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Optimal design of a torsional shaft system using Pontryagin’s Maximum Principle

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Abstract

Optimal problems are investigated in the present work in order to control the natural frequencies of a torsional shaft system including the total weight constraint and effects of tuned mass dampers. Maier objective functional is used. Pontryagin’s Maximum Principle is employed to derive necessary optimality conditions of the optimal problems. Numerical simulations are performed to study effects of tuned mass dampers on controlling natural frequencies as well as minimizing the system’s weight. Advantages of the proposed method are also discussed.

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References

  1. Dresig H, Holzweißig F (2005) Machine dynamic. Springer, Berlin (in German)

    Google Scholar 

  2. Szymczak C (1984) Optimal design of thin walled I beams for a given natural frequency of torsional vibrations. J Sound Vib 97(1):137–144

    Article  ADS  MATH  Google Scholar 

  3. Ivanov AG (1992) Optimal control of almost-periodic motions. J Appl Math Mech 56:737–746

    Article  Google Scholar 

  4. Glavardanov VB, Atanackovic TM (2001) Optimal shape of a twisted and compressed rod. Eur J Mech A, Solids 20:795–809

    Article  MATH  Google Scholar 

  5. Atanackovic TM (2007) Optimal shape of a strongest inverted column. J Comput Appl Math 203:209–218

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Braun DJ (2008) On the optimal shape of compressed rotating rod with shear and extensibility. Int J Non-Linear Mech 43:131–139

    Article  MATH  Google Scholar 

  7. Atanackovic TM, Braun DJ (2005) The strongest rotating rod. Int J Non-Linear Mech 40:747–754

    Article  MathSciNet  MATH  Google Scholar 

  8. Atanackovic TM, Jelicic ZD (2007) Optimal shape of a vertical rotating column. Int J Non-Linear Mech 42:172–179

    Article  Google Scholar 

  9. Atanackovic TM, Novakovic BN (2006) Optimal shape of an elastic column on elastic foundation. Eur J Mech A, Solids 25:154–165

    Article  MathSciNet  MATH  Google Scholar 

  10. Atanackovic TM, Simic SS (1999) On the optimal shape of a Pflüger column. Eur J Mech A, Solids 18:903–913

    Article  MathSciNet  MATH  Google Scholar 

  11. Hagedorn P, DasGupta A (2007) Vibrations and waves in continuous mechanical systems. Wiley, New York

    Book  MATH  Google Scholar 

  12. Thorby D (2008) Structural dynamics and vibration in practice. Elsevier, Amsterdam

    Google Scholar 

  13. Geering HP (2007) Optimal control with engineering applications. Springer, Berlin

    MATH  Google Scholar 

  14. Lebedev LP, Cloud MJ (2003) The calculus of variations and functional analysis with optimal control and applications in mechanics. World Scientific, Singapore

    Book  MATH  Google Scholar 

  15. Rao SS (1990) Mechanical vibrations. Addison-Wesley, Reading

    MATH  Google Scholar 

  16. ASM International (1990) Metals handbook, vol 1—properties and selection: irons, steels, and high-performance alloys, 10th edn. ASM International, Materials Park

    Google Scholar 

  17. ASM International (1990) Metals handbook, vol 2—properties and selection: nonferrous alloys and special-purpose materials, 10th edn. ASM International, Materials Park

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics of Materials, School of Mechanical Engineering, Hanoi University of Science and Technology, No 1—Dai Co Viet Road, Hanoi, Vietnam

    Minh-Quy Le, Duc-Trung Tran & Hai-Le Bui

  2. International Center for Computational Materials Science, Hanoi University of Science and Technology, No 1—Dai Co Viet Road, Hanoi, Vietnam

    Minh-Quy Le

Authors
  1. Minh-Quy Le
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  2. Duc-Trung Tran
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  3. Hai-Le Bui
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Correspondence to Minh-Quy Le.

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Le, MQ., Tran, DT. & Bui, HL. Optimal design of a torsional shaft system using Pontryagin’s Maximum Principle. Meccanica 47, 1197–1207 (2012). https://doi.org/10.1007/s11012-011-9504-3

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  • DOI: https://doi.org/10.1007/s11012-011-9504-3

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