Smart Structures and Systems

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The influence of nonlinear damping on the response of a piezoelectric cantilever sensor in a symmetric or asymmetric configuration

  • Habib, Giuseppe (Department of Applied Mechanics, Budapest University of Technology and Economics) ;
  • Fainshtein, Emanuel (Department of Mechanical Engineering, Technion - Israel Institute of Technology) ;
  • Wolf, Kai-Dietrich (Institute for Security Systems, University of Wuppertal) ;
  • Gottlieb, Oded (Department of Mechanical Engineering, Technion - Israel Institute of Technology)
  • Received : 2022.05.13
  • Accepted : 2022.06.09
  • Published : 2022.09.25
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Abstract

We investigate the influence of nonlinear viscoelastic damping on the response of a cantilever sensor covered by piezoelectric layers in a symmetric or asymmetric configuration. We formulate an initial-boundary-value problem which consistently incorporates both geometric and material nonlinearities including the effect of viscoelastic damping which cannot be ignored for micro- and nano-mechanical sensor operation in a vacuum environment. We employ an asymptotic multiple-scales methodology to yield the system nonlinear frequency response near its primary resonance and employ a model-based estimation procedure to deduce the system damping backone curve from controlled experiments in vacuum. We discuss the effect of nonlinear damping on sensor applications for scanning probe microscopy.

Keywords

Acknowledgement

The research described in this paper was supported in part by the Israel Science Foundation (Grant no. 136/16). O.G. was partially supported by the Henri Garih Chair in Mechanical Engineering. E.F. and K.W. acknowledge the support of their Technion graduate studies and postdoctoral fellowships, respectively.

References

  1. Anderson, T.A., Nayfeh, A.H. and Balachandran, B. (1996), "Experimental verification of the importance of nonlinear curvature in the response of a cantilever beam", J. Vib. Acoust. 118(4), 21-27. https://doi.org/10.1115/1.2889630
  2. Betts, D.N., Kim, H.A., Bowen, C.R. and Inman, D.J. (2012), "Optimal configurations of bistable piezo-composites for energy harvesting", Appl. Phys. Lett., 100, 114104. https://doi.org/10.1063/1.3693523
  3. Berman, G.P. and Tsifrinovich, V.I. (2022), "Magnetic resonance force microscopy with matching frequencies of cantilever and spin", J. Appl. Phys., 131, 044301. https://doi.org/10.1063/5.0073237
  4. Berman, G.P., Borgonovi, F., Gorshkov, V.N. and Tsifrinovich, V.I. (2006), Magnetic Resonance Force Microscopy and a Single-Spin Measurement, World Scientific, Singapore.
  5. Da Silva, M.R.M.C. and Glynn, C.C. (1978), "Nonlinear flexural flexural-torsional dynamics of inextensional beams - equations of motion", J. Struct. Mech., 6(4), 437-448. https://doi.org/10.1080/03601217808907348
  6. Fainshtein, E. (2005), "Nonlinear dynamics and stability of piezoelectric microbeams with application for atomic microscopy", M.Sc. Thesis; Technion - Israel Institute of Technology, Haifa, Israel.
  7. Gottlieb, O. and Habib, G. (2012), "Non-linear model-based estimation of quadratic and cubic damping mechanisms governing the dynamics of a chaotic spherical pendulum", J. Vib. Control, 18(4), 536-547. https://doi.org/10.1177/1077546310395969
  8. Gottlieb, O., Feldman M. and Yim, S.C.S. (1996), "Paramter identification of nonlinear ocean mooring systems using the Hilbert transform", J. Offshore Mech. And Arctic Eng,. 118, 29-36. https://doi.org/10.1115/1.2828798
  9. Habib, G. (2008), "Experimental analysis of linear and nonlinear vibrations of a piezoelectric cantilever in several conditions", M.Sc. Thesis; Sapienza University of Rome, Rome, Italy.
  10. Habib, G., Miklos, A., Enilov, E.T., Stepan, G. and Rega, G. (2017), "Nonlinear model-based parameter estimation and stability analysis of an aero-pendulum subject to digital delayed control", Int. J. Dyn. Contr., 5, 629-643. https://doi.org/10.1007/s40435-015-0203-0
  11. Hacker, E. and Gottlieb, O. (2017), "Application of reconstitution multiple scale asymptotics for a two-to-one internal resonance in Magnetic Resonance Force Microscopy", Int. J. Nonlin. Mech., 94, 174-199. https://doi.org/10.1016/j.ijnonlinmec.2017.04.013
  12. Hacker, E. and Gottlieb, O. (2020), "Local and global bifurcations in magnetic resonance force microscopy", Int. J. Nonlin. Mech., 99, 201-225. https://doi.org/10.1007/s11071-019-05401-y
  13. Kambali, P.N., Torres, F., Barniol, N. and Gottlieb, O. (2019), "Nonlinear multi-element interactions in an elastically coupled microcantitlever array subject to electrodynamic excitation", Nonlin. Dyn., 98, 3067-3094. https://doi.org/10.1007/s11071-019-05074-7
  14. Kazakova, O., Puttock, R., Barton, C., Corte-Leon, H., Jaafar, M., Neu, V. and Asenjo, A. (2017), "Frontiers of magnetic force microscopy", J. Appl. Phys. 125, 060901. https://doi.org/10.1063/1.5050712
  15. Kumar, V., Boley, J.W., Yang, Y., Ekowaluyo, H., Miller, J.K., Chiu, G.T.C. and Rhoads, J.F. (2011), "Bifurcation-based mass sensing using piezoelectrically-actuated microcantilevers", Appl. Phys. Lett., 98, 153510. https://doi.org/10.1063/1.3574920
  16. Manna, M.C., Sheikh, A.H. and Bhattacharyya, R. (2009), "Static analysis of rubber components with piezoelectric patches using nonlinear finite elements", Smart Struct. Syst., Int. J., 5(1), 23-42. https://doi.org/10.12989/sss.2009.5.1.023
  17. Maugin, G.A. (1985), Nonlinear Electromechanical Effects and Applications, World Scientific, Singapore.
  18. Minne, S., Manalis, S. and Quate, C. (1999), Bringing Scanning Probe Microscopy up to Speed, Springer Science & Business Media, Kluwer, Dordrecht, The Netherlands.
  19. Mishra K., Panda, S.K., Kumar, V. and Dewangan, H.C. (2020), "Analytical evaluation and experimental validation of energy harvesting using low-frequency band of piezoelectric bimorph actuator", Smart Struct. Syst., Int. J., 26(3), 391-401. https://doi.org/10.12989/sss.2020.26.3.391
  20. Mora, K. and Gottlieb, O. (2017), "Parametric excitation of a microbeam-string with asymmetric electrodes: multimode dynamics and the effect of nonlinear damping", J. Vib. Acoust., 139, 040903. https://doi.org/10.1115/1.4036632
  21. Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, Wiley, New York, USA.
  22. Nayfeh, A.H. and Mook, D.T. (1979), Nonlinear Oscillations, Wiley, New York, USA.
  23. Pai, P.B., Wen, A.N. and Schultz, M. (1998), "Structural vibration control using pzt patches and nonlinear phenomena", J. Sound Vib., 215, 273-296. https://doi.org/10.1006/jsvi.1998.1612
  24. Poh, S., Baz, A. and Balachandran, B. (1996), "Experimental adaptive control of sound radiation from a panel into an acoustic cavity using active constrained layer damping", Smart Mater. Struct., 5, 649-659. https://doi.org/10.1088/0964-1726/5/5/013
  25. Providakis, C.P., Kontoni, D.P.N., Voutetaki, M.E. and Stavroulaki, M.E. (2008), "Comparisons of smart damping treatments based on FEM modeling of electromechanical impedance", Smart Struct. Syst., Int. J., 4(1), 35-46. https://doi.org/10.12989/sss.2008.4.1.035
  26. Rangelow, I.W., Ivanov, T., Ivanova, K., Volland, B.E., Grabiec, P., Sarov, Y., Persaud, A., Gotszalk, T., Zawierucha, P., Zielony, M. and Dontzov, D. (2007), "Piezoresistive and self-actuated 128-cantilever arrays for nanotechnology applications", Microelect. Eng., 84, 1260-1264. https://doi.org/10.1016/j.mee.2007.01.219
  27. Roccia, B.A., Verstaete, M.L., Ceballos, L.R., Balachandran, B. and Preidikman, S. (2020), "Computational study on aerodynamically coupled piezoelectric harvesters", J. Intel. Mater. Sys., 31(13), 1578-1593. https://doi.org/10.1177/1045389X20930093
  28. Roeser, D., Gutschmidt, S., Sattel, T. and Rangelow, I.W. (2016), "Tip motion-sensor signal relation for a composite SPM/SPL cantilever", J. Microelectromech. Syst., 25(1), 78-90. https://doi.org/10.1109/JMEMS.2015.2482389
  29. Rugar, D., Budakian, R., Mamin, H.J. and Chui, B.W. (2004), "Single spin detection by magnetic resonance force microscopy", Nature, 430, 329-332. https://doi.org/10.1038/nature02658
  30. Sunar, M. and Rao, S. (1999), "Recent advances in sensing and control of flexible structures via piezoelectric materials technology", Appl. Mech. Rev., 52(1) 1-16. https://doi.org/10.1115/1.3098923
  31. Tabaddor, M. (2000), "Influence of nonlinear boundary conditions on the single-mode response of a cantilever beam", Int. J. Solids Struct., 37, 4915-4931. https://doi.org/10.1016/S0020-7683(99)00197-3
  32. Tzou, H. and Tzeng, C. (1990), "Distributed piezoelectric sensor/actuation design for dynamic measurement control of distributed systems: a piezoelectric finite element approach", J. Sound Vib., 138(1), 17-34. https://doi.org/10.1016/0022-460X(90)90701-Z.
  33. Usher, T. and Sim, A. (2005), "Nonlinear dynamics of piezoelectric high displacement actuators in cantilever mode", J. Appl. Phys., 98, 064102, 1-7. https://doi.org/10.1063/1.2041844
  34. Vokoun, D., Samal, S. and Stachiv, I. (2022), "Magnetic force microscopy in physics and biomedical applications", Magnetochemistry, 8(42), 1-14. https://doi.org/10.3390/magnetochemistry8040042
  35. Wolf, K. and Gottlieb, O. (2001), "Nonlinear dynamics of a cantilever beam actuated by piezoelectric layers in symmetric and asymmetric configurations", Research Report No. ETR-2001-02, Technion-Israel Institute of Technology.
  36. Wolf, K. and Gottlieb, O. (2002), "Nonlinear dynamics of a noncontacting atomic force microscope cantilever actuated by a piezoelectric layer", J. Appl. Phys. 91(7), 4701-4709. https://doi.org/10.1063/1.1458056
  37. Zaitsev, S., Shtempluck, O., Buks, E. and Gottlieb, O. (2019), "Nonlinear damping in a micromechanical oscillator", Nonlin. Dyn., 67, 859-883. https://doi.org/10.1007/s11071-011-0031-5
  38. Zaretsky, C.L. and da Silva, M.R.M.C. (1994), "Experimental investigation of nonlinear modal coupling in the response of cantilever beams", J. Sound Vib., 174(2), 145-167. https://doi.org/10.1006/jsvi.1994.1268
  39. Zuger, O. and Rugar, D. (1994), "Magnetic resonance detection and imaging using force microscope techniques", J. Appl. Phys., 75(10), 6211-6216. https://doi.org/10.1063/1.355403