Acoustics AACTx R150 L01 Introduction to Acoustics

2011 ANSYS, Inc. March 4, 2014 1

Introduction to Acoustics

Acoustics ACTx R150


Acoustics ACTx


Expose 3D acoustic features in Mechanical without the need for APDL

Define acoustics properties Apply acoustic boundary conditions & loads Postprocess acoustic results

Acoustics ACT Extension


ACT allows customization in the Mechanical application :

Replace command snippets with interactive objects

Create customized Loads / BCs

Create customized Results

Ability to connect a third party solver in a standard Workbench process

ACT Acoustics extension is a customization made with ACT to integrate ANSYS acoustics capabilities in Mechanical. The extension consists of one XML file (Configures the UI content) and one python script (Implements the extension functionality).

If you need more information about ACT please contact your sales representative.

ACT: Application Customization Toolkit

2013 ANSYS, Inc. 5 March 4, 2014

ACT Extension Library

Great place to get started Extensions made available in either

binary format (.wbex file) or binary plus scripted format (python and XML files)

Scripted extensions are great examples Links to ACT documentation and training

material

Goals for an ACT developers forum

ANSYS Customer Portal support.ansys.com A library of helpful ACT extensions

available to any ANSYS customer

Roughly one dozen available More being added continually

2013 ANSYS, Inc. 6 March 4, 2014

Download the Acoustics ACT Extension

The Acoustics ACT Extension for ANSYS 15.0 is available for download on the ACT Extension Library of the Customer Portal:

https://support.ansys.com/AnsysCustomerPortal/en_us/Downloads/Extens

ion+Library/ACT+Library

Please pay attention to paragraph 9 of the CLICKWRAP SOFTWARE LICENSE AGREEMENT FOR ACS EXTENSIONS regarding TECHNICAL ENHANCEMENTS AND CUSTOMER SUPPORT (TECS): TECS is not included with the Program(s).

So to report an issue or provide your feedback in regards to this extension please contact: David Roche: [email protected]


Installing ACT Extensions

Installing from WB Project page:

1. Select the Install Extension option

2. It will open a file dialog to select a *.wbex file

3. The extension is installed

In order to work properly please note English language in WorkBench have to be chosen.


ACT Acoustics extension can be used to create acoustic boundary conditions and defining fluid bodies (elements & material properties):

Acoustics ACT Extension


Introduction to Acoustics

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Acoustics is the study of the generation, propagation, absorption, and reflection of sound pressure waves in a fluid medium. Applications for acoustics include the following:

Sonar - the acoustic counterpart of radar

Design of concert halls, where an even distribution of sound pressure is desired

Noise minimization in machine shops

Noise cancellation in automobiles

Underwater acoustics

Design of speakers, speaker housings, acoustic filters, mufflers, and many other similar devices.

Geophysical exploration

Applications

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An acoustic analysis, available in the ANSYS Multiphysics and ANSYS Mechanical programs only, usually involves modeling the fluid medium and the surrounding structure. Typical quantities of interest are the pressure distribution in the fluid at different frequencies, pressure gradient, particle velocity, the sound pressure level, as well as, scattering, diffraction, transmission, radiation, attenuation, and dispersion of acoustic waves.

A coupled acoustic analysis takes the fluid-structure interaction into account. An uncoupled acoustic analysis models only the fluid and ignores any fluid-structure interaction.

The program assumes that the fluid is compressible, but allows only relatively small pressure changes with respect to the mean pressure. Also, the fluid is assumed to be non-flowing.

The pressure solution is the deviation from the mean pressure, not the absolute pressure.

Acoustic Analysis

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Noise can be defined as " undesired sound or disagreeable. From the acoustics point of view, sound and noise constitute the same phenomenon of atmospheric pressure fluctuations about the mean atmospheric pressure. The differentiation is greatly subjective. Sound (or noise) is the result of pressure variations, or oscillations, in an elastic medium (e.g., air, water, solids), generated by a vibrating surface, or turbulent fluid flow. Sound propagates in the form of longitudinal (as opposed to transverse) waves, involving a succession of compressions and rarefactions in the elastic medium. When a sound wave propagates in air, the oscillations in pressure are above and below the mean pressure.

Sound

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As sound propagates through air (or any elastic medium), it causes measurable fluctuations in pressure, velocity, temperature and density. We can describe the physical state in terms of mean (steady state) values and small fluctuations about that mean.

For our purposes in acoustics and noise control, all we care about is the fluctuating portion.

Acoustics Variables

Physical Quantity State Variable Units

Pressure Ptotal = P + p(r,t) Pascals

Velocity Utotal = U + u(r,t) meters/second

Temperature Ttotal = T + (r,t) Celsius

Density total = + (r,t) kg/m3

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The sound travels in space. There is energy transport but there is no net transfer of mass. Each particle in the fluid moves back and forth about one position. In general, sound waves in any medium can be a mixture of longitudinal and shear waves, depending primarily on the boundary conditions.

Longitudinal Wave Simplest type of wave is compressional (or longitudinal wave) where the particle oscillation is in the same direction as the energy transport. The disturbance propagates in the direction of the particle motion. This is the predominant mechanism in fluids and gases because shear stresses are negligible.

Shear Wave The particle motion direction is orthogonal (perpendicular) to direction in which the disturbance (and the energy) propagates. In solids, you can have transverse shear and torsional waves. Bending waves (in a beam or plate), and water waves are a mixture of shear and longitudinal waves.

Sound waves

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For a longitudinal wave in an unbounded medium, sound travels at a speed of c:

E = Youngs modulus for a solid material, or the bulk modulus for a fluid = density of the material V=Volume

In normal gases, at audible frequencies, the pressure fluctuations occur under essentially adiabatic conditions (no heat is transferred between adjacent gas particles). Speed of sound then becomes:

where : =Cp/Cv=1.4 for air and P =RT (Ideal Gas Law)

Speed of sound

=

=

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In acoustics we define the wavelength as the distance between repeating features of the wave:

The time for wave to repeat (its period):

Another useful equation which relates frequency to wavelength is: c = f

Wave length

kc

2

21

fT

-1.1

-0.1

0.9

0 2 4 6 8 10 12Pre

ssu

re

Distance - x

Wavelength

-1.1

-0.1

0.9

0 2 4 6 8 10 12Pre

ssu

re

Time - t

Period T

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Human response to sound is roughly proportional to the logarithm of sound power. A logarithmic level (measured in decibels or dB) is:

An increase in 1 dB is the minimum increment necessary for a noticeably louder sound.

Other quantities of interest in acoustics are the sound power level and the sound pressure level.

Sound Intensity Level:

Sound Pressure Level:

Units & Levels

=

=

=

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The range of audible sound ranges from approximately 1 to 140 dB, although everyday sounds rarely rise above about 120 dB. The chart below shows typical noise levels of common noise sources.

Sound Pressure Levels

Sound Sources Qualitative Descriptions Sound Pressure level (dB)

Jet Tackoff, Artillery fire Intolerable 140

Rock group, Trail bike 120

Discotheque, Inside subway train very noisy 100

Noisy urban daytime noisy 80

Conversation at 1 meter 60

Quiet urban nighttime, whisper quiet 40

Recording studio very quiet 20

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The human ear responds more to frequencies between 500 Hz and 8 kHz and is less sensitive to very low-pitch or high-pitch noises. The frequency weightings used in sound level meters are often related to the response of the human ear, to ensure that the meter is measuring pretty much what you actually hear. The most common weighting that is used in noise measurement is A-Weighting. Like the human ear, this effectively cuts off the lower and higher frequencies that the average person cannot hear.

Frequency Weighting

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Most sources do not radiate equally in all directions. Example a circular piston in an infinite baffle (which is a good approximation of a loudspeaker).

Define a directivity factor Q (called D in some references):

where: P = actual rms sound pressure at angle PS = rms sound pressure of a uniform point source radiating the same total

power W as the actual source

Directivity

Piston

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All acoustic energy is dissipated into thermal energy. Dissipation is often very slow and it can be ignored for small distances or short times.

Sources of dissipation are due to:

Losses at the boundaries (relevant for porous materials, thin ducts, and small rooms)

Losses in the medium (important when the volume of uid is large). Here, the losses are associated with:

viscosity

heat conduction

Acoustic Energy Dissipation

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A useful quantity in acoustics is impedance. It is a measure of the amount by which the motion induced by a pressure applied to a surface is impeded. Or in other words: a measure of the lumpiness of the surface. Since frictional forces are, by and large, proportional to velocity, a natural choice for this measure is the ratio between pressure and velocity:

If we define the reflection coefficient R:

The impedance with no reflection (of a plane wave) is thus:

Impedance & Reflection coefficient

u

pZ

00

00

cZ

cZ

p

pR

00cZ

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As sound strikes a wall, some of it is reflected, while some is absorbed by the wall. A measure of that absorption is the absorption coefficient , defined as:

While some of the absorbed sound is dissipated as heat in the material, some re-radiates from the other side. The amount of energy that gets into the next room is quantified by the transmission coefficient:

Absorption can be obtained by three primary mechanisms: porous materials, panel resonators or volume resonators

Sound Absorption

Incident

Reflected

Transmitted

incident

reflectedincident

incident

absorbed

I

II

I

I

incident

transmited

I

I

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Quarter wave tubes are commonly used in applications such as air intake induction system on engines, pump pulsation abatement, and other narrow band noise mitigation applications. The length of a quarter wave tube is a quarter of a wavelength of the noise it is tuned to. The acoustic wave travels down the quarter wave tube and back, travelling half the wavelength which in turn experiencing 180 degree phase shift interfering with the incoming acoustic wave, destructively, abating the target noise.

Quarter Wave Resonator

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Helmholtz resonator is a side branch acoustic absorber.

Its make-up consists of a rigid cavity communicating with the external medium through a port (neck). The fluid in the resembles a mechanical mass element. The pressure in the cavity changes by the influx and efflux of fluid through the neck, making the cavity to act as a spring element. The break-up of vortices created in the shear layer dissipates energy, acting as a damper.

Helmholtz Resonator

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There are different ways to determine the impedance or the absorption coefficient of a material:

Free field methods under anechoic conditions

Reverberant field methods

Impedance tube methods

Impedance & Absorption coefficient

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The two important noise-related quantities of a material are:

Ability to absorb acoustic energy -

Ability to reflect or block sound energy - STL or

Good absorbing materials allow sound pressure fluctuations to enter their surface and dissipate energy by air friction. The are generally porous and lightweight, such as fiberglass, open cell foam, or acoustical ceiling tiles. Good barrier materials reflect sound, and are dense and nonporous (concrete, lead, steel, brick, glass, gypsum board). In general, a single homogeneous material will not be both a good absorber and a barrier. Fiberglass insulation makes a terrible barrier, and a sealed concrete wall has virtually no absorption. To get the best of both worlds, it is common to see an absorbing layer laminated to a barrier material, for instance a layer of gypsum board and a layer of fiberglass, or loaded vinyl laminated to open cell foam.

What is the difference between an absorbing material and a barrier material?

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There are three different types of boundary conditions in Acoustics:

Dirichlet condition:

Homogeneous (Open tube: Sound Soft Boundary):

Inhomogeneous (Applied pressure):

Neumann condition:

Homogeneous (Closed tube: Sound Hard Boundary):

Inhomogeneous (Velocity excitation):

Robin condition (Given admittance):

Note: By default the natural boundary condition is acoustics corresponds to a rigid wall.

Boundary Conditions

0p

Pp

0v 0

x

p

Vv x

p

jV

1

Ypjx

p0

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In fluid dynamics, slosh refers to the movement of liquid inside another object (which is, typically, also undergoing motion). Strictly speaking, the liquid must have a free surface to constitute a slosh dynamics problem, where the dynamics of the liquid can interact with the container to alter the system dynamics significantly.

Important examples include propellant slosh in spacecraft tanks and rockets (especially upper stages), and cargo slosh in ships and trucks transporting liquids (for example oil and gasoline).

Sloshing

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Sloshing in a rigid tank

Sloshing Modes Analytical Numerical

Mode 1 0.88 Hz 0.8819 Hz

Mode 2 1.05 Hz 1.0506 Hz

Mode 3 1.25 Hz 1.2496 Hz

Mode 4 1.32 Hz 1.3213 Hz

Mode 1 Mode 2 Mode 3 Mode 4

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The following common terms are used throughout this guide:

Interior problem: The sound wave oscillates in an enclosure or propagates to the infinity in a constrained structure

Exterior problem: The sound wave radiates or is scattered into the infinite open space

Coupled element: Acoustic element with FSI interface

Uncoupled element: Acoustic element without FSI interface

PML: Perfectly matched layers

Sound-hard surface: A surface on which particle normal velocity is zero

Sound-soft surface: A surface on which sound pressure is constrained

Transparent port: An exterior surface on which incident pressure is launched into the acoustic model and the reflected pressure wave is fully absorbed by a defined matched impedance that represents the infinity

Understanding Acoustic Analysis Terminology

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Governing Equations

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In acoustic fluid-structural interaction (FSI) problems, the structural dynamics equation must be considered along with the Navier-Stokes equations of fluid momentum and the flow continuity equation. The discretized structural dynamics equation can be formulated using the structural elements. The fluid momentum (Navier-Stokes) equations and continuity equations are simplified to get the acoustic wave equation using the following assumptions:

The fluid is compressible (density changes due to pressure variations).

There is no mean flow of the fluid.

Governing Equations

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Since the viscous dissipation has been taken in account using the Stokes hypothesis, the wave equation is referred to as the lossy wave equation for propagation of sound in fluids. The discretized structural and the lossy wave must be considered simultaneously in FSI problems.

The acoustic pressure exerting on the structure at the FSI interface will be considered in Derivation of Acoustics matrices to form the coupling stiffness matrix.

Harmonically varying pressure is given by:

The wave equation is reduced to the following inhomogeneous Helmholtz equation:

Governing Equations

tjerptrp Re,

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The finite element formulation is obtained by testing wave using

the Galerkin procedure. The wave equation is multiplied by

testing function w and integrated over the volume of the with

some manipulation to yield the following:

Governing Equations

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From the equation of momentum conservation, the normal velocity on the boundary of the acoustic domain is given by:

The weak form of equation is given by:

Governing Equations

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The normal acceleration of the fluid particle can be presented using the normal displacement of the fluid particle, given by:

After using the above equation:

Governing Equations

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Other terms are defined in Acoustic Fundamentals. The wave equation can be written in matrix notation to create the following discretized wave equation:

Derivation of Acoustic Matrices

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Analysis Types

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In Acoustics we can currently perform three different types of analysis:

Modal Analysis (frequency domain)

Harmonic Response Analysis (frequency domain)

Transient Analysis (time domain)

These analysis can be resolved as pure acoustic problem as well as vibro-acoustic simulation.

Analysis Types

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The goal of modal analyses is to determine frequencies and standing wave patterns within a structure

We have the ability to include impedance and interaction with structure (FSI)

Block Lanczos, Damped, Subspace and unsymmetric eigensolvers are available

Modal Analyses

Image on the right

shows standing

wave patterns in

an acoustic cavity

2011 ANSYS, Inc. March 4, 2014 42

The objective of harmonic analyses is to calculate response of system as a function of frequency based on volumetric flow rate or pressure excitation

Plot of transmission loss on bottom left, sound waves in a room shown on right.

Support Full Harmonic only

Sparse, QMR and ICCG solvers are available.

Harmonic Response Analyses

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Transient simulations allow to investigate time-dependent response of system

Example of time-history pressure plot showing beat phenomenon on left, acoustic waves generated from offshore pile driving on right (courtesy of MENCK)

Support Full Transient only

Transient Analyses

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Acoustic Material Properties

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The wave equation resolved in acoustic simulation requires mass density and sound velocity of the fluid media.

Thus these properties have to be inputted for the acoustic domains. An acoustic domain is defined with the Acoustic Body object. Man can then scope the bodies representing the fluid domain and input the mass density and the sound velocity:

Mass Density & Sound Speed

Note: MAPDL commands: MP,,DENS & MP,,SONC

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Viscosity is the degree to which a fluid resists flow. The acoustic media can sometimes be viscous (water, oil). In this case the wave equation must be modified to include the bulk viscosity term.

Governing equation Momentum and mass conservation equation

2nd order acoustic pressure equation

Acoustic Viscosity

)()3

4(0 a

B

aa vpt

v

aa vt

0

0)]1

(3

4[

1)

1(

2

000

2

2

2

000

t

p

ct

p

cp aaa

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The viscosity introduces a dissipative effect in the acoustic media as illustrated below:

The dynamic viscosity (Pa.s) can be inputted in the detail properties of the Acoustics Body:

Acoustic Viscosity

0

10

20

30

40

500 1000 1500

Tran

smis

sio

n L

oss

(d

B)

Frequency (Hz)

Transmission Loss

No Viscosity

Viscosity

Note: MAPDL command: MP,,VISC

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It is possible to define temperature varying material properties. In this goal you can set the Temperature Dependency of the Acoustics Body to Yes. Thus the material properties will become tabular data as illustrated below:

Temperature Dependent Properties

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Non Uniform Acoustic Media

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The speed of sound is variable and depends on the properties of the substance through which the wave is travelling. In fluids, only the medium's compressibility and density are the important factors.

Non-uniform Acoustic Media

Adiabatic compressibility is directly related to pressure through the heat capacity ratio (adiabatic index), and pressure and density are inversely related at a given temperature and composition, thus making only the latter independent properties (temperature, molecular composition, and heat capacity ratio) important. At a constant temperature, the ideal gas pressure has no effect on the speed of sound, because pressure and density (also proportional to pressure) have equal but opposite effects on the speed of sound, and the two contributions cancel out exactly.

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In non-uniform acoustic media the mass density and sound speed vary with the spatial position.

The wave equation in lossless media is written by:

According to the ideal gas law the equation of state and the speed of sound in an ideal gas are given by:


))(

()()(

1)

)(

1(

0

2

2

2

00 r

Q

tt

p

rcrp

r

)()(2 rRTrc

)()()( rRTrrPstate

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Assuming the density 0 and sound speed c0 at the reference temperature T0 (inputted as the Environment Temperature) and the reference static pressure (inputted in the properties of the Acoustics Body) casts the density and sound speed in media as follow:


0,

00

0

0)(

)()(;

)()(

state

state

p

T

xT

xpx

T

xTcxc

2011 ANSYS, Inc. March 4, 2014 53

Man can see the evolution of the sound speed in the acoustic media for a spatial variation of the temperature of the fluid:

Non-Uniform Acoustic Medium

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Step change in temperature shown on left, which affects propellant properties. Modal analysis predicts correct results

C.L. Oberg, N.W. Ryan, A.D. Baer, A Study of T-Burner Behavior, AIAA Journal, Vol. 6, No. 6, pp 1131-1137.

Non-Uniform Acoustic Medium

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The thermal condition can be applied on bodies using the Acoustics Temperature object available in the Loads drop down menu :

The static pressure can be applied on bodies using the Acoustics Static Pressure object available in the Loads drop down menu :

ACT Acoustics Extension

Note: MAPDL command: BF,,TEMP, value

Note: MAPDL command: BF,,CHRGD, value

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Mesh Requirement

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The mesh should be fine enough to capture the mode shapes of the structure.

For linear elements, at least 12 elements per wavelength are needed, while 6 elements per wavelength are needed for quadratic elements.

Also note that all acoustic domain must be mesh connected (nonconformed mesh not supported for acoustic domains).

Meshing Guidelines

f

c

Wavelength:

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Solving Fluid-Structure Interaction (FSI)

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If you want to take into account the fluid-structure interaction (pressure waves generated by the structure vibration or/and structure deformation due to fluid pressure) you can use coupled acoustic analysis.

Then the interaction of the fluid and the structure at a mesh interface causes the acoustic pressure to exert a force applied to the structure and the structural motions produce an effective "fluid load." The governing finite element matrix equations then become:

The analyses available with FSI are modal (symmetric & unsymmetric algorithm), harmonic (symmetric & unsymmetric algorithm) and transient (unsymmetric algorithm).

Acoustic Structure Coupling

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The interaction of the fluid and the structure at a mesh interface causes the acoustic pressure to exert a force applied to the structure and the structural motions produce an effective "fluid load." The governing finite element matrix equations then become:

[R] is a "coupling" matrix that represents the effective surface area associated with each node on the fluid-structure interface (FSI). The coupling matrix [R] also takes into account the direction of the normal vector defined for each pair of coincident fluid and structural element faces that comprises the interface surface. The positive direction of the normal vector, as the program uses it, is defined to be outward from the fluid mesh and in towards the structure. Both the structural and fluid load quantities that are produced at the fluid-structure interface are functions of unknown nodal degrees of freedom. Placing these unknown "load" quantities on the left hand side of the equations and combining the two equations into a single equation produces the following:

The foregoing equation implies that nodes on a fluid-structure interface have both displacement and pressure degrees of freedom.


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There are different approaches to define acoustic structure coupling depending of the vibro-acoustic analysis:

For modal analyses: Uncoupled, Coupled with symmetric algorithm, Coupled with Unsymmetric algorithm

For harmonic analyses: Uncoupled, Coupled with symmetric algorithm, Coupled with Unsymmetric algorithm

For transient analyses: Uncoupled, Coupled with Unsymmetric algorithm

The default approach is to use unsymmetric matrices but in V13 we introduced a more efficient symmetry formulation (for modal and harmonic).

With unsymmetric matrices we required twice of much memory because we need to store the full matrix and not only the upper triangular half so the memory required doubled and also the CPU time increases maybe about 1.5 time. So with the symmetric formulation this allow to maintain the symmetric nature of the matrices so the memory requirement doesnt double and the CPU time doesnt increase.


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Symmetric formulation:

All the elements in the model must use the symmetric formulation

Unsymmetric formulation:

In this case its possible to use both unsymmetric and uncoupled formulations. The best solution here in terms of number of DOF to compute is to create a single of layer of elements using unsymmetric algorithm at the FSI boundary and use uncoupled algorithm for all other elements.


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The coupling algorithm is chosen in the properties of the Acoustic Body depending on the analysis type:


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The FSI interfaces correspond to the acoustic domain faces in contact with structure bodies (where pressure are transferred to the structure). The acoustic Fluid-Structure interface can be identified using the FSI Interface object available in the Boundary Conditions drop down menu.

Its worth noting that if no FSI flags defined, MAPDL solver will try to automatically detect FSI surfaces. However, its good practice to define FSI manually.


Note: MAPDL command: SF,,FSI,1

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The displacements of the structure can be transferred to the fluid domain using a connected mesh or contact regions.

Please note that when you perform vibroacoustic analyses, it is strongly recommended to use a multibody part definition rather than contact.

Also, the acoustic fluid side should generally be the contact side. MPC contact works better than penalty-based, although if you have Contact Regions sharing an edge, you can get overconstraints. That is why using a multibody part is best to get accurate results.

Structure/Fluid domains connection

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Automatic creation of boundary conditions

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Clicking on this button will create an FSI Interface object scoped on all faces used by contact regions and belonging to the defined acoustic bodies (Fluid-Structure interface faces of the acoustics side when contact is used between acoustic and structural domains).

Structure/Fluid domains connection

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This tool is used to automatically create boundary conditions & loads based of the existing named selections. When the button is pressed its checked for each named selection if it contains one of the following keyword. If its the case the corresponding object is created scoped on this named selection.

Automatic creation of BC

Keyword Corresponding Object

acousticbody Acoustic Body

normalvelocity Normal Surface Velocity

normalacceleration Normal Surface Acceleration

masssource Mass Source

massrate Mass Source Rate

surfacevelocity Surface Velocity

surfaceacceleration Surface Acceleration

staticpressure Static Pressure

impsheet Impedance Sheet

temperature Temperature

pressure Acoustic Pressure

impedance Impedance Boundary

thermovisc Thermo-viscous BLI Boundary

free Free Surface

fsi FSI Interface

radiation Radiation Boundary

absorbingelem Absorbing Elements

attenuation Attenuation Surface

plot Acoustic Time_Frequency Plot

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Applications

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Underwater Example

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Speaker Example

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Acoustics AACTx R150 L01 Introduction to Acoustics

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