Optimal configurations of circular bars under free torsional and longitudinal vibration based on Pontryagin’s maximum principle

Optimal configurations of circular bars under free torsional and longitudinal vibration are investigated using the Pontryagin’s maximum principle (PMP). The necessary optimality condition of PMP is analysed by considering the cross-sectional area of bars as control variable and by using Maier object...

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Bibliographic Details
Published inMeccanica (Milan) Vol. 51; no. 6; pp. 1491 - 1502
Main Authors Bui, Hai-Le, Tran, Minh-Thuy, Le, Minh-Quy, Tran, Duc-Trung
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2016
Subjects
Automotive Engineering
Bars
Boundary conditions
Circularity
Civil Engineering
Classical Mechanics
Cross sections
Mathematical models
Maximum principle
Mechanical Engineering
Optimization
Physics
Physics and Astronomy
Vibration
Eigen frequencies
Optimal configuration
Pontryagin’s maximum principle
Circular bar
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Summary:Optimal configurations of circular bars under free torsional and longitudinal vibration are investigated using the Pontryagin’s maximum principle (PMP). The necessary optimality condition of PMP is analysed by considering the cross-sectional area of bars as control variable and by using Maier objective functional to control the final state of the objective functional. Optimal configurations associated to different orders of eigen frequencies, eigen vectors, and specific boundary conditions are demonstrated. Their relations are also explained qualitatively. Numerical results show the equivalent about optimal configurations and eigen frequencies under specific boundary conditions.
Bibliography:ObjectType-Article-1
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ISSN:0025-6455
1572-9648
DOI:10.1007/s11012-015-0324-8