nach oben

Structural and Multidisciplinary Optimization

Erschienen in:

11.12.2017 | RESEARCH PAPER

On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation

verfasst von: Bin Niu, Xiaomeng He, Yao Shan, Rui Yang

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 6/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This work deals with the topological design of vibrating continuum structures. The vibration of continuum structure is excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. In comparison with well-known compliance minimization in static topology optimization, various objective functions are proposed in literature to minimize the response of vibrating structures, such as power flow, vibration transmission, and dynamic compliances, etc. Even for the dynamic compliance, different definitions are found in literature, which have quite different formulations and influences on the optimization results. The aim of this paper is to provide a comparison of these different objective functions and propose reference forms of objective functions for design optimization of vibration problems. Analytical solutions for two degrees of freedom system and topological design of plane structures in numerical examples are compared using different optimization formulations for given various excitation frequencies. The results are obtained by the finite element method and gradient based optimization using analytical sensitivity analysis. The optimized topologies and vibration response of the optimized structures are presented. The influence of excitation frequencies and the eigenfrequencies of the structure are discussed in the numerical examples.

Vorheriger Artikel Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

Nächster Artikel An integrated optimization for laminate design and manufacturing of a CFRP wheel hub based on structural performance

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Allaire G (2002) Shape optimization by the homogenization method. Springer Verlag, New YorkCrossRefMATH

Allaire G, Aubry S, Jouve F (2001) Eigenfrequency optimization in optimal design. Comput Methods Appl Mech Eng 190(28):3565–3579MathSciNetCrossRefMATH

Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202CrossRef

Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefMATH

Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654MATH

Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer-Verlag, BerlinMATH

Cheng G, Olhoff N (1981) An investigation concerning optimal design of solid elastic plates. Int J Solids Struct 17(3):305–323MathSciNetCrossRefMATH

Cherkaev A (2000) Variational methods for structural optimization. Springer Verlag, New YorkCrossRefMATH

Cremer L, Heckl M, Petersson BAT (2005) Structure-borne sound. Springer, BerlinCrossRef

Diaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35(7):1487–1502MathSciNetCrossRefMATH

Du J, Olhoff N (2007a) Minimization of sound radiation from vibrating bi-material structures using topology optimization. Struct Multidiscip Optim 33(4–5):305–321CrossRef

Du JB, Olhoff N (2007b) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim 34(2):91–110MathSciNetCrossRefMATH

Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–389CrossRef

Gardonio P, Elliott SJ (1998) Driving point and transfer mobility matrices for thin plates excited in flexure. In: ISVR technical report no 277. University of, Southampton

Goyder HGD, White RG (1980) Vibrational power flow from machines into built-up structures, part I: introduction and approximate analyses of beam and plate-like foundations. J Sound Vib 68(1):59–75CrossRefMATH

Guo X, Cheng G-D (2010) Recent development in structural design and optimization. Acta Mech Sinica 26(6):807–823MathSciNetCrossRefMATH

Jensen JS (2007) Topology optimization of dynamics problems with Pade approximants. Int J Numer Methods Eng 72(13):1605–1630MathSciNetCrossRefMATH

Jensen JS (2011) Waves and vibrations in inhomogeneous structures - bandgaps and optimal designs. Technical University of Denmark, Lyngby

Jog CS (2002) Topology design of stpuctures subjected to periodic loading. J Sound Vib 253(3):687–709CrossRef

Jung J, Hyun J, Goo S, Wang S (2015) An efficient design sensitivity analysis using element energies for topology optimization of a frequency response problem. Comput Methods Appl Mech Eng 296:196–210MathSciNetCrossRef

Kang Z, Zhang X, Jiang S, Cheng G (2012) On topology optimization of damping layer in shell structures under harmonic excitations. Struct Multidiscip Optim 46(1):51–67MathSciNetCrossRefMATH

Krog LA, Olhoff N (1999) Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives. Comput Struct 72(4):535–563CrossRefMATH

Larsen AA, Laksafoss B, Jensen JS, Sigmund O (2009) Topological material layout in plates for vibration suppression and wave propagation control. Struct Multidiscip Optim 37(6):585–594MathSciNetCrossRefMATH

Le C, Bruns TE, Tortorelli DA (2012) Material microstructure optimization for linear elastodynamic energy wave management. J Mech Phys Solids 60(2):351–378MathSciNetCrossRefMATH

Liu H, Zhang W, Gao T (2015) A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations. Struct Multidiscip Optim 51(6):1321–1333MathSciNetCrossRef

Ma ZD, Kikuchi N, Hagiwara I (1993) Structural topology and shape optimization for a frequency-response problem. Comput Mech 13(3):157–174MathSciNetCrossRefMATH

Ma ZD, Kikuchi N, Cheng HC (1995) Topological Design for Vibrating Structures. Comput Methods Appl Mech Eng 121(1–4):259–280MathSciNetCrossRefMATH

Min S, Kikuchi N, Park YC, Kim S, Chang S (1999) Optimal topology design of structures under dynamic loads. Struct Optim 17(2–3):208–218

Niu B, Yan J, Cheng G (2009) Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency. Struct Multidiscip Optim 39(2):115–132CrossRef

Olhoff N, Du JB (2006). Topological design optimization of vibrating structures. Cjk-Osm 4: the fourth China-Japan-Korea joint symposium on optimization of structural and mechanical systems. Kunming, China, November 6-9, 2006 G. D. Cheng, S. T. Liu and X. Guo (eds): 509–514

Olhoff N, Du J (2014). Topological design for minimum dynamic compliance of structures under forced vibration. Topology Optimization in Structural and Continuum Mechanics, 325-339. G. Rozvany and T. Lewiński. Springer, Heidelberg

Olhoff N, Du J (2016) Generalized incremental frequency method for topological designof continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency. Struct Multidiscip Optim 54(5):1113–1141MathSciNetCrossRef

Olhoff N, Niu B (2016) Minimizing the vibrational response of a lightweight building by topology and volume optimization of a base plate for excitatory machinery. Struct Multidiscip Optim 53(3):567–588MathSciNetCrossRef

Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solids Struct 49(22):3158–3169CrossRef

Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(1):2–11CrossRef

Rivin EI (2003) Passive vibration isolation. ASME Press, New YorkCrossRef

Rivin EI (2010) Handbook on stiffness and damping in mechanical design. ASME Press, New YorkCrossRef

Rozvany GIN, Lewiński T (2014) Topology optimization in structural and continuum mechanics. Springer, HeidelbergCrossRefMATH

Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4(3–4):250–252CrossRef

Shu L, Wang MY, Fang Z, Ma Z, Wei P (2011) Level set based structural topology optimization for minimizing frequency response. J Sound Vib 330(24):5820–5834CrossRef

Sigmund O (1994) Design of material structures using topology optimization. Technical University of Denmark, Lyngby

Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4–5):401–424CrossRef

Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans R Soc A Math Phys Eng Sci 361(1806):1001–1019MathSciNetCrossRefMATH

Sigmund O, Maute K (2013) Topology optimization approaches - A comparative review. Struct Multidiscip Optim:1–25

Sun HL, Chen HB, Zhang K, Zhang PQ (2008) Research on performance indices of vibration isolation system. Appl Acoust 69(9):789–795CrossRef

Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH

Tartar L (2000) An introduction to the homogenization method in optimal design in optimal shape design (Troia, 1998). In: Cellina A, Ornelas A (eds) Lecture notes in mathematics, vol 1740. Springer, Berlin, pp 47–156

Tavakoli R (2016) Optimal design of multiphase composites under elastodynamic loading. Comput Methods Appl Mech Eng 300:265–293MathSciNetCrossRef

Tcherniak D (2002) Topology optimization of resonating structures using SIMP method. Int J Numer Methods Eng 54(11):1605–1622CrossRefMATH

Tenek LH, Hagiwara I (1994) Eigenfrequency maximization of plates by optimization of topology using homogenization and mathematical-programming. JSME Int J Ser C 37(4):667–677

Tortorelli DA, Michaleris P (1994) Design sensitivity analysis: overview and review. Inverse Prob Eng 1(1):71–105CrossRef

Wang J, Mak CM (2013) An indicator for the assessment of isolation performance of transient vibration. J Vib Control 19(16):2459–2468CrossRef

Yi G, Youn BD (2016) A comprehensive survey on topology optimization of phononic crystals. Struct Multidiscip Optim 54(5):1315–1344MathSciNetCrossRef

Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199(25–28):1744–1763MathSciNetCrossRefMATH

Zargham S, Ward TA, Ramli R, Badruddin IA (2016) Topology optimization: a review for structural designs under vibration problems. Struct Multidiscip Optim 53(6):1157–1177MathSciNetCrossRef

Zhao J, Wang C (2016) Dynamic response topology optimization in the time domain using model reduction method. Struct Multidiscip Optim 53(1):101–114MathSciNetCrossRef

Titel: On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation
verfasst von: Bin Niu
Xiaomeng He
Yao Shan
Rui Yang
Publikationsdatum: 11.12.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 6/2018
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-017-1859-1

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 6/2018

Discrete Material and Thickness Optimization of laminated composite structures including failure criteria

Kriging-assisted design optimization of the impeller geometry for an automotive torque converter

Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review

Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method

Optimization of an auxetic jounce bumper based on Gaussian process metamodel and series hybrid GA-SQP algorithm

Topology optimization of continuum structures under hybrid uncertainties

Premium Partner

Marktübersichten