4] Gonzalo Robledo . Feedback stabilization for a chemostat with delayed output. Mathematical Biosciences and Engineering, 2009, 6(3): 629-647. doi: 10.3934/mbe.2009.6.629
    [5] Harry J. Dudley, Zhiyong Jason Ren, David M. Bortz . Competitive exclusion in a DAE model for microbial electrolysis cells. Mathematical Biosciences and Engineering, 2020, 17(5): 6217-6239. doi: 10.3934/mbe.2020329
    [6] Xiaomeng Ma, Zhanbing Bai, Sujing Sun . Stability and bifurcation control for a fractional-order chemostat model with time delays and incommensurate orders. Mathematical Biosciences and Engineering, 2023, 20(1): 437-455. doi: 10.3934/mbe.2023020
    [7] Frédéric Mazenc, Michael Malisoff, Patrick D. Leenheer . On the stability of periodic solutions in the perturbed chemostat. Mathematical Biosciences and Engineering, 2007, 4(2): 319-338. doi: 10.3934/mbe.2007.4.319
    [8] Manel Dali Youcef, Alain Rapaport, Tewfik Sari . Study of performance criteria of serial configuration of two chemostats. Mathematical Biosciences and Engineering, 2020, 17(6): 6278-6309. doi: 10.3934/mbe.2020332
    [9] Alain Rapaport, Jérôme Harmand . Biological control of the chemostat with nonmonotonic response and different removal rates. Mathematical Biosciences and Engineering, 2008, 5(3): 539-547. doi: 10.3934/mbe.2008.5.539
    [10] Alexis Erich S. Almocera, Sze-Bi Hsu, Polly W. Sy . Extinction and uniform persistence in a microbial food web with mycoloop: limiting behavior of a population model with parasitic fungi. Mathematical Biosciences and Engineering, 2019, 16(1): 516-537. doi: 10.3934/mbe.2019024
  • Vibration based energy harvesting has been widely investigated to target ambient vibration sources as a means to generate small amounts of electrical energy. While cantilever-based geometries have been pursued frequently in the literature, here membrane-based geometries for the energy harvesting device is considered, with the effects of an added mass and tension on the effective resonant frequency of the membranes studied. An analytical model is developed to describe the vibration response for a circular membrane with added mass structure, with the results closely agreeing with finite element simulation in ANSYS. A complementary study of square membranes loaded with a central mass shows analogous behavior. The analytical model is then used to interpret the experimentally observed shift in resonance frequency of a circular membrane with a proof mass. The impact of membrane tension and central proof mass on the resonant frequency of the membrane suggests that this approach may be used as a tuning method to optimize the response of membrane-based designs for maximum power output for vibration energy harvesting applications.


    [1] Beeby SP, Tudor MJ, White NM (2006) Energy harvesting vibration sources for microsystems applications. Meas Sci Technol 17: R175-R195. doi: 10.1088/0957-0233/17/12/R01
    [2] Cook-Chennault KA, Thambi N, Sastry AM (2008) Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Mater Struct 17: 043001. doi: 10.1088/0964-1726/17/4/043001
    [3] Dutoit NE, Wardle BL, Kim SG (2005) Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters. Integr Ferroelectr 71: 121-160. doi: 10.1080/10584580590964574
    [4] Harrop P, Das R (2010) IDTechEx Report: Energy harvesting and storage for electronic devices 2010-2020. IDTechEx. Ltda.
    [5] Roundy S, Wright PK, Rabaey J (2003) A study of low level vibrations as a power source for wireless sensor nodes. Comput Commun 26: 1131-1144. doi: 10.1016/S0140-3664(02)00248-7
    [6] Scheibner D, Mehner J, Reuter D, et al. (2005) A spectral vibration detection system based on tunable micromechanical resonators. Sensor Actuat A-Phys 123-124: 63-72. doi: 10.1016/j.sna.2005.03.034
    [7] Peters C, Maurath D, Schock W, et al. (2008) Novel electrically tunable mechanical resonator for energy harvesting. Proceedings of Power MEMS 2008 November 9-12, Sendai, Japan, 253-256.
    [8] Leland ES, Wright PK (2006) Resonance tuning of piezoelectric vibration energy scavenging generators using compressive axial preload. Smart Mater Struct 15: 1413-1420. doi: 10.1088/0964-1726/15/5/030
    [9] Challa VR, Prasad MG, Shi Y, et al. (2008) A vibration energy harvesting device with bidirectional resonance frequency tunability. Smart Mater Struct 17: 015035. doi: 10.1088/0964-1726/17/01/015035
    [10] Zhu D, Roberts S, Tudor MJ, et al. (2010) Design and experimental characterization of a tunable vibration-based electromagnetic micro-generator. Sensor Actuat A-Phys 158: 284-293. doi: 10.1016/j.sna.2010.01.002
    [11] Rezaeisaray M, Gowini MEI, Sameoto D, et al. (2015) Wide-bandwidth piezoelectric energy harvester with polymeric structure. J Micromech Microeng 25: 015018. doi: 10.1088/0960-1317/25/1/015018
    [12] Mo C, Davidson J, Clark WW (2014) Energy harvesting with piezoelectric circular membrane under pressure loading. Smart Mater Struct 23: 045005. doi: 10.1088/0964-1726/23/4/045005
    [13] Wang W, Yang T (2012) Vibration energy harvesting using a piezoelectric circular diaphragm array. IEEE T Ultrason Ferr 59: 2022-2026. doi: 10.1109/TUFFC.2012.2422
    [14] Williams CB, Yates RB (1996) Analysis of a micro-electric generator for microsystems. Sensor Actuat A-Phys 52: 8-11. doi: 10.1016/0924-4247(96)80118-X
    [15] Fletcher NH (1992) Acoustic Systems in Biology. New York: Oxford University Press, Inc, 73-82.
    [16] Timoshenko S, Young DH (1955) Vibration Problems in Engineering, ed. 3rd., New York, NY: D. Van Nostrand Co., Inc, 439-440.
    [17] Pelrine R, Kornbluh R, Pei Q, et al. (2000) High-speed electrically actuated elastomers with strain greater than 100%. Science 287: 836-839. doi: 10.1126/science.287.5454.836
    [18] Kofod G (2001) Dielectric elastomer actuators [Ph.D. Thesis] [Kongens Lyngby, Denmark]: The Technical University of Denmark.
    [19] Kofod G (2008) The static actuation of dielectric elastomer actuators: How does pre-stretch improve actuation? Journal Phys D Appl Phys 41: 215405. doi: 10.1088/0022-3727/41/21/215405
    [20] Wissler M, Mazza E (2005) Modeling and simulation of dielectric elastomer actuators. Smart Mater Struct 14: 1396. doi: 10.1088/0964-1726/14/6/032
    [21] Zhu D, Tudor M J, Beeby SP (2010) Strategies for increasing the operating frequency range of vibration energy harvesters: A review. Meas Sci Technol 21: 022001. doi: 10.1088/0957-0233/21/2/022001
    [22] Challa VR, Prasad MG, Fisher FT (2011) Towards an autonomous self-tuning vibration energy harvesting device for wireless sensor network applications. Smart Mater Struct 20: 025004. doi: 10.1088/0964-1726/20/2/025004
  • This article has been cited by:

    1. Xinzhi Ren, Xianning Liu, A competition un-stirred chemostat model with virus in an aquatic system, 2019, 98, 0003-6811, 2329, 10.1080/00036811.2018.1460811
    2. Wendi Wang, Rui Fu, Mengshi Shu, A bacteriophage model based on CRISPR/Cas immune system in a chemostat, 2017, 14, 1551-0018, 1361, 10.3934/mbe.2017070
    3. Saptarshi Sinha, Rajdeep K. Grewal, Soumen Roy, 2018, 103, 9780128151839, 103, 10.1016/bs.aambs.2018.01.005
    4. Saptarshi Sinha, Rajdeep Kaur Grewal, Soumen Roy, 2020, Chapter 18, 978-1-0716-0388-8, 309, 10.1007/978-1-0716-0389-5_18
    5. Sukhitha W. Vidurupola, Analysis of deterministic and stochastic mathematical models with resistant bacteria and bacteria debris for bacteriophage dynamics, 2018, 316, 00963003, 215, 10.1016/j.amc.2017.08.022
    6. Daniel A. Korytowski, Hal L. Smith, How nested and monogamous infection networks in host-phage communities come to be, 2015, 8, 1874-1738, 111, 10.1007/s12080-014-0236-6
    7. Saroj Kumar Sahani, Sunita Gakkhar, A Mathematical Model for Phage Therapy with Impulsive Phage Dose, 2020, 28, 0971-3514, 75, 10.1007/s12591-016-0303-0
    8. Sukhitha W. Vidurupola, Linda J. S. Allen, Impact of Variability in Stochastic Models of Bacteria-Phage Dynamics Applicable to Phage Therapy, 2014, 32, 0736-2994, 427, 10.1080/07362994.2014.889922
    9. WENDI WANG, DYNAMICS OF BACTERIA-PHAGE INTERACTIONS WITH IMMUNE RESPONSE IN A CHEMOSTAT, 2017, 25, 0218-3390, 697, 10.1142/S0218339017400010
    10. Hayriye Gulbudak, Paul L. Salceanu, Gail S. K. Wolkowicz, A delay model for persistent viral infections in replicating cells, 2021, 82, 0303-6812, 10.1007/s00285-021-01612-3
    11. Ei Ei Kyaw, Hongchan Zheng, Jingjing Wang, Htoo Kyaw Hlaing, Stability analysis and persistence of a phage therapy model, 2021, 18, 1551-0018, 5552, 10.3934/mbe.2021280
    12. Ei Ei Kyaw, Hongchan Zheng, Jingjing Wang, Stability and Hopf Bifurcation Analysis for a Phage Therapy Model with and without Time Delay, 2023, 12, 2075-1680, 772, 10.3390/axioms12080772
    13. Ei Ei Kyaw, Hongchan Zheng, Jingjing Wang, Hopf bifurcation analysis of a phage therapy model, 2023, 18, 2157-5452, 87, 10.2140/camcos.2023.18.87
    14. Zainab Dere, N.G. Cogan, Bhargav R. Karamched, Optimal control strategies for mitigating antibiotic resistance: Integrating virus dynamics for enhanced intervention design, 2025, 00255564, 109464, 10.1016/j.mbs.2025.109464
    15. Carli Peterson, Darsh Gandhi, Austin Carlson, Aaron Lubkemann, Emma Richardson, John Serralta, Michael S. Allen, Souvik Roy, Christopher M. Kribs, Hristo V. Kojouharov, A SIMPL Model of Phage-Bacteria Interactions Accounting for Mutation and Competition, 2025, 87, 0092-8240, 10.1007/s11538-025-01478-2
  • Reader Comments
  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(8507) PDF downloads(1666) Cited by(16)

Article outline

Figures and Tables

Figures(11)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog