OUTPU T 29 OUTPU T 30 OUTPU T 31 OUTPU T 32 OUTPU T 25 OUTPU T 26 OUTPU T 27 OUTPU T 28 OUTPU T 21 OUTPU T 22 OUTPU T 23 OUTPU T 24 OUTPU T 17 OUTPU T 18 OUTPU T 19 OUTPU T 20 OUTPU T 13 OUTPU T 14 OUTPU T 15 OUTPU T 16 OUTPU T 9 OUTPU T 10 OUTPU T 11 OUTPU T 12 OUTPU T 5 OUTPU T 6 OUTPU T 7 OUTPU T 8 OUTPU T 1 OUTPU T 2 OUTPU T 3 OUTPU T 4 29 30 31 32 25 26 27 28 21 22 23 24 17 18 19 20 13 14 15 16 9

A User’s Guide

The Bootstrap and Edgeworth Expansion

Sound-absorbing materials absorb most of the sound energy striking them, making them very useful for the control of noise. They are used in a variety of locations - close to sources of noise, in various paths, and sometimes close to receivers. Although all materials absorb some incident sound, the term "acoustical material" has been primarily applied to those materials that have been produced for the specific purpose of providing high values of absorption. The major uses of absorbing materials are almost invariably found to include the reduction of reverberant sound pressure levels and, consequently, the reduction of the reverberation time in enclosures, or rooms. A wide range of sound-absorbing materials exist. In the 1970s, public health concerns helped change the main constituents of sound-absorbing materials from asbestos-based materials to new synthetic fibers. Although, these new fibers are much safer for human health, more recently, issues related to global warming may increase the use of natural fibers instead of synthetic ones.

Recent Trends in Porous Sound-Absorbing Materials

A method for evaluating the acoustical properties of homogeneous and isotropic porous materials that may be modeled as fluids having complex properties is described here. To implement the procedure, a conventional, two-microphone standing wave tube was modified to include: a new sample holder; a section downstream of the sample holder that accommodated a second pair of microphone holders and an approximately anechoic termination. Sound-pressure measurements at two upstream and two downstream locations were then used to estimate the two-by-two transfer matrix of porous material samples. The experimental transfer matrix method has been most widely used in the past to measure the acoustical properties of silencer system components. That procedure was made more efficient here by taking advantage of the reciprocal nature of sound transmission through homogeneous and isotropic porous layers. The transfer matrix of a homogeneous and isotropic, rigid or limp porous layer can easily be used to identify the material’s characteristic impedance and wave number, from which other acoustical quantities of interest can be calculated. The procedure has been used to estimate the acoustical properties of a glass fiber material: good agreement was found between the estimated acoustical properties and those predicted by using the formulas of Delany and Bazley.

A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials

Wave field synthesis is a spatial sound field reproduction technique aiming at authentic reproduction of auditory scenes. Its theoretical foundation has been developed almost 20 years ago and has been improved considerably since then. Most of the original work on wave field synthesis is restricted to the reproduction in a planar listening area using linear loudspeaker arrays. Extensions like arbitrarily shaped distributions of secondary sources and three-dimensional reproduction in a listening volume have not been discussed in a unified framework so far. This paper revisits the theory of wave field synthesis and presents a unified theoretical framework covering arbitrarily shaped loudspeaker arrays for twoand three-dimensional reproduction. The paper additionally gives an overview on the artifacts resulting in practical setups and briefly discusses some extensions to the traditional concepts of WFS.

The Theory of Wave Field Synthesis Revisited

The radiation of sound from a baffled, rectangular plate with edges elastically restrained against deflection and rotation is analyzed. The elastic constants along the contour can be varied to reproduce simply supported, clamped, free, or guided edges as limiting cases. The formulation is based on a variational method for the vibration of the plate, and assumes no fluid loading of the structure. The elastic boundary conditions appear in the Hamiltonian of the plate through a dynamic contribution, which is expressed in terms of nondimensional edge parameters. The extremalization of the Hamiltonian is achieved using a Rayleigh–Ritz method, and both the free vibrations and the forced vibrations of the plate are presented. The radiation of sound from the plate is analyzed in the far field, and is calculated from one‐dimensional Fourier transforms. Numerical results are presented for the radiation efficiency of modes of simply supported, clamped, free, and guided plates. The values found agree well with predic...

A general formulation for the sound radiation from rectangular, baffled plates with arbitrary boundary conditions

This paper describes the simulations and results obtained when applying optimal control to progressive sound-field reproduction (mainly for audio applications) over an area using multiple monopole loudspeakers. The model simulates a reproduction system that operates either in free field or in a closed space approaching a typical listening room, and is based on optimal control in the frequency domain. This rather simple approach is chosen for the purpose of physical investigation, especially in terms of sensing microphones and reproduction loudspeakers configurations. Other issues of interest concern the comparison with wave-field synthesis and the control mechanisms. The results suggest that in-room reproduction of sound field using active control can be achieved with a residual normalized squared error significantly lower than open-loop wave-field synthesis in the same situation. Active reproduction techniques have the advantage of automatically compensating for the room’s natural dynamics. For the considered cases, the simulations show that optimal control results are not sensitive (in terms of reproduction error) to wall absorption in the reproduction room. A special surrounding configuration of sensors is introduced for a sensor-free listening area in free field.

Sound-field reproduction in-room using optimal control techniques: simulations in the frequency domain.

This paper presents a new volume displacement sensor (made of shaped strips of PVDF film) and the experimental implementation of this sensor in an active control system. A design strategy for a PVDF sensor detecting the volume displacement induced by a vibrating 2D structure is presented. It is based on the modal representation of the plate response. It actually consists in designing a PVDF sensor, composed of several shaped PVDF strips bonded to the surface of the structure, in such a way that the output signal of the sensor is directly proportional to the volume displacement. The design methodology is based on the experimental measurements of the plate mode shapes (eigenfunctions) and is valid for any type of boundary conditions. The experimental implementation of such a volumetric sensor in an active control system is then presented. The experimental results obtained validates this new type of volume displacement sensor.

/pdf/active-control-of-sound-radiation-from-a-plate-using-a-49dabzjue5.pdf

Active control of sound radiation from a plate using a polyvinylidene fluoride volume displacement sensor

Sound field reproduction finds applications in music or audio reproduction and experimental acoustics. For audio applications, sound field reproduction can be used to artificially reproduce the spatial character of natural hearing. The general objective is then to reproduce a sound field in a real reproduction environment. Wave field synthesis (WFS) is a known open-loop technology which assumes that the reproduction environment is anechoic. For classical WFS, the room response thus reduces the quality of the physical sound field reproduction. In this paper, adaptive wave field synthesis (AWFS) is analytically investigated as an adaptive sound field reproduction system combining WFS and active control with a limited number of reproduction error sensors to compensate the response of the listening environment. The primary point of this paper is the definition of AWFS. Therefore, the fundamental behavior of AWFS is illustrated by analytical considerations and simple free-field simulation results. As demonstrated, AWFS is fundamentally related to WFS and “Ambisonics.” The paper introduces independent adaptive control of sound field reproduction on the basis of radiation modes, via the singular value decomposition of the transfer impedance matrix. Possible practical independent control of radiation modes for AWFS is discussed.

Alain Berry

Papers

A general formulation for the sound radiation from rectangular, baffled plates with arbitrary boundary conditions

Sound-field reproduction in-room using optimal control techniques: simulations in the frequency domain.

Active control of sound radiation from a plate using a polyvinylidene fluoride volume displacement sensor

Adaptive wave field synthesis with independent radiation mode control for active sound field reproduction : Theory

Identification of dynamic loading on a bending plate using the virtual fields method