Skip to main content
SpringerLink
Log in

Characterization of Sensor and Actuator Materials

  • Chapter
  • First Online:
Book cover Piezoelectric Sensors and Actuators

Part of the book series: Topics in Mining, Metallurgy and Materials Engineering ((TMMME))

Abstract

The chapter starts with standard approaches for characterizing active and passive materials. The fundamentals of the inverse method regarding material characterization are detailed in Sect. 5.2. In Sects. 5.3 and 5.4, the inverse method will be used to identify the complete data set of piezoceramic materials and the dynamic mechanical behavior of homogenous passive materials such as thermoplastics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The standard approaches for characterizing piezoceramic materials are abbreviated as IEEE/CENELEC Standard.

  2. 2.

    The underscore denotes a complex-valued quantity, which is represented either by real and imaginary part or by magnitude and phase (see Chap. 2).

  3. 3.

    Bessel function \(J_0\!\left( \zeta _1 \right) \) of first kind and zero order; Bessel function \(J_1\!\left( \zeta _1 \right) \) of first kind and first order.

  4. 4.

    Bending resonance means that the beam deflection is high at a certain frequency, which represents the so-called bending resonance frequency.

  5. 5.

    The quadratic deviation corresponds to the squared \(L_2\) norm of the deviation.

  6. 6.

    An impedance curve corresponds to the frequency-resolved electrical impedance.

  7. 7.

    The Cauchy principal value allows solving improper integrals, which would otherwise be undefined [8].

  8. 8.

    Laser Doppler vibrometers are also known as laser Doppler velocimeters.

References

  1. ASTM International: Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Impulse Excitation of Vibration. ASTM E1875-09 (2009)

    Google Scholar 

  2. ASTM International: Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance. ASTM E1875-13 (2013)

    Google Scholar 

  3. Bakushinskii, A.B.: The problem of the convergence of the iteratively regularized Gauss-Newton method. Comput. Math. Math. Phys. 32(9), 1353–1359 (1992)

    Google Scholar 

  4. Banks, H.T., Hu, S., Kenz, Z.R.: A brief review of elasticity and viscoelasticity for solids. Adv. Appl. Math. Mech. 3(1), 1–51 (2011)

    Article  Google Scholar 

  5. Barkanov, E., Skukis, E., Petitjean, B.: Characterisation of viscoelastic layers in sandwich panels via an inverse technique. J. Sound Vib. 327(3–5), 402–412 (2009)

    Article  Google Scholar 

  6. Blaschke, B., Neubauer, A., Scherzer, O.: On convergence rates for the iteratively regularized Gauss-Newton method. IMA J. Numer. Anal. 17(3), 421–436 (1997)

    Article  Google Scholar 

  7. Brissaud, M.: Three-dimensional modeling of piezoelectric materials. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(9), 2051–2065 (2010)

    Article  Google Scholar 

  8. Bronstein, I.N., Semendjajew, K.A., Musiol, G., Mühlig, H.: Handbook of Mathematics, 6th edn. Springer, Berlin (2015)

    Google Scholar 

  9. Cappon, H., Keesman, K.J.: Numerical modeling of piezoelectric transducers using physical parameters. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(5), 1023–1032 (2012)

    Article  Google Scholar 

  10. Collaborative Research Center TRR 39: Production Technologies for Lightmetal and Fiber Reinforced Composite based Components with Integrated Piezoceramic Sensors and Actuators (PT-PIESA) (2018). http://www.pt-piesa.tu-chemnitz.de

  11. Czichos, H., Seito, T., Smith, L.E.: Springer Handbook of Metrology and Testing, 2nd edn. Springer, Berlin (2011)

    Book  Google Scholar 

  12. Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer Academic Publishers, Dordrecht (1996)

    Book  Google Scholar 

  13. European Committe for Electrotechnical Standardization (CENELEC): Piezoelectric properties of ceramic materials and components – Part 2: Methods of measurement – Low power. EN 50324-2 (2002)

    Google Scholar 

  14. Ferry, J.: Viscoelastic Properties of Polymers. Wiley-Interscience, Chichester (1980)

    Google Scholar 

  15. Göpel, W., Hesse, J., Zemel, J.N.: Sensors Volume 6 - Optical Sensors. VCH, Weinheim, New York (1992)

    Google Scholar 

  16. Hadamard, J.: Lectures on the Cauchy Problem in Linear Partial Differential Equations. Yale University Press, New Haven (1923)

    Google Scholar 

  17. Holland, R.: Representation of dielectric, elastic, and piezoelectric losses by complex coefficients. IEEE Trans. Sonics and Ultrason. 14(1), 18–20 (1967)

    Article  Google Scholar 

  18. Ilg, J.: Bestimmung, Verifikation und Anwendung frequenzabhängiger mechanischer Materialkennwerte. Ph.D. thesis, Friedrich-Alexander-University Erlangen-Nuremberg (2015)

    Google Scholar 

  19. Ilg, J., Rupitsch, S.J., Sutor, A., Lerch, R.: Determination of dynamic material properties of silicone rubber using one-point measurements and finite element simulations. IEEE Trans. Instrum. Meas. 61(11), 3031–3038 (2012)

    Article  CAS  Google Scholar 

  20. Ilg, J., Rupitsch, S.J., Lerch, R.: Impedance-based temperature sensing with piezoceramic devices. IEEE Sens. J. 13(6), 2442–2449 (2013)

    Article  CAS  Google Scholar 

  21. Institute of Electrical and Electronics Engineers (IEEE): IEEE Standard on Piezoelectricity. ANSI-IEEE Std. 176-1987 (1987)

    Google Scholar 

  22. Isakov, V.: Inverse Problems for Partial Differential Equations. Springer, Berlin (1998)

    Book  Google Scholar 

  23. Jonsson, U.G., Andersson, B.M., Lindahl, O.A.: A FEM-based method using harmonic overtones to determine the effective elastic, dielectric, and piezoelectric parameters of freely vibrating thick piezoelectric disks. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60(1), 243–255 (2013)

    Article  Google Scholar 

  24. Joo, H.W., Lee, C.H., Rho, J.S., Jung, H.K.: Identification of material constants for piezoelectric transformers by three-dimensional, finite-element method and a design-sensitivity method. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50(8), 965–971 (2003)

    Article  Google Scholar 

  25. Kaltenbacher, B., Neubauer, A., Scherzer, O.: Iterative Regularization Methods for Nonlinear Ill-Posed Problems. Walter de Gruyter, Berlin (2009)

    Google Scholar 

  26. Kay, S.M.: Fundamentals of Statistical Signal Processing – Estimation Theory. Prentice Hall, Englewood Cliffs (1993)

    Google Scholar 

  27. Keysight Technologies Inc.: Product portfolio (2018). http://www.keysight.com

  28. Kim, S.Y., Lee, D.H.: Identification of fractional-derivative-model parameters of viscoelastic materials from measured FRFs. J. Sound Vib. 324(3–5), 570–586 (2009)

    Article  Google Scholar 

  29. Kronig, R.d.L.: On the theory of dispersion of X-Rays. J. Opt. Soc. Am. 12(6), 547–557 (1926)

    Article  Google Scholar 

  30. Kulshreshtha, K., Jurgelucks, B., Bause, F., Rautenberg, J., Unverzagt, C.: Increasing the sensitivity of electrical impedance to piezoelectric material parameters with non-uniform electrical excitation. J. Sens. Sens. Syst. 4(1), 217–227 (2015)

    Article  Google Scholar 

  31. Kwok, K.W., Lai, H., Chan, W., Choy, C.L.: Evaluation of the material parameters of piezoelectric materials by various methods. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44(4), 733–742 (1997)

    Article  Google Scholar 

  32. Lahmer, T.: Forward and inverse problems in piezoelectricity. Ph.D. thesis, Friedrich-Alexander-University Erlangen-Nuremberg (2014)

    Google Scholar 

  33. Lahmer, T., Kaltenbacher, M., Kaltenbacher, B., Lerch, R., Leder, E.: FEM-based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 55(2), 465–475 (2008)

    Article  Google Scholar 

  34. Lakes, R.S.: Viscoelastic Solids. CRC Press, Boca Raton (1998)

    Google Scholar 

  35. Li, S., Zheng, L., Jiang, W., Sahul, R., Gopalan, V., Cao, W.: Characterization of full set material constants of piezoelectric materials based on ultrasonic method and inverse impedance spectroscopy using only one sample. J. Appl. Phys. 114(10), 104505 (2013)

    Article  CAS  Google Scholar 

  36. Malkin, A., Isayev, A.: Rheology: Concepts, Methods, and Applications, 2nd edn. Elsevier, Oxford (2012)

    Google Scholar 

  37. Martinez-Agirre, M., Elejabarrieta, M.J.: Dynamic characterization of high damping viscoelastic materials from vibration test data. J. Sound Vib. 330(16), 3930–3943 (2011)

    Article  Google Scholar 

  38. Matter, M., Gmür, T., Cugnoni, J., Schorderet, A.: Numerical-experimental identification of the elastic and damping properties in composite plates. Compos. Struct. 90(2), 180–187 (2009)

    Article  Google Scholar 

  39. Morozov, V.A.: On the solution of functional equations by the method of regularization. Sov. Math. Dokl. 7, 414–417 (1966)

    Google Scholar 

  40. O’Donnell, M., Jaynes, E.T., Miller, J.G.: Kramers-Kronig relationship between ultrasonic attenuation and wave velocity. J. Acoust. Soc. Am. 69(3), 696–701 (1981)

    Article  Google Scholar 

  41. Ogo, K., Kakimoto, K.I., Weiß, M., Rupitsch, S.J., Lerch, R.: Determination of temperature dependency of material parameters for lead-free alkali niobate piezoceramics by the inverse method. AIP Adv. 6, 065,101–1–065,101–9 (2016)

    Article  CAS  Google Scholar 

  42. Pardo, L., Algueró, M., Brebol, K.: A non-standard shear resonator for the matrix characterization of piezoceramics and its validation study by finite element analysis. J. Phys. D: Appl. Phys. 40(7), 2162–2169 (2007)

    Article  CAS  Google Scholar 

  43. Park, J.: Transfer function methods to measure dynamic mechanical properties of complex structures. J. Sound Vib. 288(1–2), 57–79 (2005)

    Article  Google Scholar 

  44. Pérez, N., Andrade, M.A.B., Buiochi, F., Adamowski, J.C.: Identification of elastic, dielectric, and piezoelectric constants in piezoceramic disks. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(12), 2772–2783 (2010)

    Article  Google Scholar 

  45. PI Ceramic GmbH: Product portfolio (2018). https://www.piceramic.com

  46. Polytec GmbH: Product portfolio (2018). http://www.polytec.com

  47. Pritz, T.: Analysis of four-parameter fractional derivative model of real solid materials. J. Sound Vib. 195(1), 103–115 (1996)

    Article  Google Scholar 

  48. Pritz, T.: Frequency dependences of complex moduli and complex Poisson’s ratio of real solid materials. J. Sound Vib. 214(1), 83–104 (1998)

    Article  Google Scholar 

  49. Research Unit FOR 894: Fundamental Flow Analysis of the Human Voice (2018). http://gepris.dfg.de/gepris/projekt/35819142

  50. Rieder, A.: Keine Probleme mit Inversen Problemen. Vieweg, Wiesbaden (2003)

    Chapter  Google Scholar 

  51. Rupitsch, S.J.: Simulation-based characterization of piezoceramic materials. In: Proceedings of IEEE Sensors, pp. 1–3 (2016)

    Google Scholar 

  52. Rupitsch, S.J., Ilg, J.: Complete characterization of piezoceramic materials by means of two block-shaped test samples. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62(7), 1403–1413 (2015)

    Article  Google Scholar 

  53. Rupitsch, S.J., Kindermann, S., Zagar, B.G.: Estimation of the surface normal velocity of high frequency ultrasound transducers. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 55(1), 225–235 (2008)

    Article  Google Scholar 

  54. Rupitsch, S.J., Lerch, R.: Inverse method to estimate material parameters for piezoceramic disc actuators. Appl. Phys. A: Mater. Sci. Process. 97(4), 735–740 (2009)

    Article  CAS  Google Scholar 

  55. Rupitsch, S.J., Ilg, J., Lerch, R.: Enhancement of the inverse method enabling the material parameter identification for piezoceramics. In: Proceedings of International IEEE Ultrasonics Symposium (IUS), pp. 357–360 (2011)

    Google Scholar 

  56. Rupitsch, S.J., Ilg, J., Sutor, A., Lerch, R., Döllinger, M.: Simulation based estimation of dynamic mechanical properties for viscoelastic materials used for vocal fold models. J. Sound Vib. 330(18–19), 4447–4459 (2011)

    Article  Google Scholar 

  57. Rupitsch, S.J., Wolf, F., Sutor, A., Lerch, R.: Reliable modeling of piezoceramic materials utilized in sensors and actuators. Acta Mech. 223, 1809–1821 (2012)

    Article  Google Scholar 

  58. Rupitsch, S.J., Ilg, J., Lerch, R.: Inverse scheme to identify the temperature dependence of electromechanical coupling factors for piezoceramics. In: Proceedings of Joint IEEE International Symposium on Applications of Ferroelectric and Workshop on Piezoresponse Force Microscopy (ISAF/PFM), pp. 183–186 (2013)

    Google Scholar 

  59. Schmidt, E.: Landolt-Börnstein - Zahlenwerte und Funktionen aus Naturwissenschaft und Technik - Band IV/1, 6th edn. Springer, Berlin (1955)

    Google Scholar 

  60. Sherrit, S., Gauthier, N., Wiederick, H.D., Mukherjee, B.K.: Accurate evaluation of the real and imaginary material constantsfor a piezoelectric resonator in the radial mode. Ferroelectrics 119(1), 17–32 (1991)

    Article  Google Scholar 

  61. Sherrit, S., Masys, T.J., Wiederick, H.D., Mukherjee, B.K.: Determination of the reduced matrix of the piezoelectric, dielectric, and elastic material constants for a piezoelectric material with C\(\infty \) symmetry. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58(9), 1714–1720 (2011)

    Article  Google Scholar 

  62. Shi, Y., Sol, H., Hua, H.: Material parameter identification of sandwich beams by an inverse method. J. Sound Vib. 290(3–5), 1234–1255 (2006)

    Article  Google Scholar 

  63. Smooth-On, Inc.: Product portfolio (2018). https://www.smooth-on.com

  64. TIRA GmbH: Product portfolio (2018). https://www.tira-gmbh.de/en/

  65. Tränkler, H.R., Reindl, L.M.: Sensortechnik - Handbuch für Praxis und Wissenschaft. Springer, Berlin (2014)

    Google Scholar 

  66. Van Dyke, K.S.: The piezo-electric resonator and its equivalent network. Proc. Inst. Radio Eng. 16(6), 742–764 (1928)

    Google Scholar 

  67. Wada, Y., Ito, R., Ochiai, H.: Comparison between mechanical relaxations associated with volume and shear deformations in styrene-butadiene rubber. J. Phys. Soc. Jpn. 17(1), 213–218 (1962)

    Article  Google Scholar 

  68. Weiß, S.: Messverfahren zur Charakterisierung synthetischer Stimmlippen. Ph.D. thesis, Friedrich-Alexander-University Erlangen-Nuremberg (2014)

    Google Scholar 

  69. Weiß, M., Ilg, J., Rupitsch, S.J., Lerch, R.: Inverse method for characterizing the mechanical frequency dependence of isotropic materials. Tech. Messen 83(3), 123–130 (2016)

    Google Scholar 

  70. Weiß, S., Sutor, A., Ilg, J., Rupitsch, S.J., Lerch, R.: Measurement and analysis of the material properties and oscillation characteristics of synthetic vocal folds. Acta Acust. United Acust. 102(2), 214–229 (2016)

    Article  Google Scholar 

  71. Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77(14), 3701–3707 (1955)

    Article  CAS  Google Scholar 

  72. Willis, R.L., Shane, T.S., Berthelot, Y.H., Madigosky, W.M.: An experimental-numerical technique for evaluating the bulk and shear dynamic moduli of viscoelastic materials. J. Am. Chem. Soc. 102(6), 3549–3555 (1997)

    CAS  Google Scholar 

  73. Willis, R.L., Wu, L., Berthelot, Y.H.: Determination of the complex young and shear dynamic moduli of viscoelastic materials. J. Acoust. Soc. Am. 109, 611–621 (2001)

    Article  CAS  Google Scholar 

  74. Yoshida, K., Kakimoto, K.I., Weiß, M., Rupitsch, S.J., Lerch, R.: Determination of temperature dependences of material constants for lead-free (Na0.5K0.5)NbO3-Ba2NaNb5O15 piezoceramics by inverse method. Jpn. J. Appl. Phys. 55(10), 10TD02 (2016)

    Article  CAS  Google Scholar 

  75. Ziegler, F.: Mechanics of Solids and Fluids, 2nd edn. Springer, Berlin (1995)

    Book  Google Scholar 

  76. Zörner, S., Kaltenbacher, M., Lerch, R., Sutor, A., Döllinger, M.: Measurement of the elasticity modulus of soft tissues. J. Biomech. 43(8), 1540–1545 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Sensorik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Stefan Johann Rupitsch

Authors
  1. Stefan Johann Rupitsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Johann Rupitsch .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag GmbH Germany, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rupitsch, S.J. (2019). Characterization of Sensor and Actuator Materials. In: Piezoelectric Sensors and Actuators. Topics in Mining, Metallurgy and Materials Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57534-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-57534-5_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-57532-1

  • Online ISBN: 978-3-662-57534-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation