4. Commands specific to acoustic modeling#

During an acoustic finite element modeling study with*Code_Aster* we use general commands and commands that are specific to acoustics, or whose keywords and options are specific to this discipline; we present the list below.

The nodal values of the sound pressure on the finite element (degrees of freedom) are noted: PRES.

4.1. Definition of the characteristics of propagation media#

It is necessary to give the density (real value) and the speed of propagation (complex value); to do this, we use the command DEFI_MATERIAU < https://www.code-aster.org/V2/doc/default/fr/man_u/u4/u4.43.01.pdf>` [U4.43.01 ===`_with the following keywords:

keyword factor:	FLUIDE
keywords:	RHO	(density \({\mathrm{\rho }}_{0}\))
	CELE_C	(complex speed \({c}_{0}\))

Example:

air = DEFI_MATERIAU (FLUIDE =_F (RHO = 1.3, CELE_C = (“RI”,343.0,0.,.,))

In this case: \({c}_{0}=343.0\) is real (the imaginary part — which would represent a dissipation of material energy — is zero).

4.2. Boundary conditions#

Normal vibratory speed values per face (or two-dimensional edge) must be assigned to the cells defining the source boundaries, and also acoustic impedance values per face (two-dimensional edge) must be assigned to the cells defining the boundaries with imposed impedance. We use the acoustics-specific control AFFE_CHAR_ACOU < https://www.code-aster.org/V2/doc/default/fr/man_u/u4/u4.44.04.pdf>` [U4.44.04] ==_

4.3. Calculation of elementary matrices#

The various elementary matrices (stiffness, mass and damping) are calculated by specific options. We use the command CALC_MATR_ELEM `[U4.61.01 =”_] < https://www.code-aster.org/V2/doc/default/fr/man_u/u4/u4.61.01.pdf> with the keyword OPTION for which the possible assignment values are specified:

Keywords:	OPTION	“RIGI_ACOU”	Equation ()
		“MASS_ACOU”	Equation ()
		“AMOR_ACOU”	Equation ()

These matrices are of a complex type.

Note:

Assembled matrices can be obtained directly with the macro command ASSEMBLAGEet the same options.

4.4. Calculation of the elementary source vector#

The elementary vector is calculated by a specific option; the load must be indicated. We use the command CALC_VECT_ELEM < https://www.code-aster.org/V2/doc/default/fr/man_u/u4/u4.61.02.pdf>` [U4.61.02] ==_ with the keyword OPTION

4.5. Calculating the solution#

After assembling the elementary matrices and vectors, the harmonic solution can be calculated directly with the command DYNA_VIBRA. < https://www.code-aster.org/V2/doc/default/fr/man_u/u4/u4.53.03.pdf>` [u4.53.03]] `_.

It is also possible to calculate with the assembled matrices the perfect acoustic modes (without viscosity, therefore with real speed) on the modelled bounded domain. It is therefore necessary to use the real parts of the matrices assembled at the input of the modal calculation command. < https://www.code-aster.org/V2/doc/default/fr/man_u/u4/u4.52.02.pdf>` [U4.52.02]] `_. The concept of the result is then of the type or “MODE_ACOU”.

4.6. Post-treatments#

From the result of the resolution, post-processing commands make it possible to obtain the nodal fields of the following acoustic quantities:

Sound pressure level \({L}_{p}\) \(p\) in \(\mathit{dB}\): \({L}_{p}=20{\mathrm{log}}_{10}\left[\frac{\mid p\mid }{\mathrm{2,0}\times {10}^{-5}}\right]\)
real part of the sound pressure
imaginary part of the sound pressure

active sound intensity :math:`I=frac{1}{2}text{Re}left[p{v}^{text{}}right]`

reactive sound intensity :math:`J=frac{1}{2}text{Im}left[p{v}^{text{}}right]`

These fields are calculated using the post-processing command CALC_CHAMP (the concept of the result is of the type “ACOU_HARMO” or “MODE_ACOU”) with the keywords RESULTAT and OPTION.

« Keyword: », « RESULTAT « , « « , « » « Keyword: », « ACOUSTIQUE « , « “PRAC_ELNO” », « (pressure level in decibels) » « « , « « , « « , « (real part of the pressure) » « « , « « , « « , « (imaginary part of the pressure) » « « , « « , « “INTE_ELNO” », « » (active intensity) » « « , « « , « « , « (reactive intensity) »