×

zbMATH — the first resource for mathematics

Optimal design of a torsional shaft system using Pontryagin’s maximum principle. (English) Zbl 1293.74349
Summary: 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.

MSC:
74P10 Optimization of other properties in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dresig H, Holzweißig F (2005) Machine dynamic. Springer, Berlin (in German)
[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 · Zbl 0562.73085 · doi:10.1016/0022-460X(84)90474-7
[3] Ivanov AG (1992) Optimal control of almost-periodic motions. J Appl Math Mech 56:737–746 · doi:10.1016/0021-8928(92)90059-H
[4] Glavardanov VB, Atanackovic TM (2001) Optimal shape of a twisted and compressed rod. Eur J Mech A, Solids 20:795–809 · Zbl 0998.74058 · doi:10.1016/S0997-7538(01)01165-2
[5] Atanackovic TM (2007) Optimal shape of a strongest inverted column. J Comput Appl Math 203:209–218 · Zbl 1113.49021 · doi:10.1016/j.cam.2006.03.019
[6] Braun DJ (2008) On the optimal shape of compressed rotating rod with shear and extensibility. Int J Non-Linear Mech 43:131–139 · Zbl 1203.74077 · doi:10.1016/j.ijnonlinmec.2007.11.001
[7] Atanackovic TM, Braun DJ (2005) The strongest rotating rod. Int J Non-Linear Mech 40:747–754 · Zbl 1349.74217 · doi:10.1016/j.ijnonlinmec.2004.09.002
[8] Atanackovic TM, Jelicic ZD (2007) Optimal shape of a vertical rotating column. Int J Non-Linear Mech 42:172–179 · doi:10.1016/j.ijnonlinmec.2006.10.020
[9] Atanackovic TM, Novakovic BN (2006) Optimal shape of an elastic column on elastic foundation. Eur J Mech A, Solids 25:154–165 · Zbl 1083.74040 · doi:10.1016/j.euromechsol.2005.06.008
[10] Atanackovic TM, Simic SS (1999) On the optimal shape of a Pflüger column. Eur J Mech A, Solids 18:903–913 · Zbl 0978.74057 · doi:10.1016/S0997-7538(99)00128-X
[11] Hagedorn P, DasGupta A (2007) Vibrations and waves in continuous mechanical systems. Wiley, New York · Zbl 1156.74002
[12] Thorby D (2008) Structural dynamics and vibration in practice. Elsevier, Amsterdam
[13] Geering HP (2007) Optimal control with engineering applications. Springer, Berlin · Zbl 1121.49001
[14] Lebedev LP, Cloud MJ (2003) The calculus of variations and functional analysis with optimal control and applications in mechanics. World Scientific, Singapore
[15] Rao SS (1990) Mechanical vibrations. Addison-Wesley, Reading · Zbl 0714.73050
[16] ASM International (1990) Metals handbook, vol 1–properties and selection: irons, steels, and high-performance alloys, 10th edn. ASM International, Materials Park
[17] ASM International (1990) Metals handbook, vol 2–properties and selection: nonferrous alloys and special-purpose materials, 10th edn. ASM International, Materials Park
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.