Multi-objective optimal control for eigen-frequencies of a torsional shaft using Pontryagin’s maximum principle

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• 作者：Hai-Le Bui ; Duc-Trung Tran ; Minh-Quy Le ; Minh-Thuy Tran
• 关键词：Eigen frequencies ; Multi ; objective optimal control ; Torsional shaft ; Pontryagin’s maximum principle
• 刊名：Meccanica
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：50
• 期：9
• 页码：2409-2419
• 全文大小：847 KB
• 参考文献：1.Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF (1962) The mathematical theory of optimal processes. Wiley, England
  2.Szymczak C (1983) Optimal design of thin walled I beams for extreme natural frequency of torsional vibrations. J Sound Vib 86:235-41ADS View Article
  3.Szymczak C (1984) Optimal design of thin walled I beams for a given natural frequency of torsional vibrations. J Sound Vib 97:137-44ADS View Article
  4.Atanackovic TM, Djukic DS (1991) The influence of shear on the stability of a Pflüger column. J Sound Vib 144:531-35ADS View Article
  5.Atanackovic TM, Simic SS (1999) On the optimal shape of a Pflüger column. Eur J Mech A Solids 18:903-13MathSciNet View Article
  6.Glavardanov VB, Atanackovic TM (2001) Optimal shape of a twisted and compressed rod. Eur J Mech A Solids 20:795-09View Article
  7.Atanackovic TM, Braun DJ (2005) The strongest rotating rod. Int J Non-Linear Mech 40:747-54MathSciNet View Article
  8.Atanackovic TM, Novakovic BN (2006) Optimal shape of an elastic column on elastic foundation. Eur J Mech A Solids 25:154-65MathSciNet View Article
  9.Atanackovic TM (2007) Optimal shape of a strongest inverted column. J Comput Appl Math 203:209-18MathSciNet ADS View Article
  10.Atanackovic TM (2007) Optimal shape of a rotating rod with unsymmetrical boundary conditions. J Appl Mech 74:1234View Article
  11.Jelicic ZD, Atanackovic TM (2007) Optimal shape of a vertical rotating column. Int J Non-Linear Mech 42:172-79View Article
  12.Braun DJ (2008) On the optimal shape of compressed rotating rod with shear and extensibility. Int J Non-Linear Mech 43:131-39View Article
  13.Atanackovic TM, Jakovljevic BB, Petkovic MR (2010) On the optimal shape of a column with partial elastic foundation. Eur J Mech A Solids 29:283-89MathSciNet View Article
  14.Glavardanov VB, Spasic DT, Atanackovic TM (2012) Stability and optimal shape of Pflüger micro/nano beam. Int J Solids Struct 49:2559-567View Article
  15.Atanackovic TM, Novakovic BN, Vrcelj Z (2012) Shape optimization against buckling of micro- and nano-rods. Arch Appl Mech 82:1303-311View Article
  16.Le MQ, Tran DT, Bui HL (2012) Optimal design of a torsional shaft system using Pontryagin’s maximum principle. Meccanica 47:1197-207MathSciNet View Article
  17.Hagedorn P, DasGupta A (2007) Vibrations and waves in continuous mechanical systems. Wiley, EnglandView Article
  18.Thorby D (2008) Structural dynamics and vibration in Practice. Elsevier, USA
  19.Geering HP (2007) Optimal control with engineering applications. Springer, Berlin
  20.Lebedev LP, Cloud MJ (2003) The calculus of variations and functional analysis with optimal control and applications in mechanics. World Scientific, Singapore
  
• 作者单位：Hai-Le Bui (1)
  Duc-Trung Tran (1)
  Minh-Quy Le (1) (2)
  Minh-Thuy Tran (1)
  
  1. School of Mechanical Engineering, Hanoi University of Science and Technology, No. 1, Dai Co Viet Road, Hanoi, Vietnam
  2. Institute for Computational Science and Engineering, Hanoi University of Science and Technology, No. 1, Dai Co Viet Road, Hanoi, Vietnam
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Civil Engineering
  Automotive and Aerospace Engineering and Traffic
  Mechanical Engineering
  
• 出版者：Springer Netherlands
• ISSN：1572-9648

文摘

The present work investigates through Pontryagin’s maximum principle the multi-objective optimal control for eigen frequencies of a torsional shaft. Control variables are diameters of the shaft’s segments. Maier objective functional is used to control the final state of the objective functional for solving multi-objective optimal problem, in which maximizing eigen frequencies and minimizing system’s weight are simultaneously involved. The analogy coefficient k in the necessary optimality condition is explicitly determined by considering eigen frequencies as state variables. Numerical simulations demonstrate the relationship between the optimal configuration of the shaft and their eigen modes. The Pareto fronts and the boundary of the feasible region are constructed for the objectives. The Pareto fronts and the feasible region facilitate the estimation of the level of the trade-off between objectives, and the selection of a suitable solution among a set of competitive objectives.