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Linearization of embedded patterns for optimization of structural natural frequencies

  • Rodrigo NicolettiEmail author
Technical Paper
  • 14 Downloads

Abstract

The dynamic characteristics of structures (beams and plates) can be significantly changed by embossing small out-of-plane patterns in these structures. Recent results in literature show, both numerically and experimentally, that shaping a beam in the geometry of its first mode shape significantly increases the value of the first natural frequency of the beam. This phenomenon also occurs when the beam is shaped in the geometry of other mode shapes, and in the case of plates. This work presents new results (numerical and experimental) regarding the linearization of the forms to be imposed to the structure, focusing on shapes composed of straight regions, which would ease the design of stamping tools for example. The results show that the use of straight regions in the geometry of the beams (linear embossed pattern) has a similar effect to that obtained with curved shapes but requiring bigger distances to the baseline (higher shaping deformations). It is also shown that the linearized shapes can be used to optimize the shape of a beam for desired natural frequencies.

Keywords

Embedded pattern Natural frequency Mechanical vibration Linearization 

Notes

Acknowledgements

This project was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq (Brazil) under Grant No. 301118/2018-3.

References

  1. 1.
    Arora JS (1989) Introduction to optimum design. Mc-Graw Hill, New YorkGoogle Scholar
  2. 2.
    Ercoli L, Laura PAA, Gil R, Carnicer R, Sanzi HC (1990) Fundamental frequency of vibration of rectangular plates of discontinuously varying thickness with a free edge: analytical and experimental results. J Sound Vib 141:221–229.  https://doi.org/10.1016/0022-460X(90)90836-O CrossRefGoogle Scholar
  3. 3.
    Hinton E, Özakça M, Rao NVR (1995) Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells. Part 2: shape optimization. J Sound Vib 181:567–581.  https://doi.org/10.1006/jsvi.1995.0158 CrossRefGoogle Scholar
  4. 4.
    Maalawi KY, Badr MA (2010) Frequency optimization of a wind turbine blade in pitching motion. Proc IMechE Part A J Power Energy 224:545–554.  https://doi.org/10.1243/09576509JPE907 CrossRefGoogle Scholar
  5. 5.
    Topal U (2015) Frequency optimization of laminated composite annular sector plates. J Vib Control 21:320–327.  https://doi.org/10.1177/1077546313487763 CrossRefGoogle Scholar
  6. 6.
    Duan Z, Yan J, Lee I, Wang J, Yu T (2018) Integrated design optimization of composite frames and materials for maximum fundamental frequency with continuous fiber winding angles. Acta Mech Sin 34:1084–1094.  https://doi.org/10.1007/s10409-018-0784-x MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ou D, Mak CM (2018) Modification of boundary condition for the optimization of natural frequencies of plate structures with fluid loading. Adv Mech Eng 10:1–11.  https://doi.org/10.1177/1687814018796008 CrossRefGoogle Scholar
  8. 8.
    Park YH, Park YS (2000) Structure optimization to enhance its natural frequencies based on measured frequency response functions. J Sound Vib 229:1235–1255.  https://doi.org/10.1006/jsvi.1999.2591 CrossRefzbMATHGoogle Scholar
  9. 9.
    Lim OK, Lee JS (2000) Structural topology optimization for the natural frequency of a designated mode. KSME Int J 14:306–313.  https://doi.org/10.1007/BF03186423 CrossRefGoogle Scholar
  10. 10.
    Choi SH, Kim SR, Park JY, Han SY (2007) Multi-objective optimization of the inner reinforcement for a vehicle hood considering static stiffness and natural frequency. Int J Autom Technol 8:337–342 http://www.ijat.net/journal/view.php?number=428
  11. 11.
    Dong G (2015) Topology optimization for the natural frequency of multibody dynamics systems with multi-functional components. In: ASME 2015 international design engineering technical conferences and computers and information in engineering conference IDETC/CIE 2015, Boston MA, US, August 2–5, DETC2015-47891.  https://doi.org/10.1115/DETC2015-47891
  12. 12.
    Reis DB, Nicoletti R (2010) Positioning of deadeners for dibration reduction in vehicle roof using embedded sensitivity. J Vib Acoust 132:021007.  https://doi.org/10.1115/1.4000769 CrossRefGoogle Scholar
  13. 13.
    Cheng L, Liang X, Belski E, Wang X, Sietins JM, Ludwick S, To A (2018) Natural frequency optimization of variable-density additive manufactured lattice structure: theory and experimental validation. J Manuf Sci Eng 140:1050002.  https://doi.org/10.1115/1.4040622 CrossRefGoogle Scholar
  14. 14.
    Fredö CR, Hedlung A (2005) NVH optimization of truck cab floor panel embossing pattern. SAE technical paper 2005-01-2342.  https://doi.org/10.4271/2005-01-2342
  15. 15.
    Silva GAL, Nicoletti R (2017) Optimization of natural frequencies of a slender beam shaped in a linear combination of its mode shapes. J Sound Vib 397:92–107.  https://doi.org/10.1016/j.jsv.2017.02.053 CrossRefGoogle Scholar
  16. 16.
    Thomson WT, Dahleh MD (1998) Theory of vibration with applications. Prentice Hall, Upper Saddle RiverGoogle Scholar
  17. 17.
    Maia NMM, Silva JMM (1997) Theoretical and experimental modal analysis. Research Studies Press Ltd, TauntonGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Sao Carlos School of EngineeringUniversity of Sao PauloSao CarlosBrazil

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