Design of stop-band filter by use of curved pipe segments and shape optimization.

*(English)*Zbl 1274.74292Summary: It is often desirable to isolate some parts of a compound slender spatial structure from vibrations in connected substructures. An example of such a problem is found in domestic pipe systems where vibration from pumps and valves installed in an assembled pipe system should be suppressed before it reaches installations in dwellings. By use of Floquet theory and a shape optimization procedure a stop-band design is tuned into a specified frequency range. The structures with prescribed stop-band characteristics are composed of curved and straight pipe segments. For comparison vibro-acoustic energy transmission analysis is made on periodic piping systems where a finite series of the same substructures are implemented as a stop-band filter. The influence of production tolerances of such a stop-band filter is also assessed.

##### MSC:

74P10 | Optimization of other properties in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

49Q10 | Optimization of shapes other than minimal surfaces |

##### Software:

EDA
PDF
BibTeX
XML
Cite

\textit{A. Søe-Knudsen}, Struct. Multidiscip. Optim. 44, No. 6, 863--874 (2011; Zbl 1274.74292)

Full Text:
DOI

##### References:

[1] | Bendsøe MP, Sigmund O (2003) Topology optimization, theory, methods and applications, 2nd edn. Springer, Berlin, pp 138–148 |

[2] | Bendsøe MP, Olhoff N, Taylor JE (1983) A variational formulation for multicriteria structural optimization. J Struct Mech 11:523–544 |

[3] | Brillouin L (1953) Wave propagation in periodic structures, 2nd edn. Dover, New York · Zbl 0050.45002 |

[4] | Cox SJ, Dobson DC (1999) Maximizing band gaps in two-dimensional photonic crystals. Soc Ind Appl Mat 59:2108–2120 · Zbl 1027.78521 |

[5] | Diaz AR, Haddow AG, Ma L (2005) Design of band-gap grid structures. Struct Multidisc Optim 29:418–431 |

[6] | Fahy F (2001) Foundation of engineering acoustics. Academic, London, pp 181–183 |

[7] | Floquet MG (1883) Sur les equations differentiells linéaires á coefficents périodiques (in French). Ann Sci de L’ÉNS 2:47–88 |

[8] | Halkjær S, Sigmund O, Jensen JS (2005) Inverse design of phononic crystals by topology optimization. Zeitscrift für Kristallographie 220:895–905 |

[9] | Hinch EJ (1991) Perturbation methods. Cambrige University Press, Cambrige, pp 1–13 |

[10] | Holst-Jensen O, Sorokin SV (2010) An Investigation of periodic structure to suppress the transmission of energy in an elastic tube, and 6 DOF techniques to detect it. In: Brennan MJ, Kovacic I, Lopes V Jr, Murphy KD, Petersson BAT, Rizzi SA, Yang T (eds) Proceedings of the X international conference on recent advances in structural dynamics, Southampton, 12–14 July. ISBN 9780854329106 |

[11] | Jensen JS (2003) Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. J Sound Vib 266:1053–1078 |

[12] | Krang B, Riedel CH (2003) Free vibration analysis of planar curved beams. J Sound Vib 260:19–44 |

[13] | Krause EF (1986) Taxicab geometry: an adventure in non-euclidean geometry. Dover, New York |

[14] | Lee S-K, Mace BR, Brennan MJ (2007) Wave propagation, reflection and transmission in curved beams. J Sound Vib 306:636–656 |

[15] | Martinez WL, Martinez AR (2005) Exploratory data analysis with MATLAB®. Chapmann & Hall/CRC, London, chapter 5 |

[16] | Martinsson PG, Movchan AB (2003) Vibrations of lattice structures and phononic band-gaps. Q J Mech Appl Math 56:45–64 · Zbl 1044.74020 |

[17] | Mead DJ (1998) Passive vibration control. Wiley, Chichester |

[18] | Miller DW, von Flotow A (1989) A travelling wave approach to power flow in structural networks. J Sound Vib 128:145–162 |

[19] | Misra AK, Païdoussis MP, Van KS (1988a) On the dynamics of curved pipes transporting fluid Part I: inextensible theory. J Fluid Struct 2:221–244 · Zbl 0661.73035 |

[20] | Misra AK, Païdoussis MP, Van KS (1988b) On the dynamics of curved pipes transporting fluid Part II: Extensible theory. J Fluid Struct 2:245–261 · Zbl 0661.73036 |

[21] | Olhoff N (1989) Multicriterion structural optimization via bound formulation and mathematical programming. Struct Optim 1:11–17 |

[22] | Païdoussis MP (1998) Slender structures and axial flow volume 1. Academic, San Diego, pp 415–426 |

[23] | Paland E-G (2002) Technisches Taschenbuch (in German). INA-Schaeffler KG, Bavaria, p 171 |

[24] | Price WL (1983) Global optimization by controlled random search. J Optim Theory Appl 40:333–348 · Zbl 0494.90063 |

[25] | Rostafinski W (1974) Analysis of propagation of waves of acoustic frequencies in curved ducts. J Acoust Soc Am 56:11–15 |

[26] | Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans R Soc 361:1001–1019 · Zbl 1067.74053 |

[27] | Sorokin SV, Olhoff N, Ershova OA (2008) Analysis of energy transmission in spatial piping systems with heavy internal fluid loading. J Sound Vib 310:1141–1166 |

[28] | Svanberg K (1987) The method of moving asymptotes–a new method for structural optimization. Int J Numer Methods Eng 24:359–383 · Zbl 0602.73091 |

[29] | Søe-Knudsen A (2010) On advantage of derivation of exact dynamical stiffness matrices from boundary integral equations (L). J Acoust Soc Am 128:551–554 |

[30] | Søe-Knudsen A, Sorokin SV (2010a) Modelling of linear wave propagation in spatial fluid filled pipe systems consisting of elastic curved and straight elements. J Sound Vib 329:5116–5146 |

[31] | Søe-Knudsen A, Sorokin SV (2010b) Analysis of linear elastic wave propagation in piping systems by a combination of the boundary integral equations method and the finite element method. Contin Mech Thermodyn 22:647–662 · Zbl 1234.74027 |

[32] | Walsh SJ, White RG (2000) Vibration power transmission in curved beams. J Sound Vib 233:455–488 |

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.