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Acoustics, aeroacoustics and vibrations by Fabien Anselmet, Pierre-Olivier Mattei

By Fabien Anselmet, Pierre-Olivier Mattei

This didactic ebook provides the most components of acoustics, aeroacoustics and vibrations.

Illustrated with a variety of concrete examples associated with reliable and fluid continua, Acoustics, Aeroacoustics and Vibrations proposes a range of purposes encountered within the 3 fields, even if in room acoustics, shipping, strength creation platforms or environmental difficulties. Theoretical techniques allow us to research different tactics in play. general effects, more often than not from numerical simulations, are used to demonstrate the most phenomena (fluid acoustics, radiation, diffraction, vibroacoustics, etc.).

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In the case of a perfect fluid for which the viscosity effects are negligible, the relation above is reduced to σ = −pI and shows that stress is reduced to a pressure. In the case of an incompressible viscous fluid, the normal stresses, proportional to the cubic expansion rate, are zero and the viscous stress tensor takes the following form : T = 2μ ddtD . 4. Hamilton principle We will use this principle to establish the propagation equations of mechanical waves. It is, therefore, beneficial to remember [GER 93, CRE 05].

32 Acoustics, Aeroacoustics and Vibrations domain. All these notions, initially quite different from each other, in fact form a unified whole with each part depending heavily on the others and is thereof thus inseparable. Rather than formulating a list of properties, we have voluntarily set aside the “big chunk” that the Fourier transform constitutes. This integral transform plays a primordial role in the computations of the Green kernel. It is very often the only way to explicitly compute these kernels.

Poisson’s ratio (or lateral contraction coefficient) is the ratio of the lateral contraction to the elongation. As we have just seen, ν is comprised between -1 and 1/2; but in practice, no natural material (with the 18 Acoustics, Aeroacoustics and Vibrations exception of pyrite [ZEN 48]) presents a Poisson ratio ν < 0 at the macroscopic level (it is then referred to as auxetic material) that is to say whose elongation is accompanied by a transversal dilatation; however, it is commonly known how to manufacture wire mesh-based materials that exhibit a negative Poisson ratio.

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