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By Fabien Anselmet, Pierre-Olivier Mattei

This didactic booklet offers the most parts of acoustics, aeroacoustics and vibrations.

Illustrated with quite a few concrete examples associated with strong and fluid continua, Acoustics, Aeroacoustics and Vibrations proposes a range of purposes encountered within the 3 fields, no matter if in room acoustics, delivery, strength creation structures or environmental difficulties. Theoretical techniques let us to research different tactics in play. usual effects, normally from numerical simulations, are used to demonstrate the most phenomena (fluid acoustics, radiation, diffraction, vibroacoustics, etc.).

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Example text

We (t) = ˆ exp(ıωt). It then gives σ ˆ = Dˆ 12 As a matter of fact, if we impose and ˙ equal to zero, it can be easily shown that the solution to σ + τ σ˙ = 0 is given by σ(t) = σ0 exp(−t/τ ). 30] for a real ν. The loss angle presents a maximum for ωτ = 1 and is then equal to tan δm = ΔE/2. The usual value of Young’s modulus is the relaxed modulus which is valid in low frequency (below the pulse 1/τ ). At high frequencies (beyond the pulse 1/τ ), the instantaneous modulus should be used. Zener has characterized this loss angle for thin metal structures.

We assume that f is twice differentiable inside S. 32]: Δf = {Δf } + σ∂n f δS + ∇ · (nσf δS ) , Take the duality product of this equality with the test function Φ. 40] because f and its partial derivatives are zero outside the surface. It should be remembered that the jump of a function when crossing a discontinuity surface is defined by “value after minus value before the surface”. 41] ∂f Let Δf, Φ = {Δf } , Φ − ∂n , Φ + f δS , ∂Φ ∂n = f, ΔΦ , n is the normal external to the surface S. If we express the duality product within the meaning of the functions (the duality product is then an integral scalar product), we easily obtain Green’s formula: Δf ΦdV − V S ∂f ΦdS + ∂n f S ∂Φ dS = ∂n f ΔΦdV.

23] If in this equation, Fourier’s law is introduced that characterizes the thermal −−→ conduction q = −kθ gradT as well as the expression of the entropy [LAN 89b] ρs = ρs0 + ρcv (T − T0 )/T0 + 3ασll , where s0 is the entropy at rest and cv is the specific heat per unit volume at constant strain, the linearized heat conduction equation is obtained: ρcv dT dσll − kθ ΔT + αT0 = ρqe . 24] represents the thermomechanical coupling. The Duhamel–Neumann law coupled with the thermal conduction equation allows thermoelastic losses to be characterized in structures.

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