Skip to main content
SpringerLink
Log in

Piezoelectric sensor location by the observability Gramian maximization using topology optimization

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

This work presents an optimal design methodology for piezoelectric material positioning in structures aiming at vibration measurements. The main objective is to find the optimal location of piezoelectric sensors using a suitable topology optimization strategy. The sensors location is determined by an optimization formulation that defines where the material should have piezoelectric properties. The objective of the optimization is maximizing observability, measured by means of the trace of the Gramian matrix. The control strategy development is based on a truncated modal system model. A case study and its results are presented and discussed, showing that the optimal placement of the piezoelectric sensors in a cantilever beam can be suitably achieved through the proposed approach.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Alvelid M (2008) Optimal position and shape of applied damping material. J Sound Vib 310(4):947–965

    Article  Google Scholar 

  • Balamurugan V, Narayanan S (2002) Finite element formulation and active vibration control study on beams using smart constrained layer damping (SCLD) treatment. J Sound Vib 249(2):227–250

    Article  Google Scholar 

  • Becker J, Fein O, Maess M, Gaul L (2006) Finite element-based analysis of shunted piezoelectric structures for vibration damping. Comput Struct 84(31):2340–2350

    Article  Google Scholar 

  • Bendsoe MP, Sigmund O (2013) Topology optimization: theory, methods, and applications. Springer Science and Business Media, New York

    MATH  Google Scholar 

  • Carbonari RC, Silva EC, Nishiwaki S (2007) Optimum placement of piezoelectric material in piezoactuator design. Smart Mater Struct 16(1):207

    Article  Google Scholar 

  • Da Silveira OAA, Fonseca JSO, Santos IF (2015) Actuator topology design using the controllability gramian. Struct Multidiscip Optim 51(1):145–157

    Article  MathSciNet  Google Scholar 

  • Donoso A, Bellido JC (2009) Distributed piezoelectric modal sensors for circular plates. J Sound Vib 319(1):50–57

    Article  Google Scholar 

  • Gawronski W (2004) Advanced structural dynamics and active control of structures. Springer Science and Business Media, New York

    Book  Google Scholar 

  • Gawronski W, Lim K (1996) Balanced actuator and sensor placement for flexible structures. Int J Control 65(1):131–145

    Article  MathSciNet  Google Scholar 

  • Goncalves JF, Fonseca JS, Silveira OA (2016) A controllability-based formulation for the topology optimization of smart structures. Smart Struct Syst 17(5):773–793

    Article  Google Scholar 

  • Gupta V, Sharma M, Thakur N (2010) Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure: a technical review. J Intell Mater Syst Struct 21(12):1227–1243

    Article  Google Scholar 

  • Hać A, Liu L (1993) Sensor and actuator location in motion control of flexible structures. J Sound Vib 167(2):239–261

    Article  Google Scholar 

  • Kang Z, Wang R, Tong L (2011) Combined optimization of bi-material structural layout and voltage distribution for in-plane piezoelectric actuation. Comput Methods Appl Mech Eng 200(13):1467–1478

    Article  MathSciNet  Google Scholar 

  • Kumar KR, Narayanan S (2008) Active vibration control of beams with optimal placement of piezoelectric sensor/actuator pairs. Smart Mater Struct 17(5):055008

    Article  Google Scholar 

  • Lee YS (2011) Comparison of collocation strategies of sensor and actuator for vibration control. J Mech Sci Technol 25(1):61–68

    Article  Google Scholar 

  • Lin ZQ, Gea HC, Liu ST (2011) Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization. Acta Mech Sin 27(5):730–737

    Article  MathSciNet  Google Scholar 

  • Marcelo Tusset A, Piccirillo V, Bueno AM, Manoel Balthazar J, Sado D, Felix JLP, Brasil RMLRdF (2016) Chaos control and sensitivity analysis of a double pendulum arm excited by an rlc circuit based nonlinear shaker. J Vib Control 22(17):3621–3637

    Article  MathSciNet  Google Scholar 

  • Mecchi ACL, Nader G, Silva ECN, Adamowski JC (2004) Development and characterization of a unimorph-type piezoelectric actuator applied to a michelson interferometer. Mechatronics 1(2):653–661

    Google Scholar 

  • Moheimani SR, Fleming AJ (2006) Piezoelectric transducers for vibration control and damping. Springer Science and Business Media, New York

    MATH  Google Scholar 

  • Pereira MdFV, Balthazar JM, dos Santos DA, Tusset AM, de Castro DF, Prado IAA (2017) A note on polynomial chaos expansions for designing a linear feedback control for nonlinear systems. Nonlinear Dyn 87(3):1653–1666

    Article  MathSciNet  Google Scholar 

  • Peruzzi N, Chavarette FR, Balthazar JM, Tusset AM, Perticarrari ALPM, Brasil R (2016) The dynamic behavior of a parametrically excited time-periodic mems taking into account parametric errors. J Vib Control 22(20):4101–4110

    Article  MathSciNet  Google Scholar 

  • Preumont A (2011) Vibration control of active structures: an introduction, vol 179. Springer Science and Business Media, New York

    MATH  Google Scholar 

  • Qi H, Fang D, Yao Z (1997) Fem analysis of electro-mechanical coupling effect of piezoelectric materials. Comput Mater Sci 8(4):283–290

    Article  Google Scholar 

  • Qiu Zc, Zhang Xm, Wu Hx, Zhang Hh (2007) Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate. J Sound Vib 301(3):521–543

    Article  MathSciNet  Google Scholar 

  • Rubio WM, Silva EC, Paulino GH (2009) Toward optimal design of piezoelectric transducers based on multifunctional and smoothly graded hybrid material systems. J Intell Mater Syst Struct 20(14):1725–1746

    Article  Google Scholar 

  • Schwantz M (2002) Encyclopedia of smart materials. Wiley-Interscience Publication, New York

    Book  Google Scholar 

  • Tzou H, Tseng C (1990) Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach. J Sound Vib 138(1):17–34

    Article  Google Scholar 

  • Vasques C, Rodrigues JD (2006) Active vibration control of smart piezoelectric beams: comparison of classical and optimal feedback control strategies. Comput Struct 84(22):1402–1414

    Article  Google Scholar 

  • Wang S (2004) A finite element model for the static and dynamic analysis of a piezoelectric bimorph. Int J Solids Struct 41(15):4075–4096

    Article  Google Scholar 

  • Wang X, Kang Z, Wang Y (2011) Topology design of slender piezoelectric actuators with repetitive component patterns. J Intell Mater Syst Struct 22(18):2161–2172

    Article  Google Scholar 

  • Wu B, Xu Z, Li Z (2007) A note on computing eigenvector derivatives with distinct and repeated eigenvalues. Int J Numer Methods Biomed Eng 23(3):241–251

    MathSciNet  MATH  Google Scholar 

  • Xu B, Ou J, Jiang J (2013) Integrated optimization of structural topology and control for piezoelectric smart plate based on genetic algorithm. Finite Elem Anal Design 64:1–12

    Article  MathSciNet  Google Scholar 

  • Zorić ND, Simonović AM, Mitrović ZS, Stupar SN (2013) Optimal vibration control of smart composite beams with optimal size and location of piezoelectric sensing and actuation. J Intell Mater Syst Struct 24(4):499–526

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support of the Brazilian agencies CAPES and CNPq.

Author information

Authors and Affiliations

  1. Farroupilha Federal Institute of Education, Science and Technology, Rua Otaviano Castilho Mendes 355, São Borja, RS, 97670-000, Brazil

    Odair Menuzzi

  2. Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Sarmento Leite 425, Porto Alegre, RS, 90050-170, Brazil

    Jun S. O. Fonseca, Eduardo A. Perondi & Juliano F. Gonçalves

  3. Farroupilha Federal Institute of Education, Science and Technology, Rodovia RS-377, Alegrete, RS, 97555-000, Brazil

    Eduardo Padoin

  4. Department of Civil Engineering, Federal University of Santa Catarina, Rua João Pio Duarte da Silva 205, Florianópolis, SC, 88040-970, Brazil

    Otávio A. A. Silveira

Authors
  1. Odair Menuzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun S. O. Fonseca
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eduardo A. Perondi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Juliano F. Gonçalves
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eduardo Padoin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Otávio A. A. Silveira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Odair Menuzzi.

Additional information

Communicated by Eduardo Souza de Cursi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Menuzzi, O., Fonseca, J.S.O., Perondi, E.A. et al. Piezoelectric sensor location by the observability Gramian maximization using topology optimization. Comp. Appl. Math. 37 (Suppl 1), 237–252 (2018). https://doi.org/10.1007/s40314-017-0517-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40314-017-0517-y

Keywords

Mathematics Subject Classification

Search

Navigation