Multi-physics optimisation of ‘brass’ instruments—a new method to include structural and acoustical interactions

Brackett, David; Ashcroft, Ian; Hague, Richard

doi:10.1007/s00158-009-0394-0

Cited by 10 publications

(7 citation statements)

References 38 publications

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“…For instance, if a darker sound is desired, a stiffer structure would be required with the opposite being true for a brighter sound. At the same time, it should not be forgotten that the structure of the instrument does not affect its acoustical behavior as much as the shape of it and that of its bore (Brackett et al, 2010). According to Moore (2002), virtually everything about how a brass instrument sounds can be understood by measurements that use the input impedance profile of its geometry.…”

Section: Structural Parameters Of Brass Instrumentsmentioning

confidence: 98%

Trumpet mouthpiece manufacturing and tone quality

Zicari

MacRitchie²,

Ghirlanda³

et al. 2013

The Journal of the Acoustical Society of America

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This article investigates the relationship between the shape of the mouthpiece and its acoustical properties in brass instruments. The hypothesis is that not only different volumes but also particular cup shapes affect the embouchure and the tone quality in both a physical and perceivable way. Three professional trumpet players were involved, and two different internal cup contours characterized by a "U" and a "V" shape with two types of throat junction (round and sharp) were chosen, based on a Vincent Bach 1 [1/2] C medium mouthpiece. A third intermediate contour was designed as a combination of these. Over 600 sound samples were produced under controlled conditions, the study involving four different stages: (1) Simulation of air-flow, (2) analysis of the sound spectra, (3) study of the players' subjective responses, and (4) perceptual analysis of their timbral differences. Results confirm the U shape is characterized by a stronger air recirculation and produces stronger spectral components above 8 kHz, compared to the V shape. A round throat junction may also be preferable to a sharp one in terms of playability. There is moderate agreement on the aural perception of these differences although the verbal attributes used to qualify these are not shared.

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Section: Structural Parameters Of Brass Instrumentsmentioning

confidence: 98%

Trumpet mouthpiece manufacturing and tone quality

Zicari

MacRitchie²,

Ghirlanda³

et al. 2013

The Journal of the Acoustical Society of America

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“…47,75,76,[130][131][132][133][134][135][136][137][138][139] Many studies have addressed control-structure design interaction directly, 9,46,102,106,116,120,[140][141][142][143][144][145][146][147] while some focus on passive dynamic systems. 112,[148][149][150][151] Sensor and actuator placement combined with control design is another extensively studied area of dynamic system design optimization. 135,[152][153][154][155][156] Other important applications include automotive suspension and powertrain design, 24, 96, 99, 157-165 robotic system design, 5,7,8,20,21,91,100,101,105,…”

Section: Existing Uses Of Mdo For Dynamic System Designmentioning

confidence: 99%

Multidisciplinary Design Optimization of Dynamic Engineering Systems

Allison

Herber

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Dynamic engineering systems are playing an increasingly important role in society, especially as active and autonomous dynamic systems become more mature and prevalent across a variety of domains. Successful design of complex dynamic systems requires multidisciplinary analysis and design techniques. While multidisciplinary design optimization (MDO) has been used successfully for the development of many dynamic systems, the established MDO formulations were developed around fundamentally static system models. We still lack general MDO approaches that address the specific needs of dynamic system design. In this article we review the use of MDO for dynamic system design, identify associated challenges, discuss related efforts such as optimal control, and present a vision for fully integrated design approaches. Finally, we lay out a set of exciting new directions that provide an opportunity for fundamental work in MDO. Nomenclature a(·)= analysis function a, b = example problem parameters α, β = energy domain designations A = state matrix for a linear and time invariant system B = input matrix for a linear and time invariant system c = suspension damping coefficient ε = convergence tolerance f (·)= design objective function f (·)= derivative function f a (·) = algebraic constraint g(·)= design constraint functions g p (·) = physical system constraints γ(t) = algebraic variable vector h i = time step i = time step index j = Gauss-Seidel block index, multiple-shooting time segment index k = iteration counter k s = suspension spring stiffness K = gain matrix K * = optimal gain matrix L(·) = Lagrange or running cost term m = number of Gauss-Seidel coordinate blocks n s = number of states n t = number of time steps n T = number of time segments φ(·) = cost function φ * (·) = optimal-value function (inner loop solution) φ(·) = alternative plant design objective function ψ(·) = Mayer or terminal cost term π(·) = augmented Lagrangian penalty function t = time t F = length of the time horizon t i = time at step i T j = time at the end of time segment j u(t) = control input trajectories u * (t) = optimal control trajectories u i = control input at time step i U = matrix discretization of u(t) x = optimization variable vector x * = optimal solution x k = solution estimate at iteration k x c = control system design variable vector x p = physical system design variable vector x p * = optimal plant design X = Cartesian product of closed convex sets ξ(t) = state variable trajectories ξ * (t) = optimal state trajectories ξ i = state at time step î ξ(t) = subset of state trajectorieṡ ξ(·) = time derivative of ξ(t) Ξ = discretization of ξ(t) Ξ = subset of discretized state trajectories y = coupling variable Y = matrix of initial state values for multiple shooting time segments ζ(·) = defect constraint functions (residuals) ζ i (·) = defect constraint between time segments

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“…Braden et al 11 report on different optimization criteria for trombone bore optimization. In a recent paper by Brackett et al, 12 first steps toward inclusion of structural vibrations in brass instrument optimization are taken. Le Vey 13 treats the design as an optimal control problem where an internal energy functional is maximized with the horn profile as the control.…”

Section: Introductionmentioning

confidence: 99%

A hybrid scheme for bore design optimization of a brass instrument

Noreland

Udawalpola²,

Berggren³

2010

The Journal of the Acoustical Society of America

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This paper presents how the shape of a brass instrument can be optimized with respect to its intonation properties. The instrument is modeled using a hybrid method between a lossy one-dimensional transmission line analogy for the slowly flaring part of the instrument, and a two-dimensional finite element model for the rapidly flaring part. The optimization employs gradient-based algorithms, and allows for a large number of design variables. Through the use of an appropriate choice of design variables, the algorithm is capable of rapidly finding horn profiles that are optimal subject to various geometric constraints, such as increasing or convex bell flares. It is found that under a convexity constraint, brass wind bells that are optimal with respect to an intonation condition can be constructed of piecewise conical sections.

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Multi-physics optimisation of ‘brass’ instruments—a new method to include structural and acoustical interactions

Cited by 10 publications

References 38 publications

Trumpet mouthpiece manufacturing and tone quality

Trumpet mouthpiece manufacturing and tone quality

Multidisciplinary Design Optimization of Dynamic Engineering Systems

A hybrid scheme for bore design optimization of a brass instrument

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