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Modeling analysis and tuning of shunt piezoelectric damping controller for structural vibration

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Abstract

When the passive control technology is used to control the bending vibration of flexible structures, the shunt piezoelectric damping technology is commonly regarded as a straightforward and efficient approach. However, its performance is sensitive to the changes of the components' parameter values on the piezoelectric transducer, and usually requires more accurate tuning. This study introduces a novel optimization algorithm and criteria to optimize the parameters of the components in the shunt piezoelectric damping circuit. Specifically, the evaluation criteria for suppressing bending vibration are formulated using the frequency response and kinetic energy power spectrum. The improved Sine Cosine Algorithm (SCA) is then employed to optimize the parameters of the frequently used parallel, series, and negative capacitance impedance circuits. The accuracy of the model is verified by comparing the derived dynamic model and transfer function model with the results obtained from finite element software Workbench. Subsequently, the system's response is analyzed under different parameter values, damping conditions, and excitations. The convergence and feasibility of the improved SCA algorithm are demonstrated through an example that involves suppressing the bending vibration of a rectangular plate. Furthermore, the optimization calculation of component parameter values in the example circuit is conducted, and the results are compared with those obtained through previous methods, thereby affirming the effectiveness and advantages of the proposed algorithm for optimizing component parameter values in shunt piezoelectric damping circuits.

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References

  1. Berardengo, M., Cigada, A., Manzoni, S., Vanali, M.: Vibration control by means of piezoelectric actuators shunted with LR impedances: performance and robustness analysis. Shock Vib. 2015, 1–30 (2015). https://doi.org/10.1155/2015/704265

    Article  Google Scholar 

  2. Raze, G., Dietrich, J., Kerschen, G.: Passive control of multiple structural resonances with piezoelectric vibration absorbers. J. Sound Vib. 515, 116490 (2021). https://doi.org/10.1016/j.jsv.2021.116490

    Article  Google Scholar 

  3. Aridogan, U., Basdogan, I., Erturk, A.: Analytical modeling and experimental validation of a structurally integrated piezoelectric energy harvester on a thin plate. Smart Mater. Struct. 23(4), 45039 (2014). https://doi.org/10.1088/0964-1726/23/4/045039

    Article  Google Scholar 

  4. Yan, B., Wang, K., Hu, Z., Wu, C., Zhang, X.: Shunt damping vibration control technology: a review. Appl. Sci. 7(5), 494 (2017). https://doi.org/10.3390/app7050494

    Article  Google Scholar 

  5. Gripp, J.A.B., Rade, D.A.: Vibration and noise control using shunted piezoelectric transducers: a review. Mech. Syst. Signal Pr. 112, 359–383 (2018). https://doi.org/10.1016/j.ymssp.2018.04.041

    Article  Google Scholar 

  6. 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). https://doi.org/10.1088/1361-665X/ab36e4

    Article  Google Scholar 

  7. Marakakis, K., Tairidis, G.K., Koutsianitis, P., Stavroulakis, G.E.: Shunt piezoelectric systems for noise and vibration control: a review. Front. Built Environ. (2019). https://doi.org/10.3389/fbuil.2019.00064

    Article  Google Scholar 

  8. Fleming, A.J., Moheimani, S.O.R.: Control orientated synthesis of high-performance piezoelectric shunt impedances for structural vibration control. IEEE T. Contr. Syst. T. 13(1), 98–112 (2005). https://doi.org/10.1109/TCST.2004.838547

    Article  Google Scholar 

  9. Bo, L.D., He, H., Gardonio, P., Li, Y., Jiang, J.Z.: Design tool for elementary shunts connected to piezoelectric patches set to control multi-resonant flexural vibrations. J. Sound Vib. 520, 116554 (2022). https://doi.org/10.1016/j.jsv.2021.116554

    Article  Google Scholar 

  10. Ducarne, J., Thomas, O., Deü, J.F.: Placement and dimension optimization of shunted piezoelectric patches for vibration reduction. J. Sound Vib. 331(14), 3286–3303 (2012). https://doi.org/10.1016/j.jsv.2012.03.002

    Article  Google Scholar 

  11. Aridogan, U., Basdogan, I., Erturk, A.: Random vibration energy harvesting on thin plates using multiple piezopatches. J. Intel. Mat. Syst. Str. 27(20), 2744–2756 (2016). https://doi.org/10.1177/1045389X16635846

    Article  Google Scholar 

  12. Bricault, C., Pézerat, C., Collet, M., Pyskir, A., Perrard, P., Matten, G., Romero-García, V.: Multimodal reduction of acoustic radiation of thin plates by using a single piezoelectric patch with a negative capacitance shunt. Appl. Acoust. 145, 320–327 (2019). https://doi.org/10.1016/j.apacoust.2018.10.016

    Article  Google Scholar 

  13. Zhao, Y.: Vibration suppression of a quadrilateral plate using hybrid piezoelectric circuits. J. Vib. Control 16(5), 701–720 (2010). https://doi.org/10.1177/1077546309106529

    Article  MATH  Google Scholar 

  14. Ji, H., Guo, Y., Qiu, J., Wu, Y., Zhang, C., Tao, C.: A new design of unsymmetrical shunt circuit with negative capacitance for enhanced vibration control. Mech. Syst. Signal Pr. 155, 107576 (2021). https://doi.org/10.1016/j.ymssp.2020.107576

    Article  Google Scholar 

  15. Pohl, M.: Increasing the performance of negative capacitance shunts by enlarging the output voltage to the requirements of piezoelectric transducers. J. Intel. Mat. Syst. Str. 28(11), 1379–1390 (2017). https://doi.org/10.1177/1045389X16666181

    Article  Google Scholar 

  16. Berardengo, M., Thomas, O., Giraud-Audine, C., Manzoni, S.: Improved resistive shunt by means of negative capacitance: new circuit, performances and multi-mode control. Smart Mater. Struct. 25(7), 75033–75055 (2016). https://doi.org/10.1088/0964-1726/25/7/075033

    Article  Google Scholar 

  17. Soltani, P., Kerschen, G., Tondreau, G., Deraemaeker, A.: Piezoelectric vibration damping using resonant shunt circuits: an exact solution. Smart Mater. Struct. 23(12), 125014 (2014). https://doi.org/10.1088/0964-1726/23/12/125014

    Article  Google Scholar 

  18. Ducarne, J., Thomas, O., Deü, J.F.: Structural vibration reduction by switch shunting of piezoelectric elements: modeling and optimization. J. Intel. Mat. Syst. Str. 21(8), 797–816 (2010). https://doi.org/10.1177/1045389X10367835

    Article  Google Scholar 

  19. Ravi, S., Zilian, A.: Monolithic modeling and finite element analysis of piezoelectric energy harvesters. Acta Mech. 228(6), 2251–2267 (2017). https://doi.org/10.1007/s00707-017-1830-7

    Article  MathSciNet  MATH  Google Scholar 

  20. Yamada, K., Matsuhisa, H., Utsuno, H., Sawada, K.: Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements. J. Sound Vib. 329(24), 5036–5057 (2010). https://doi.org/10.1016/j.jsv.2010.06.021

    Article  Google Scholar 

  21. Wang, G., Lu, Y.: An improved lumped parameter model for a piezoelectric energy harvester in transverse vibration. Shock Vib. 2014, 1–12 (2014). https://doi.org/10.1155/2014/935298

    Article  Google Scholar 

  22. Høgsberg, J., Krenk, S.: Balanced calibration of resonant shunt circuits for piezoelectric vibration control. J. Intel. Mat. Syst. Str. 23(17), 1937–1948 (2012). https://doi.org/10.1177/1045389X12455727

    Article  Google Scholar 

  23. Gardonio, P., Zientek, M., Dal Bo, L.: Panel with self-tuning shunted piezoelectric patches for broadband flexural vibration control. Mech. Syst. Signal Pr. 134, 106299 (2019). https://doi.org/10.1016/j.ymssp.2019.106299

    Article  Google Scholar 

  24. Beck, B.S., Cunefare, K.A., Collet, M.: Response-based tuning of a negative capacitance shunt for vibration control. J. Intel. Mat. Syst. Str. 25(13), 1585–1595 (2014). https://doi.org/10.1177/1045389X13510216

    Article  Google Scholar 

  25. Toftekær, J.F., Benjeddou, A., Høgsberg, J.: General numerical implementation of a new piezoelectric shunt tuning method based on the effective electromechanical coupling coefficient. Mech. Adv. Mater. Struc. 27(22), 1908–1922 (2020). https://doi.org/10.1080/15376494.2018.1549297

    Article  Google Scholar 

  26. Heuss, O., Salloum, R., Mayer, D., Melz, T.: Tuning of a vibration absorber with shunted piezoelectric transducers. Arch. Appl. Mech. 86(10), 1715–1732 (2016). https://doi.org/10.1007/s00419-014-0972-5

    Article  Google Scholar 

  27. Lumentut, M.F., Howard, I.M.: Effect of shunted piezoelectric control for tuning piezoelectric power harvesting system responses-analytical techniques. Smart Mater. Struct. 24(10), 105029 (2015). https://doi.org/10.1088/0964-1726/24/10/105029

    Article  Google Scholar 

  28. Mirjalili, S.C.A.: A Sine Cosine Algorithm for solving optimization problems. Knowl. Based Syst. 96, 120–133 (2016). https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  29. Donoso, A., Bellido, J.C.: Robust design of multimodal piezoelectric transducers. Comput. Method. Appl. M. 338, 27–40 (2018). https://doi.org/10.1016/j.cma.2018.04.016

    Article  MathSciNet  MATH  Google Scholar 

  30. Liao, Y., Liang, J.: Unified modeling, analysis and comparison of piezoelectric vibration energy harvesters. Mech. Syst. Signal Pr. 123, 403–425 (2019). https://doi.org/10.1016/j.ymssp.2019.01.025

    Article  Google Scholar 

  31. Behrens, S., Fleming, A.J., Moheimani, S.O.R.: A broadband controller for shunt piezoelectric damping of structural vibration. Smart Mater. Struct. 12(1), 18–28 (2003). https://doi.org/10.1088/0964-1726/12/1/303

    Article  Google Scholar 

  32. Gardonio, P., Casagrande, D.: Shunted piezoelectric patch vibration absorber on two-dimensional thin structures: tuning considerations. J. Sound Vib. 395, 26–47 (2017). https://doi.org/10.1016/j.jsv.2017.02.019

    Article  Google Scholar 

  33. Yıldız, B.S., Yıldız, A.R.: Comparison of grey wolf, whale, water cycle, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod. Mater. Test. 60(3), 311–315 (2018). https://doi.org/10.3139/120.111153

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Key R&D Program of China (No. 2019YFE0116200).

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Authors and Affiliations

  1. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, People’s Republic of China

    Tao Wu, Hui Yan & Jianjun Qu

  2. College of Engineering, University of Michigan, Ann Arbor, USA

    Tong Chen

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Correspondence to Tao Wu.

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Wu, T., Chen, T., Yan, H. et al. Modeling analysis and tuning of shunt piezoelectric damping controller for structural vibration. Acta Mech 234, 4407–4426 (2023). https://doi.org/10.1007/s00707-023-03619-x

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