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A User’s Guide

流体力学用語集 非線形音響学(Nonlinear acoustics)

https://www.win.tue.nl/~sjoerdr/papers/boek.pdf

An introduction to acoustics

With the advent of `multimedia', digital signal processing (DSP) of sound has emerged from the shadow of bandwidth limited speech processing to become a research field of its own. To date, most research in DSP applied to sound has been concentrated on speech, which is bandwidth limited to about 4 kilohertz. Speech processing is also limited by the low fidelity typically expected in the telephone network. Today, the main applications of audio DSP are high quality audio coding and the digital generation and manipulation of music signals. They share common research topics including perceptual measurement techniques and analysis/synthesis methods. Additional important topics are hearing aids using signal processing technology and hardware architectures for digital signal processing of audio. In all these areas the last decade has seen a significant amount of application-oriented research. The frequency range of wideband audio has an upper limit of 20 kilohertz and the resulting difference in frequency range and Signal to Noise Ratio (SNR) due to sample size must be taken into account when designing DSP algorithms. There are whole classes of algorithms that the speech community is not interested in pursuing or using. These algorithms and techniques are revealed in this book. This book is suitable for advanced level courses and serves as a valuable reference for researchers in the field. Interested and informed engineers will also find the book useful in their work.

Applications of digital signal processing to audio and acoustics

Lattice Boltzmann equations (LBE) are a useful tool for simulating the incompressible Navier-Stokes equations. However, LBE actually simulate a compressible but usually isothermal fluid at some small but finite Mach number. There has been recent interest in using LBE at larger, but still subsonic, Mach numbers, for which the viscous terms in the resulting momentum equation depart appreciably from those in the compressible Navier-Stokes equations. In particular, the isothermal constraint implies a nonzero ``bulk'' viscosity in addition to the usual shear viscosity. This difficulty arises at the level of the isothermal continuum Boltzmann equation prior to discretization. A remedy is proposed, and tested in numerical experiments with decaying sound waves. Conversely, an enhanced bulk viscosity is found useful for identifying or suppressing artifacts in under-resolved simulations of supposedly incompressible shear flows.

/pdf/bulk-and-shear-viscosities-in-lattice-boltzmann-equations-2itxalg2h7.pdf

Bulk and shear viscosities in lattice Boltzmann equations.

Based on physical models of musical instruments and of the human voice, a new generation of sound synthesizers is born: virtual instruments. The models used for wind instruments are simple feedback loops in which a nonlinear sound source drives a linear filter representing the pipe of the instrument. While very rewarding musical sounds have been obtained with these models, it has become obvious that some essential phenomena escape such a description. In particular the brightness of the sound generated by trombones is expected to be due to the essential nonlinearity of the wave propagation in the pipe. At fortissimo levels this leads to shock wave formation observed in our experiments both from pressure measurements and flow visualization. A modest modification of the physical model could already take this phenomenon into account. The key idea is that the nonlinear effect is essential for the transfer of sound from the source toward the listener, but can be ignored in a model of the generation of the pipe ...

/pdf/shock-waves-in-trombones-2oh3uq49g4.pdf

Shock waves in trombones

A wind instrument can be described as a closed feedback loop made up of a linear passive element-the resonator-and a lumped nonlinear element-the mouthpiece. A method for measuring the nonlinear characteristics of the mouthpiece-nonlinear flow relationship-in static condition is given. An artificial mouth is used in which the volume flow is deduced from the pressure difference between both sides of a constriction (orifice) which takes place in the resonator. The orifice also plays the role of a nonlinear absorber, thwarting possible reed oscillations. This allows the measurement of the complete characteristics. In addition, the reed opening is measured using an optical device. Results are compared to a model in which the reed is reduced to its stiffness and the flow is governed by the Bernoulli equation. It is shown that the reed stiffness and the ratio of the effective surface of the jet and the reed opening are constant in a large range of openings. Standard range values of embouchure parameters are given.

/pdf/nonlinear-characteristics-of-single-reed-instruments-4itd4u4tnv.pdf

Nonlinear characteristics of single-reed instruments: quasistatic volume flow and reed opening measurements

The harmonic balance technique is known as a time‐frequency simulation technique used for the study of large signal regimes of microwave circuits driven in forced oscillation. The technique can be adapted to self‐sustained oscillations, especially for wind musical instruments such as clarinets. The resonator (i.e., the instrument body) is the linear part, treated in the frequency domain, while the driving system (the reed) is the nonlinear part, treated in the time domain. The harmonic balance method is shown to connect the results of two known methods, so‐called weakly nonlinear (in frequency domain) and strongly nonlinear (in time domain). The advantages and disadvantages of the method are discussed.

Calculation of the steady‐state oscillations of a clarinet using the harmonic balance technique

The self-sustained oscillation of a brass wind musical instrument involves a complex aerodynamic coupling between a multimode mechanical vibratory system (the lips of the player) and a multimode acoustical vibratory system (the air column of the instrument). In this paper the behaviour of the coupled system near the threshold of oscillation is investigated using a simplified mode] in which a single meehaniea] lip mode is coupled to a single mode of the acoustical resonator. Linear stability analysis is used to study the theoretical variation of threshold blowing pressure and threshold playing frequency as functions of lip and air column parameters. The theoretical results are compared with experimental results obtained from a systematic study of the near threshold behaviour of a trombone sounded by an artificial lip mechanism. Comparability between theory and experiment is ensured by using model parameter values derived from mechanical response measurements on the artificial lips and input impedance measurements on the trombone. The measured mechanical response curve for the artificial lips exhibits severa] resonance peaks, each of which can be classified unambiguously as either "inward striking" or "outward striking". For each of these resonance peaks, parameters have been extracted and used in numerical simulation of threshold behaviour as a function of trombone slide extension. However, the experimentally observed threshold frequencies of the coupled system suggest a behaviour which passes smoothly from "inward striking" to "outward striking" character as the trombone slide is extended or the embouchure parameters changed. It seems unlikely that this type of behaviour can be eXplained using a lip model with only a single degree of freedom.

https://hal.archives-ouvertes.fr/hal-00474993/document

Brass Instruments: Linear Stability Analysis and Experiments with an Artificial Mouth

https://hal.archives-ouvertes.fr/hal-00475069/document

Joël Gilbert

Papers

Shock waves in trombones

Nonlinear characteristics of single-reed instruments: quasistatic volume flow and reed opening measurements

Calculation of the steady‐state oscillations of a clarinet using the harmonic balance technique

Brass Instruments: Linear Stability Analysis and Experiments with an Artificial Mouth

Some aspects of tuning and clean intonation in reed instruments