chapter 14 acoustic materials jean-louis...

© Jean-Louis Migeot – MSC Software – Free Field Technologies – Université Libre de Bruxelles – Conservatoire Royal de Musique de Liège – IJK Numerics 1

Chapter 14Acoustic materialsJean-Louis Migeot

1. Acoustic materials

2. Sandwich panels

3. Biot theory

4. Some measurement techniques




2. Sandwich panels

3. Biot theory



Path: Structure-borne Noise & Air-borne noise

Ratio of structure-borne noise to air-borne noise of a typical car

( Source: SAE International )

Air-borne Structure-borne


Ubiquity of acoustic trim

© Autoneum

Damping

Absorption

Insulation


Absorber, Insulator & Damper

➢ Absorber:

typically porous material

performance increases with material thickness

poor insulator

➢ Insulator

impervious (non-porous) material

attenuation increases with mass of the material

poor absorber

➢ Damper

visco-elastic material characterized by a complex Young’s modulus (loss factor)

example: metal-polymer-metal sandwich, butyl, elastomer, etc.

no direct acoustic effects

➢ The three behaviors can be combined in composite sandwich panels to provide a good mix of absorption, insulation and damping


Foam and felts

Viscous dissipation by friction on the skeleton


Absorption: limits of open porous layers

➢ f = 100 Hzl/4 = 0.85 m

➢ f= 1,000 Hzl = 0.09 m

➢ f=5,000 Hzl = 0.02 m


Sound absorption in a car

( Source: SAE International )


Damping: constrained vs. unconstrained layer


Damping and absorption: complementary effects




2. Sandwich panels

3. Biot theory



Sandwich panels

Heavy Layer

Porous Layer

Damping Layer

Frame

Metal Layer

© Autoneum


Vibration Insulation

➢ The multi-layer acts as a double mass-spring system where the mass is made of the sheet metal and heavy layer and the spring stiffness is determined by the skeleton stiffness, the resistivity of the porous material and the compressibility of the air inside the pores

➢ Below the cut-offfrequency, vibrations are amplified

➢ Above this frequencyvibrations are reduced


Resonance Shift

Mass Effect Stiffness Effect Compressibility

Heavy Layer (r)

Porous Layer (E and Q)

Metal Layer


Differential stiffness and damping

➢ Bending wave celerity in the top and bottom layer are much different …

➢ … and damping in the heavy layer and the porous material further reduces the vibration amplitudes on the treated side.


Impact on radiation efficiency

➢ The noise radiation by the panel without treatment is much higher than this of the treated panel because of the reduced vibration level, the increased vibration damping and the lower radiation efficiciency of the heavy layer due to the shorter wavelength of bending waves


Flow resistance

+ + + + +

- - - -

- - - - -

+ + + +


Energy dissipation


Surface impedance

➢ The surface impedance of a composite depends on all its internal parameters and its structure can be optimized to meet specific requirements.

Effect of screen resistivity

Screen




2. Sandwich panels

3. Biot theory



Maurice Anthony Biot (1905-1985)


Poro-Elastic Model

➢ A porous material contains two phases (skeleton + air in the pores). Biot’s theory describes the interactions between the 2 phases.

➢ Hypothesis:

l is much greater than the details of the porous material

displacements are small (linear elasticity)

continuous air phase (closed pores are part of the skeleton)

elastic skeleton

no viscous effects linked to fluid trapped in closed pores

no thermo-mechanical coupling effects involved

➢ The theory sets up

an overall equilibrium equation for the mixture

the generalized Darcy law for the fluid phase

➢ Constitutive relations are written for the mixture (total stresses) and for the fluid (pressure)


Variables

➢ The following variables define the state of the system

p pressure in the fluid phase

u displacement of the frame

U displacement of the fluid

U-u relative displacement of fluid with respect to frame

➢ And the following measurable material properties are used

rs density of the frame

rF density of the fluid

W porosity

R Resistivity

a Tortuosity


Porosity W

A small volume change is imposed. The porosity can be deduced from the pressure increase.

Autoneum’s Porpos Porosity

Measurement System

W = =+

= -V

V

V

V V

V

V

f

t

f

s f

s

t

1


Static Resistivity R

➢ The pressure drop between both sides of the sample directly gives the resistivity

Sample thickness h

Pressure drop Dpv


Resistivity

Autoneum’s AFR Airflow

Resistance Measurement System

Autoneum’s CARE+ portable airflow

resistance measurement system


Tortuosity a

➢ At high frequency, the sound speed is only determined by the tortuosity

Picture courtesy of Walter Lauriks - KU Leuven


Tortuosity a

➢ The difference of electric resistivity of a conducting fluid and the sample saturated with that fluid provides a measurement of the tortuosity



Dynamic Moduli

➢ The transfer function between the displacement at the top and bottom of the sample give E and G from which n is found



Biot a Parameter

➢ Measurement on a sample in a Kundt tubes allows to identify the adequate value of the acoupling coefficient

Autoneum’s Elwis

Measurement System


Key Takeaways

➢ Three functions:

Damping

Absorption

Insulation

➢ Absorption: limits of open layers

➢ Damping: constrained vs. unconstrained layers

➢ Sandwich panels

➢ Biot theory and Biot parameters

➢ Some test set-up: RTC3, alpha-cabin, …




2. Sandwich panels

3. Biot theory



Airborne vs. structure-borne transmission

chapter 14 acoustic materials jean-louis...

Documents