Skip to main content
SpringerLink
Log in

An Improved Formulation for Structural Optimization of Nonlinear Dynamic Response

  • Conference paper
  • First Online:
Advances in Nonlinear Dynamics

Part of the book series: NODYCON Conference Proceedings Series ((NCPS))

  • 1282 Accesses

Abstract

Nonlinear dynamics is widely exploited in micro-mechanical resonators with a number of applications. One of the crucial issues in these applications is to intentionally tailor the intrinsic nonlinearity in these structures. In this study, a structural optimization methodology is improved for tailoring the intrinsic nonlinearity in these resonators by manipulating their structural geometry. In the optimization, the objective function is defined based on the nonlinear modal coupling coefficients and eigenfrequencies and modal shapes of the vibration modes. A preliminary study shows that the improved formulation of the optimization problem enables better designs.

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 299.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 379.99
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

References

  1. J.F. Rhoads, S.W. Shaw, K.L. Turner, Nonlinear dynamics and its applications in micro- and nanoresonators. J. Dyn. Syst. Meas. Control 132, 034001 (2010)

    Article  Google Scholar 

  2. B. Jeong, C. Pettit, S. Dharmasena, H. Keum, J. Lee, J. Kim, S. Kim, D.M. McFarland, L.A. Bergman, A.F. Vakakis, H. Cho, Utilizing intentional internal resonance to achieve multi-harmonic atomic force microscopy. Nanotechnology 27, 125501 (2016)

    Article  Google Scholar 

  3. W. Zhang, R. Baskaran, K.L. Turner, Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor. Sens. Actuator A Phys. 102, 139–150 (2002)

    Article  Google Scholar 

  4. V.C. Meesala, M.R. Hajj, E. Abdel-Rahman, Bifurcation-based MEMS mass sensors. Int. J. Mech. Sci. 180, 105705 (2020)

    Article  Google Scholar 

  5. S.H. Nitzan, V. Zega, M. Li, C.H. Ahn, A. Corigliano, T.W. Kenny, D.A. Horsley, Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope. Sci. Rep. 5, 9036 (2015)

    Article  Google Scholar 

  6. R.P. Middlemiss, A. Samarelli, D.J. Paul, J. Hough, S. Rowan, G.D. Hammond, Measurement of the Earth tides with a MEMS gravimeter. Nature 531, 614–617 (2016)

    Article  Google Scholar 

  7. K.R. Qalandar, B.S. Strachan, B. Gibson, M. Sharma, A. Ma, S.W. Shaw, K.L. Turner, Frequency division using a micromechanical resonance cascade. Appl. Phys. Lett. 105, 244103 (2014)

    Article  Google Scholar 

  8. A. Hajati, S.G. Kim, Ultra-wide bandwidth piezoelectric energy harvesting. Appl. Phys. Lett. 99, 083105 (2011)

    Article  Google Scholar 

  9. S. Dou, J.S. Jensen, Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes. Comput. Struct. 164, 63–74 (2016)

    Article  Google Scholar 

  10. T. Detroux, J. Noël, G. Kerschen, Tailoring the resonances of nonlinear mechanical systems. Nonlinear Dyn. 103(4), 3611–3624 (2021). https://doi.org/10.1007/s11071-020-06002-w

    Article  Google Scholar 

  11. S. Dou, J.S. Jensen, Optimization of nonlinear structural resonance using the incremental harmonic balance method. J. Sound Vib. 334, 239–54 (2015)

    Article  Google Scholar 

  12. A. Tripathi, A.K. Bajaj, Computational synthesis for nonlinear dynamics based design of planar resonant structures. J. Vib. Acoust. 135, 051031 (2013)

    Article  Google Scholar 

  13. A. Tripathi, A.K. Bajaj, Topology optimization and internal resonances in transverse vibrations of hyperelastic plates. Int. J. Solids Struct. 81, 311–328 (2016)

    Article  Google Scholar 

  14. S. Dou, B.S. Strachan, S.W. Shaw, J.S. Jensen, Structural optimization for nonlinear dynamic response. Phil. Trans. R. Soc. A 373, 20140408 (2015)

    Article  MathSciNet  Google Scholar 

  15. L.L. Li, P.M. Polunin, S. Dou, O. Shoshani, B.S. Strachan, J.S. Jensen, S.W. Shaw, K.L. Turner, Tailoring the nonlinear response of MEMS resonators using shape optimization. Appl. Phys. Lett. 110, 081902 (2017)

    Article  Google Scholar 

  16. C. Touzé, M. Vidrascu, D. Chapelle, Direct finite element computation of non-linear modal coupling coefficients for reduced-order shell models. Comput. Mech. 54, 567–580 (2014)

    Article  MathSciNet  Google Scholar 

  17. A. Frangi, G. Gobat, Reduced order modelling of the non-linear stiffness in MEMS resonators. Int. J. Non Linear Mech. 116, 211–218 (2019)

    Article  Google Scholar 

  18. S.H. Chen, Y.K. Cheung, H.X. Xing, Nonlinear vibration of plane structures by finite element and incremental harmonic balance method. Nonlinear Dyn. 26, 87–104 (2001)

    Article  Google Scholar 

  19. K. Svanberg, The method of moving asymptotes–a new method for structural optimization. Int. J. Numer. Methods Eng. 24, 359–373 (1987)

    Article  MathSciNet  Google Scholar 

  20. F. Van Keulen, R.T. Haftka, N.H. Kim, Review of options for structural design sensitivity analysis. Part 1: Linear systems. Comput. Methods Appl. Mech. Eng. 194, 3213–3243 (2005)

    Google Scholar 

  21. S. Dou, J.S. Jensen, Analytical sensitivity analysis and topology optimization of nonlinear resonant structures with hardening and softening behavior, in Proceedings of the 17th U.S. National Congress on Theoretical and Applied Mechanics, East Lansing (2014). https://orbit.dtu.dk/en/publications/analytical-sensitivity-analysis-and-topology-optimization-of-nonl

  22. J.S. Jensen, S. Dou, Topology optimization in nonlinear structural dynamics using direct computation of nonlinear coefficients, in ECCOMAS Congress 2016: VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete (2016). https://orbit.dtu.dk/en/publications/topology-optimization-in-nonlinear-structural-dynamics-using-dire

  23. J.S. Jensen, S. Dou, S.W. Shaw, Tailoring nonlinear dynamics of microbeam resonators with electrostatic actuation, in Proceeding of 24th International Congress of Theoretical and Applied Mechanics, vol. 1 (2016), pp. 148–149. https://orbit.dtu.dk/en/publications/tailoring-nonlinear-dynamics-of-microbeam-resonators-with-electro

  24. M.A. Eltaher, M.E. Khater, S.A. Emam, A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Model. 40, 4109–4128 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DTU Wind Energy, Technical University of Denmark, Roskilde, Denmark

    Suguang Dou

Authors
  1. Suguang Dou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suguang Dou .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael J. Leamy

  4. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  5. ISEP-Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

  6. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dou, S. (2022). An Improved Formulation for Structural Optimization of Nonlinear Dynamic Response. In: Lacarbonara, W., Balachandran, B., Leamy, M.J., Ma, J., Tenreiro Machado, J.A., Stepan, G. (eds) Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-030-81162-4_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-81162-4_38

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81161-7

  • Online ISBN: 978-3-030-81162-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation