Chapter 17 Fluid-structure interaction in an acoustic...

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

Chapter 17Fluid-structure interaction in an acoustic contextJean-Louis Migeot

1. One-dimensional model

2. General 3D approach

3. Review of applications


Objectives

➢ In the « Radiation » section we have seen that vibrations induce noise

➢ In this section we will see how the pressure associated with a sound field acts on a structure and changes its dynamic behvaiour.

➢ Key idea: The presence of a surrounding fluid adds:

mass

stiffness

damping

to a vibrating structure.

➢ The concepts will be highlighted on very simple examples then generalized using a finite element formalism.


Fluid-structure interaction

Vibrating structure

Pressure distribution in acoustic fluid

Pressure wavesexcites thestructure

Vibrations inducesound waves in

the fluid


SDOF + open tube

k

d

mF

(r,c)

x

x=0

➢ Dynamic equations of the piston:

➢ Purely propagating plane wave (no reflection)

➢ Acoustic and piston velocity matching gives acoustic loading p

➢ Modified dynamic equation:

Sound radiation appears as additional damping for the mass-spring system

➢ Power dissipated in equivalent damper matches radiated acoustic power


SDOF + closed tube

k

c

mF

(r,c)

x

x=0 x=l

➢ Pressure in the closed tube excited by a mass with velocity iwU:

➢ Pressure acting on the mass = additional load

➢ Modified dynamic equations

➢ The resonant sound field in the closed cavity now appears as an added stiffness (when positive) or mass (when negative)

© Jean-Louis Migeot – MSC Software – Free Field Technologies – Université Libre de Bruxelles – Conservatoire Royal de Musique de Liège – IJK Numerics 71.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

0 100 200 300 400 500 600

Coupled response

Uncoupled response

Coupled vs. uncoupled response (strong coupling, no damping)

Added mass shift

Structure modes show in the acoustic response … and are followed by or follow an anti-resonance.

© Jean-Louis Migeot – MSC Software – Free Field Technologies – Université Libre de Bruxelles – Conservatoire Royal de Musique de Liège – IJK Numerics 8-4.E+06

0.E+00

4.E+06

0 100 200 300 400 500 600

Impédance acoustique

Impédance mécanique

Impédance totale

Acoustic impedance

Mechanical impedance

Total impedance

Added mass shift

Structure modes show in the acoustic response … and are followed by or follow an anti-resonance.

Coupled vs. uncoupled response: impedance


SDOF + Tube – General case

k

c

mF

(r,c)

x

x=0 x=l


Where does coupling come from ?

Uncoupled equations

Acoustic pressure loads the structure

Vibrations generate noise


Pressure loading


Vibrations


Coupled equations

Strong coupling

Weak coupling


Modal approaches

Structure:

Structure and fluid:


Weak coupling (1)

Vibrating structure



the fluid

➢ The structure is rigid

➢ The fluid is light

➢ The pressure field acting on the structure does not influence its vibrations


Example

P.T. model dimensions

1m20

Noise directivity


Weak coupling (2)

Vibrating structure



➢ The pressure field radiated by the vibrating structure is small compared to the incident pressure field

➢ The structure is excited by the “blocked pressure”

➢ Application:sound transmission through an aircraft fuselage, diffuse field excitation on payload


Weak coupling example


Strong or full coupling

Vibrating structure




the fluid

➢ Light structure and/or Heavy fluid:

both effects must be considered together


Strong coupling - Heavy fluid


Strong coupling - Light structure


Strong coupling - Transmission

Silencer Hybrid Analysis

Structure shell – Modal coordinates

Interior Finite Fluid – Physical coordinates

External Finite/Infinite Fluid – Physical coordinates

Vibro-Acoustic response Structure modes


E

Exhaust noise

E

IS

Shell noise

Tailpipe noise

Weak coupling:

Modal radiation matrix FE:


Conclusions

➢ A structure and the inner or outer acoustic fluid interact because:

vibrations generate sounds

sounds generate vibrations

➢ The effect of the fluid on the structure may be described in terms of:

added mass

added damping

➢ Coupling is always two-ways but in many cases one-way coupling is a fair approximation

Chapter 17 Fluid-structure interaction in an acoustic...

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