Top

Structural and Multidisciplinary Optimization

Published in:

01-09-2011 | Industrial Application

Design sensitivity analysis of acoustical damping and its application to design of musical bells

Authors: Yonggyun Yu, Byung Man Kwak

Published in: Structural and Multidisciplinary Optimization | Issue 3/2011

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Damping characteristics of a musical bell plays an important role in characterizing the musical sound. The total damping consists of acoustical damping and internal damping. Acoustical damping depends upon resonating frequencies and vibration patterns while internal damping is a material property. The acoustical damping of a vibrating structure is formulated via boundary element method and finite element method using eigenmode decomposition. The design sensitivity of acoustical damping is derived using an adjoint variable method of the eigenvalue problem. Design optimization of a musical bell is then performed in terms of acoustical parameters. The goal of the optimization problem is to design a harmonically tuned bell with given acoustical damping values. The proposed automated design process integrates finite element analysis, boundary element analysis, design sensitivity analysis, mode-tracking algorithm and optimization module, seamlessly. It is demonstrated by numerical examples to show practical applications.

previous article Topology optimization of pulse shaping filters using the Hilbert transform envelope extraction

next article Multi-objective optimization for bus body with strength and rollover safety constraints based on surrogate models

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

ANSYS 10.0 (2005) Website: http://www.ansys.com/

Arora JS, Cardoso JB (1992) Variational principle for shape design sensitivity analysis. AIAA J 30(2):538–547MATHCrossRef

Atalla N, Bernhard RJ (1994) Review of numerical solutions for low-frequency structural acoustic problem. Appl Acoust 43:271–294CrossRef

Bissinger G (2004) The role of radiation damping in violin sound. J Acoust Soc Am 5(3):82–87

Borrvall T (2001) Topology optimization of elastic continua using restriction. Arch Comput Methods Eng 8:351–385MathSciNetMATHCrossRef

Choi KK, Kim NH (2005) Structural sensitivity analysis and optimization I, 1st edn. Springer, New York

Cunefare KA, Koopmann GH (1989) The use of the boundary element method to quantify the radiation efficiency of acoustic sources. Proc Eleventh Int Conf Bound Elem Meth Engng 12(3):355–368

Cunefare KA, Currey MN (1994) On the exterior acoustic modes of structures. J Acoust Soc Am 96(4):2302–2312CrossRef

Cunefare KA, Currey MN, Johnson ME, Ellliott SJ (2001) The radiation efficiency grouping of free space acoustic radiation modes. J Acoust Soc Am 109(1):203–215CrossRef

Derogis P, Causse R (1994) A study on radiation pattern and radiation efficiency of an upright piano soundboard. J Acoust Soc Am 95(5):2912–2912CrossRef

Fletcher NH, Rossing TD (1999) The physics of musical instruments, 2nd edn. Springer, New York

Fox RL, Kapoor MP (1968) Rates of change of eigenvalue and eigenvectors. AIAA J 6(12):2426–2429MATHCrossRef

Fritze D, Marburg S, Hardtke HJ (2003) Reducing radiated sound power of plates and shallow shells by local modification of geometry. Acta Acoust United Ac 89:53–60

Hibbert WA (2008) The quantification of strike pitch and pitch shifts in church bells. Doctoral thesis, The Open University, UK

Houten MH (1998) Function approximation concepts for multidisciplinary design optimization, Dissertation. Eindhoven University of Technology

Junger MC (1951) Sound scattering by thin elastics shells. J Acoust Soc Am 24:366–373MathSciNetCrossRef

Kessels P (2001) Engineering toolbox for structural-acoustic design—applied to MRI-scanners. Doctoral Thesis, Technical University of Eindhoven

Koopmann GH, Fahnline JB (1999) Designing quiet structures. Academic, New York

Kuijpers AHWM (1999) Acoustic modeling and design of MRI scanners, Doctoral thesis. Eindhoven University, UK

Lee TH (1999) An Adjoint variable method for structural design sensitivity analysis of a distinct eigenvalue problem. J Mech Sci Tech 13(6):470–476

Lee TH (2007) Adjoint method for design sensitivity analysis of multiple eigenvalues and associated eigenvectors. AIAA J 45(8):1998–2004CrossRef

LMS (2000) User’s manual Sysnoise Revision 5.5. LMS-Numerical Technologies, Leuven

Luo J, Gea HC (1994) Modal sensitivity analysis of coupled acoustics-structural systems. J Vib Acoust 119(4):545–550CrossRef

Mangiarotty RA (1963) Acoustic radiation damping of vibrating structures. J Acoust Soc Am 35(3):369–377CrossRef

Marburg S (2002) Developments in structural-acoustic optimization for passive noise control. Arch Comput Methods Eng 9(4):291–370MATHCrossRef

Pan J, Li X, Tian J, Lin T (2002) Short sound decay of ancient Chinese music bells. J Acoust Soc Am 112(6):3042–3045CrossRef

Roozen-Kroon PJM (1992) Structural optimization of bells, Dissertation. Eindhoven University of Technology

Scarpa F (2000) Parametric sensitivity analysis of coupled acoustic-structural system. J Vib Acoust 122(2):109–115CrossRef

Schad CR, Warlimont H (1984) Acoustical investigation of the influence of the material on the sound of bells. Acta Acoust United Ac 29:1–14

Schoofs AJG, Asperen F, Maas P, Lehr A (1987) A carillon of major-third bells. Part I: computation of bell profiles using structural optimization. Music Percept 4:245–254

Schoofs AJG, Roozen-Kroon PJM, Campen DH (1994) Optimization of structural and acoustical parameters of bells. AIAA J 94:1167–1180

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

Sigmund O (2001) Design of multiphysics actuators using topology optimization—part II: two-material structures. Comput Methods Appl Mech Eng 190:6605–6627CrossRef

Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidiscipl Optim 16(1):68–75

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

Wang BP (1991) Improved approximate methods for computing eigenvector derivatives in structural dynamics. AIAA J 29(6):1018–1020CrossRef

Wang S, Choi KK (1994) Continumm sizing design sensitivity analysis of eigenvectors using Rizt Vectors. Aircr J 31:457–459CrossRef

Yu Y, Jang IG, Kim IK, Kwak BM (2010) Nodal line optimization and its application to violin top plate design. J Sound Vib 329:4785–4796CrossRef

Title: Design sensitivity analysis of acoustical damping and its application to design of musical bells
Authors: Yonggyun Yu
Byung Man Kwak
Publication date: 01-09-2011
Publisher: Springer-Verlag
Published in: Structural and Multidisciplinary Optimization / Issue 3/2011
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-011-0651-x

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 3/2011

Reduced representations of vector-valued coupling variables in decomposition-based design optimization

Kriging-based convex subspace single linkage method with path-based clustering technique for approximation-based global optimization

Multi-objective optimization for bus body with strength and rollover safety constraints based on surrogate models

Shape design optimization of SPH fluid–structure interactions considering geometrically exact interfaces

Topology optimization of pulse shaping filters using the Hilbert transform envelope extraction

Efficient multi-level design optimization using analytical target cascading and sequential quadratic programming

Premium Partners