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Parametric Stochastic Analysis of a Piezoelectric Vibration Absorber Applied to Automotive Body Structure

  • Francisco ScinoccaEmail author
  • Airton Nabarrete
Article
  • 13 Downloads

Abstract

Objective

This paper presents a systematic approach to quantify the uncertainties that influences directly the design of a Piezoelectric Vibration Absorber applied to shell structures with arbitrary shape, normally employed in automotive body structures.

Methodology

Sensitivity and spectral analyses are performed to study the impact of randomness in the optimal piezoelectric patch implementation in automotive structures. The randomness arising from the manufacturing process of the mechanical structure, such as stamping spring back effects, as well as in the boundary conditions, is considered in the analyses, likewise the effects of variability during the positioning process for piezoelectric patches. The effects of the inherent uncertainties in the dynamic behavior of the mechanical structure, the optimal electromechanical coupling coefficient and the piezoelectric vibration absorber attenuation are presented.

Results

The present paper has the advantage of indicating the loss in the vibration attenuation when Piezoelectric Vibration Absorbers are used in arbitrary shape structures, such as automotive hoods, fenders and doors. The Dynamic Vibration Absorber deterministically optimized provides an attenuation of approximately 18 dB in the theoretical model. However, losses of 5 dB in the attenuation can be obtained when the uncertainties are taken into account, and can reach up to 10 dB when the temperature effects are involved, representing more than 50% loss in attenuation for real applications, such as automotive body structures.

Keywords

Uncertainty propagation Stochastic analysis Piezoelectric optimization Piezoelectric vibration absorber Model updating 

Notes

Acknowledgements

The research presented in this paper is funded by the Brazilian research funding agency CAPES/PROBRAL 385-11 (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and the German federal State of Hessen [project “LOEWE Zentrum AdRIA: Adaptronik-Research, Innovation, Application”, Grant III L 4-518/14004(2008)]. This financial support is gratefully acknowledged. The authors also acknowledge the MCT/CNPq/FAPEMIG National Institute of Science and Technology on Smart Structures in Engineering, Grant no. 574001/2008-5, for the financial support received during this work. The authors also would like to thank Tobias Melz, Luiz C.S. Góes, Oliver Heuss, Torsten Bartel, Mihail Lilov and Jorge A.B. Gripp for their support during this research.

References

  1. 1.
    McKenna R et al (2013) Energy savings through direct secondary reuse: an exemplary analysis of the German automotive sector. J Clean Prod 52:103–112CrossRefGoogle Scholar
  2. 2.
    Zhang YU, Zhu P, Chen G (2007) Lightweight design of automotive front side rail based on robust optimization. Thin-Walled Structures 45:670–676. http://www.sciencedirect.com/science/journal/02638231/45/7
  3. 3.
    Neubauer M, Wallaschek K (2013) Vibration damping with shunted piezoceramics: fundamentals and technical applications. Mech Syst Signal Process 36:36–52CrossRefGoogle Scholar
  4. 4.
    Fleming AJ, Moheimani SOR (2003) Adaptive piezoelectric shunt damping. Smart Mater Struct 12(1):36–48CrossRefGoogle Scholar
  5. 5.
    Hagood NW, Flotow AV (1991) Damping of structural vibrations with piezoelectric materials and passive electrical networks. J Sound Vib 146:243–268CrossRefGoogle Scholar
  6. 6.
    Behrens S, Moheimani SOR, Fleming AJ (2003) Multiple mode current flowing passive piezoelectric shunt controller. J Sound Vib 266(5):929–942CrossRefGoogle Scholar
  7. 7.
    Santos HFL, Trindade MA (2011) Structural vibration control using extension and shear active-passive piezoelectric networks including sensitivity to electrical uncertainties. J Braz Soc Mech Sci Eng 33:287–301CrossRefGoogle Scholar
  8. 8.
    Niederberger D, Fleming AJ, Moheimani SOR, Morari M (2004) Adaptive multi-mode resonant piezoelectric shunt damping. J Smart Mater Struct 13(4):1025–1035CrossRefGoogle Scholar
  9. 9.
    Gripp JAB, Góes LCS, Heuss O, Scinocca F (2015) An adaptive piezoelectric vibration absorber enhanced by a negative capacitance applied to a shell structure. Smart Mater Struct 24:125017CrossRefGoogle Scholar
  10. 10.
    Clark WW (2000) Vibration control with state-switched piezoelectric materials. J Intell Mater Syst Struct 11(4):263–271CrossRefGoogle Scholar
  11. 11.
    Heuss O, Salloum R, Mayer D, Melz T (2014) Tuning of a vibration absorber with shunted piezoelectric transducers. Archive of applied mechanics. Springer, Berlin, pp 1–18Google Scholar
  12. 12.
    Moheimani SOR, Fleming AJ (2006) Piezoelectric transducers for vibration control and damping. Spring, LondonzbMATHGoogle Scholar
  13. 13.
    Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics, Solid Mechanics and Its Applications. Kluwer Academic Publishers Group, DordrechtCrossRefzbMATHGoogle Scholar
  14. 14.
    Maresa C, Mottersheadb JE, Friswell MI (2006) Stochastic model updating: part 1—theory and simulated example. Mech Syst Signal Process 20:1674–1695CrossRefGoogle Scholar
  15. 15.
    Mottershead JE et al (2006) Stochastic model updating: part 2—application to a set of physical structures. Mech Syst Signal Process 20:2171–2185CrossRefGoogle Scholar
  16. 16.
    ASME Y14.5-2009 (2009) Geometric dimensioning and tolerancing, American Society of Mechanical EngineersGoogle Scholar
  17. 17.
    Ewins DJ (2000) Modal testing: theory, practice and application, 2nd edn. Research Studies Press, BaldockGoogle Scholar
  18. 18.
    Shigley JE, Mischke CR (2001) Mechanical engineering design. McGraw-Hill Series in Mechanical Engineering, New YorkGoogle Scholar
  19. 19.
    Ducarne J, Thomas O, Deü JF (2012) Placement and dimension optimization of shunted piezoelectric patches for vibration reduction. J Sound Vib 331:3286–3303CrossRefGoogle Scholar
  20. 20.
    Bachmann F, Bergamini AE, Ermanni P (2012) Optimum piezoelectric patch positioning: a strain energy–based finite element approach. J Intell Mater Syst Struct 23:1575–1591CrossRefGoogle Scholar
  21. 21.
    Belloli A, Ermanni P (2007) Optimum placement of piezoelectric ceramic modules for vibration suppression of highly constrained structures. Smart Mater Struct 16:1662–1671CrossRefGoogle Scholar
  22. 22.
  23. 23.
    Vanderplaats G, Sampaio R (2015) Numerical optimization techniques for engineering design, 4th edn. Vanderplaats Research & Development, WashingtonGoogle Scholar
  24. 24.
    Cursi ES, Sampaio R (2015) Uncertainty Quantification and stochastic modeling with matlab, 1st edn. ISTE Press Ltd and Elsevier Ltd, London and New YorkzbMATHGoogle Scholar
  25. 25.
    Piovan MT, Sampaio R (2015) Parametric and non-parametric probabilistic approaches in the mechanics of thin-walled composite curved beams. Thin Walled Struct 90:95–106CrossRefGoogle Scholar
  26. 26.
    Kapur JN (1989) Maximum-entropy models in science and engineering. New Age International, New DelhizbMATHGoogle Scholar
  27. 27.
    Soize C (2017) Uncertainty quantification: an accelerated course with advanced applications in computational engineering. Springer International Publishing AG, BaselCrossRefzbMATHGoogle Scholar
  28. 28.
    Ekwaro-osire S, Gonçalves AC, Alemayehu FM (2017) Probabilistic prognostics and health management of energy systems. Springer International Publishing AG, BaselCrossRefGoogle Scholar
  29. 29.
    Cursi ES, Sampaio R (2015) Uncertainty quantification and stochastic modeling with matlab, 1st edn. ISTE Press Ltd and Elsevier Ltd, London and New YorkzbMATHGoogle Scholar
  30. 30.
    Fleming AJ, Behrens S, Moheimani SOR (2000) Synthetic impedance for implementation of piezoelectric shunt damping circuits. Electron Lett 36(18):1525–1526CrossRefGoogle Scholar
  31. 31.
    Sedra AS, Smith KC (2007) Microelectronic circuits, 5th edn. Oxford University Press, OxfordGoogle Scholar
  32. 32.
    Antoniou A (1969) Realization of gyrators using operational amplifiers, and their use in RC-active-network synthesis. In: Proceedings… [S.I]: IEE, 116(11), 1838–1850Google Scholar
  33. 33.
    Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44:335–341CrossRefzbMATHGoogle Scholar
  34. 34.
    Fishman G (2003) Monte Carlo: concepts, algorithms, and applications, corrected edition. Springer, New YorkGoogle Scholar
  35. 35.
    Robert CP, Casella G (2010) Monte Carlo statistical methods. Springer, New YorkzbMATHGoogle Scholar
  36. 36.
    Kroese DP, Taimre T, Botev ZI (2011) Handbook of Monte Carlo methods. Wiley, New JerseyCrossRefzbMATHGoogle Scholar
  37. 37.
    Cunha A Jr, Nasser R, Sampaio R, Lopes H, Breitman K (2014) Uncertainty quantification through Monte Carlo method in a cloud computing setting. Computer Physics Communications 185:1355–1363CrossRefGoogle Scholar

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© Krishtel eMaging Solutions Private Limited 2019

Authors and Affiliations

  1. 1.Engineering DivisionFederal University of Lavras-UFLALavrasBrazil
  2. 2.Aeronautical Engineering DivisionAeronautical Institute of Technology-ITASão José dos CamposBrazil

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