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Erschienen in: Structural and Multidisciplinary Optimization 3/2016

30.10.2015 | RESEARCH PAPER

Minimizing the vibrational response of a lightweight building by topology and volume optimization of a base plate for excitatory machinery

verfasst von: Niels Olhoff, Bin Niu

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 3/2016

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Abstract

This paper deals with the problem of minimizing the vibration amplitude response of a lightweight building from rotating machinery by extended topology optimization of a flexible, single material base plate for the machinery. A modular lightweight building is modeled and used for the analysis of the vibrational response. The excitation frequency is assumed to be given, and the design objective is chosen as minimization of the product of the frequency response of the building transmitted from the machinery base plate, and the volume of solid material used in the design of the base plate. The design and performance of optimized machinery base plates are illustrated and discussed by means of numerical example problems with different excitation frequencies, different levels of Rayleigh damping, and different installation positions of the base plate with the machinery in the building. Finally, the satisfaction of the KKT (Karush-Kuhn-Tucker) necessary condition for optimality is investigated for one of the numerically optimized designs.

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Literatur
Zurück zum Zitat Andersen LV, Kirkegaard PH, Persson K, Kiel N, Niu B (2012) A modular finite-element model for analysis of vibration transmission in multi-storey lightweight buildings. Proceedings of the Eleventh International Conference on Computational Structures Technology (CST2012). Civil-Comp Press, Dubrovnik Andersen LV, Kirkegaard PH, Persson K, Kiel N, Niu B (2012) A modular finite-element model for analysis of vibration transmission in multi-storey lightweight buildings. Proceedings of the Eleventh International Conference on Computational Structures Technology (CST2012). Civil-Comp Press, Dubrovnik
Zurück zum Zitat Arora JS (2004) Introduction to optimum design, 2nd edn. Elsevier Academic Press, Amsterdam Arora JS (2004) Introduction to optimum design, 2nd edn. Elsevier Academic Press, Amsterdam
Zurück zum Zitat Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optimization 1(4):193–202CrossRef Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optimization 1(4):193–202CrossRef
Zurück zum Zitat Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, BerlinMATH Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, BerlinMATH
Zurück zum Zitat Bendsøe MP, Lund E, Olhoff N, Sigmund O (2005) Topology optimization—broadening the areas of application. Control Cybern 34(1):7–35MathSciNetMATH Bendsøe MP, Lund E, Olhoff N, Sigmund O (2005) Topology optimization—broadening the areas of application. Control Cybern 34(1):7–35MathSciNetMATH
Zurück zum Zitat Bendsøe MP, Olhoff N, Sigmund O (2006) (Eds.) Proc. IUTAM Symp. topological design optimization of structures, machines and materials—status and perspectives, Copenhagen, Denmark, 26–29 October 2005. Springer, Berlin Bendsøe MP, Olhoff N, Sigmund O (2006) (Eds.) Proc. IUTAM Symp. topological design optimization of structures, machines and materials—status and perspectives, Copenhagen, Denmark, 26–29 October 2005. Springer, Berlin
Zurück zum Zitat Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26-27):3443–3459CrossRefMATH Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26-27):3443–3459CrossRefMATH
Zurück zum Zitat Calvel S, Mongeau M (2007) Black-box structural optimization of a mechanical component. Comput Ind Eng 53(3):514–530CrossRef Calvel S, Mongeau M (2007) Black-box structural optimization of a mechanical component. Comput Ind Eng 53(3):514–530CrossRef
Zurück zum Zitat Cheng G, Yan J (2014) Feasible domain and optimum topology of frames subject to frequency constraints. Proceedings of the Twelfth International Conference on Computational Structures Technology (CST2014). Civil-Comp Press, Naples Cheng G, Yan J (2014) Feasible domain and optimum topology of frames subject to frequency constraints. Proceedings of the Twelfth International Conference on Computational Structures Technology (CST2014). Civil-Comp Press, Naples
Zurück zum Zitat Christensen BB (2008) Topology optimization: chapter 4 -topology optimization of the base plate for single-stage centrifugal pump. Master Thesis, Aalborg University, Aalborg Christensen BB (2008) Topology optimization: chapter 4 -topology optimization of the base plate for single-stage centrifugal pump. Master Thesis, Aalborg University, Aalborg
Zurück zum Zitat Cook RD, Malkus DS, Plesha ME, Witt RJ (2002) Concepts and applications of finite element analysis. Wiley, New York Cook RD, Malkus DS, Plesha ME, Witt RJ (2002) Concepts and applications of finite element analysis. Wiley, New York
Zurück zum Zitat Dahl J, Jensen JS, Sigmund O (2008) Topology optimization for transient wave propagation problems in one dimensional design of filters and pulse modulators. Struct Multidiscip Optim 36(6):585–595MathSciNetCrossRefMATH Dahl J, Jensen JS, Sigmund O (2008) Topology optimization for transient wave propagation problems in one dimensional design of filters and pulse modulators. Struct Multidiscip Optim 36(6):585–595MathSciNetCrossRefMATH
Zurück zum Zitat Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38 Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38
Zurück zum Zitat 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 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
Zurück zum Zitat Du J, Olhoff N (2007a) 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 Du J, Olhoff N (2007a) 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
Zurück zum Zitat Du J, 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(6):545, Editors’s ErratumMathSciNetCrossRefMATH Du J, 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(6):545, Editors’s ErratumMathSciNetCrossRefMATH
Zurück zum Zitat Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–389CrossRef Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–389CrossRef
Zurück zum Zitat Fulford RA, Gibbs BM (1999) Structure-borne sound power and source characterization in multi-point-connected systems, part 2: about mobility functions and free velocities. J Sound Vib 220(2):203–224CrossRef Fulford RA, Gibbs BM (1999) Structure-borne sound power and source characterization in multi-point-connected systems, part 2: about mobility functions and free velocities. J Sound Vib 220(2):203–224CrossRef
Zurück zum Zitat Halkjaer S, Sigmund O, Jensen JS (2006) Maximizing band gaps in plate structures. Struct Multidiscip Optim 32(4):263–275CrossRef Halkjaer S, Sigmund O, Jensen JS (2006) Maximizing band gaps in plate structures. Struct Multidiscip Optim 32(4):263–275CrossRef
Zurück zum Zitat Hu YD (1990) Practical multi-objective optimization. Shanghai Scientific and Technical Press, Shanghai Hu YD (1990) Practical multi-objective optimization. Shanghai Scientific and Technical Press, Shanghai
Zurück zum Zitat Hussein MI, Hamza K, Hulbert GM, Scott RA, Saitou K (2006) Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics. Struct Multidiscip Optim 31(1):60–75CrossRef Hussein MI, Hamza K, Hulbert GM, Scott RA, Saitou K (2006) Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics. Struct Multidiscip Optim 31(1):60–75CrossRef
Zurück zum Zitat ISO (1997) ISO 2631-1: mechanical vibration and shock evaluation of human exposure to whole-body vibration. Part 1: general requirements. International Organization for Standardization, Geneva ISO (1997) ISO 2631-1: mechanical vibration and shock evaluation of human exposure to whole-body vibration. Part 1: general requirements. International Organization for Standardization, Geneva
Zurück zum Zitat ISO (2003) ISO 2631-2: mechanical vibration and shock evaluation of human exposure to whole-body vibration. Part 2: vibration in buildings (1 Hz to 80 Hz). International Organization for Standardization, Geneva ISO (2003) ISO 2631-2: mechanical vibration and shock evaluation of human exposure to whole-body vibration. Part 2: vibration in buildings (1 Hz to 80 Hz). International Organization for Standardization, Geneva
Zurück zum Zitat Jensen JS (2003) Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. J Sound Vib 266(5):1053–1078CrossRef Jensen JS (2003) Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. J Sound Vib 266(5):1053–1078CrossRef
Zurück zum Zitat Jensen JS (2007) Topology optimization of dynamics problems with Pade approximants. Int J Numer Methods Eng 72(13):1605–1630MathSciNetCrossRefMATH Jensen JS (2007) Topology optimization of dynamics problems with Pade approximants. Int J Numer Methods Eng 72(13):1605–1630MathSciNetCrossRefMATH
Zurück zum Zitat Jensen JS, Pedersen NL (2006) On maximal eigenfrequency separation in two-material structures: The 1D and 2D scalar cases. J Sound Vib 289(4-5):967–986CrossRef Jensen JS, Pedersen NL (2006) On maximal eigenfrequency separation in two-material structures: The 1D and 2D scalar cases. J Sound Vib 289(4-5):967–986CrossRef
Zurück zum Zitat Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709CrossRef Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709CrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat Le C, Bruns TE, Tortorelli DA (2012) Material microstructure optimization for linear elastodynamic energy wave management. J Mech Phys Solids 60(2):351–378MathSciNetCrossRefMATH Le C, Bruns TE, Tortorelli DA (2012) Material microstructure optimization for linear elastodynamic energy wave management. J Mech Phys Solids 60(2):351–378MathSciNetCrossRefMATH
Zurück zum Zitat Ma ZD, Kikuchi N, Cheng HC (1995) Topological design for vibrating structures. Comput Methods Appl Mech Eng 121(1-4):259–280MathSciNetCrossRefMATH Ma ZD, Kikuchi N, Cheng HC (1995) Topological design for vibrating structures. Comput Methods Appl Mech Eng 121(1-4):259–280MathSciNetCrossRefMATH
Zurück zum Zitat Ni C, Yan J, Cheng G, Guo X (2014) Integrated size and topology optimization of skeletal structures with exact frequency constraints. Struct Multidiscip Optim 50(1):113–128CrossRef Ni C, Yan J, Cheng G, Guo X (2014) Integrated size and topology optimization of skeletal structures with exact frequency constraints. Struct Multidiscip Optim 50(1):113–128CrossRef
Zurück zum Zitat Niu B, Olhoff N (2012) Minimization of structure-borne noise in lightweight buildings. Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM). Beijing, China Niu B, Olhoff N (2012) Minimization of structure-borne noise in lightweight buildings. Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM). Beijing, China
Zurück zum Zitat 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 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
Zurück zum Zitat Niu B, Andersen LV, Kiel N, Flodén O, Sandberg G (2012) Vibration transmission in a multi-storey lightweight building: a parameter study. Proceedings of the Eleventh International Conference on Computational Structures Technology (CST2012). Civil-Comp Press, Dubrovnik Niu B, Andersen LV, Kiel N, Flodén O, Sandberg G (2012) Vibration transmission in a multi-storey lightweight building: a parameter study. Proceedings of the Eleventh International Conference on Computational Structures Technology (CST2012). Civil-Comp Press, Dubrovnik
Zurück zum Zitat Olhoff N, Du J (2006) Topological design optimization of vibrating structures. CJK-OSM 4: The Fourth China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems: 509-514 Olhoff N, Du J (2006) Topological design optimization of vibrating structures. CJK-OSM 4: The Fourth China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems: 509-514
Zurück zum Zitat Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solids Struct 49(22):3158–3169CrossRef Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solids Struct 49(22):3158–3169CrossRef
Zurück zum Zitat Pavic G, Elliott AS (2010) Structure-borne sound characterization of coupled structures—Part I: simple demonstrator model. J Vib Acoust 132(4):041008CrossRef Pavic G, Elliott AS (2010) Structure-borne sound characterization of coupled structures—Part I: simple demonstrator model. J Vib Acoust 132(4):041008CrossRef
Zurück zum Zitat Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(1):2–11CrossRef Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(1):2–11CrossRef
Zurück zum Zitat Rozvany GIN (2009a) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217–237MathSciNetCrossRefMATH Rozvany GIN (2009a) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217–237MathSciNetCrossRefMATH
Zurück zum Zitat Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optimization 4(3–4):250–252CrossRef Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optimization 4(3–4):250–252CrossRef
Zurück zum Zitat Rozvany GIN, Querin OM, Gaspar Z, Pomezanski V (2002) Extended optimality in topology design. Struct Multidiscip Optim 24(3):257–261CrossRef Rozvany GIN, Querin OM, Gaspar Z, Pomezanski V (2002) Extended optimality in topology design. Struct Multidiscip Optim 24(3):257–261CrossRef
Zurück zum Zitat Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4-5):401–424CrossRef Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4-5):401–424CrossRef
Zurück zum Zitat Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans R Soc London, Ser A 361(1806):1001–1019MathSciNetCrossRefMATH Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans R Soc London, Ser A 361(1806):1001–1019MathSciNetCrossRefMATH
Zurück zum Zitat SIMULIA (Dassault Systèmes Corp.) (2011) ABAQUS Analysis User’s Manual Version 6.11, Providence, RI, USA SIMULIA (Dassault Systèmes Corp.) (2011) ABAQUS Analysis User’s Manual Version 6.11, Providence, RI, USA
Zurück zum Zitat Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH
Zurück zum Zitat Tcherniak D (2002) Topology optimization of resonating structures using SIMP method. Int J Numer Methods Eng 54(11):1605–1622CrossRefMATH Tcherniak D (2002) Topology optimization of resonating structures using SIMP method. Int J Numer Methods Eng 54(11):1605–1622CrossRefMATH
Zurück zum Zitat The MathWorks Inc. (2010) MATLAB version 7.11.584 (R2010b). Natick, Massachusetts The MathWorks Inc. (2010) MATLAB version 7.11.584 (R2010b). Natick, Massachusetts
Zurück zum Zitat Tortorelli DA, Michaleris P (1994) Design sensitivity analysis: overview and review. Inverse Prob Eng 1(1):71–105CrossRef Tortorelli DA, Michaleris P (1994) Design sensitivity analysis: overview and review. Inverse Prob Eng 1(1):71–105CrossRef
Zurück zum Zitat Williams FW, Wittrick WH (1970) An automatic computational procedure for calculating nature frequencies of skeletal structures. Int J Mech Sci 12(9):781–791CrossRef Williams FW, Wittrick WH (1970) An automatic computational procedure for calculating nature frequencies of skeletal structures. Int J Mech Sci 12(9):781–791CrossRef
Zurück zum Zitat Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199(25–28):1744–1763MathSciNetCrossRefMATH Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199(25–28):1744–1763MathSciNetCrossRefMATH
Metadaten
Titel
Minimizing the vibrational response of a lightweight building by topology and volume optimization of a base plate for excitatory machinery
verfasst von
Niels Olhoff
Bin Niu
Publikationsdatum
30.10.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 3/2016
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-015-1345-6

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