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

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.

[1]  A. Haddow,et al.  Design of band-gap grid structures , 2005 .

[2]  Sergey Sorokin,et al.  Modelling of linear wave propagation in spatial fluid filled pipe systems consisting of elastic curved and straight elements , 2010 .

[3]  W. Price.  Global optimization by controlled random search , 1983 .

[4]  L. Brillouin,et al.  Wave Propagation in Periodic Structures , 1946 .

[5]  Ole Sigmund,et al.  Inverse design of phononic crystals by topology optimization , 2005 .

[6]  Chin An Tan,et al.  Free vibration analysis of planar curved beams by wave propagation , 2003 .

[7]  Steven J. Cox,et al.  Maximizing Band Gaps in Two-Dimensional Photonic Crystals , 1999, SIAM J. Appl. Math..

[8]  Ole Sigmund,et al.  Systematic design of phononic band–gap materials and structures by topology optimization , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Angel R. Martinez,et al.  : Exploratory data analysis with MATLAB ® , 2007 .

[10]  E. Krause,et al.  Taxicab Geometry: An Adventure in Non-Euclidean Geometry , 1987 .

[11]  Per-Gunnar Martinsson,et al.  VIBRATIONS OF LATTICE STRUCTURES AND PHONONIC BAND GAPS , 2003 .

[12]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[13]  David W. Miller,et al.  A travelling wave approach to power flow in structural networks , 1989 .

[14]  Jakob Søndergaard Jensen,et al.  Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures , 2003 .

[15]  W. Rostafinski.  Analysis of propagation of waves of acoustic frequencies in curved ducts , 1974 .

[16]  M. Bendsøe,et al.  A Variational Formulation for Multicriteria Structural Optimization , 1983 .

[17]  N. Olhoff.  Multicriterion structural optimization via bound formulation and mathematical programming , 1989 .

[18]  D. J. Mead.  Passive Vibration Control , 1999 .

[19]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[20]  Niels Olhoff,et al.  Analysis of the energy transmission in spatial piping systems with heavy internal fluid loading , 2008 .

[21]  S. Sorokin,et al.  Analysis of linear elastic wave propagation in piping systems by a combination of the boundary integral equations method and the finite element method , 2010 .

[22]  Alf Søe-Knudsen.  On advantages of derivation of exact dynamical stiffness matrices from boundary integral equations. , 2010, The Journal of the Acoustical Society of America.

[23]  Stephen J. Walsh,et al.  Vibrational power transmission in curved beams , 2000 .

[24]  Hinch.  Perturbation Methods , 1991 .

[25]  M. P. Païdoussis,et al.  On the dynamics of curved pipes transporting fluid. Part I: Inextensible theory , 1988 .

[26]  Brian R. Mace,et al.  Wave propagation, reflection and transmission in curved beams , 2007 .