Acoustics Analysis of Speaker

1 

© 2011 ANSYS, Inc. November 22, 

2011 

Acoustics Analysis of 

Speaker

2 

Introduction 


2011 

ANSYS 14.0 offers many enhancements 

in the area of acoustics. 

In this presentation, an example speaker analysis will 

be shown to highlight some of the acoustics 

enhancements in 14.0: 

• Structural-acoustic coupling using the symmetric fluidstructure 

interaction (FSI) algorithm 

• Postprocessing velocities 

• Far-field postprocessing of acoustic field (output of 

pressure and SPL outside of meshed region)

3 

Background on Acoustics 


2011 

Acoustics in ANSYS Mechanical involves solving the 

acoustic wave equation to determine the 

propagation of acoustic waves in a fluid medium: 

2 

� 1 � � 

�� p 

� 

� 

�� 

2 

� � 

a 

a 

�x� ��x�c 

�x� �� 

� 

• The above includes non-uniform medium and mass 

source terms, new in 14.0. 

This is converted in matrix form 

to solve with finite elements: 

� ��p �� 

�C ��p� �� K ��p� � �q� M p 

p 

p 

p 

Q 

� � j� 

x

4 

� 1 � 1 

2 �� 

�� M q � 

�� 

� �o 

� g 

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0 



2011 

Vibroacoustic problems can be solved by coupling 

the acoustic and structural equations together: 

S 

q 

� 

�� 

� 

0 

M 

u 

� 

��q� 

� � � 

� 

�u� 

�� 

p � q� 

� 

� 1 

� 

� C 

j� 

�o 

� 

�� 

C fs 

j�q 

� � 1 

��q� 

�� 

K 

� � � � 

� 

o 

�u� 

� 

�� 

� 0 

• The symmetric form of the harmonic FSI equations 

shown above is introduced in 14.0 for faster solution 

times. The fluid-structure coupling term is C fs. An 

unsymmetric form from prior releases is still available. 

• The sloshing term S q exists for free surfaces. 

• Since the equations are tightly coupled, the structural 

motions generate sound, and the acoustic waves can 

vibrate the structure. 

q 

C 

C 

fs 

u 

q 

� 

0 ��q� 

� f 

� � � � 

��u� 

� f 

Ku 

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5 



2011 

Perfectly Matched Layers or PML is a special 

formulation to absorb outgoing acoustic waves in 

harmonic response analyses to prevent waves from 

reflecting back into the system. 

Sound Pressure Level or SPL is defined as follows: 

� 

L � 

p � 20log 

� 

� 

• P rms is the root-mean-square of the pressure, or the 

amplitude divided by sqrt(2) 

• SPL is measured in decibels 

• The reference pressure in air is typically taken as 20 mPa. 

p 

p 

rms 

ref 

� 

� 

� 

�

6 

Geometry & Mesh of Structure 


2011 

The geometry of the speaker in an enclosure is 

shown below. Note that ¼ symmetry is used: 

For the speaker, forces are 

exerted on the voicecoil, 

causing it to move. 

The voicecoil moves the cone 

which is what displaces the 

air to produce sound. 

The surround and spider 

connect and stabilize the cone 

to the rigid frame.

7 

Geometry and Mesh of Air 


2011 

The air surrounding the speaker enclosure is shown: 

The air around the speaker is 

meshed with acoustic fluid 

elements. 

To absorb outgoing acoustic 

waves, perfectly-matched 

layers (PML) is used. This 

PML region is shown on the 

right.

8 

Activating Acoustic Elements 


2011 

A “Commands (APDL)” object is inserted under the 

acoustic bodies 

In the example shown on 

the right, the “et” 

command changes the 

element type to be an 

acoustic element using 

the new symmetric FSI 

algorithm. 

Density and speed of 

sound are also defined. 

New in 14.0!

9 

Fluid-Structure Interaction (FSI) 


2011 

In vibroacoustic problems solved in ANSYS 

Mechanical, the term FSI refers to coupling of the 

acoustic and structural equations 

• ANSYS Mechanical can solve modal, transient, or 

harmonic response analyses with FSI 

The acoustic linear wave equations are solved with 

the structural equations of motion in a coupled 

manner (in one matrix).

10 

Created Named Selection for PML 

The outermost, 

truncated boundary 

should be specified 

through a Named 

Selection. This will be 

referenced with a 

“Commands” object, 

shown later 


2011 

A Named Selection of the truncated boundary is 

created for PML

11 

Create Named Selection for FSI 

The surfaces between 

the acoustic bodies 

and structural bodies 

should be selected and 

placed in a Named 

Selection. This will 

also be referenced 

later in a “Commands” 

object. 


2011 

A Named Selection of the FSI interface is also created

12 

Define PML and FSI Regions 

The APDL commands 

on the right define the 

boundary condition on 

the PML region as well 

as apply the FSI flag to 

the Named Selections 

indicated previously. 


2011 

Another “Commands (APDL)” object is inserted 

under the “Harmonic Response” branch

13 

User-Defined Results for Pressure 


2011 

User-Defined Results allow for postprocessing 

acoustic pressure or calculating SPL 

Isosurfaces of sound 

pressure level are shown 

on the right. 

Identifiers and 

expressions in User- 

Defined Results provide 

flexibility to manipulate 

results

14 

User-Defined Results for Velocity 


2011 

Velocities can be plotted with a User-Defined Result 

using PGVECTORS 

Standard vector plot 

controls such as solid 

vectors, uniform vector 

distribution, uniform 

vector size are available. 

Here, “line” vectors at 

each node designating 

the velocity is shown. 

New in 14.0!

15 

Perform Far-Field Postprocessing 

The lines shown in 

the highlighted 

section are used 

for far-field 

postprocessing. 

Namely, HFSYM 

defines symmetry 

planes, and PLFAR 

is used to plot 

results. 

New in 14.0! 


2011 

A “Commands (APDL)” object under the “Solution” 

branch allows for far-field postprocessing

16 

Perform Far-Field Postprocessing 


2011 

The directivity plot at 1 meter (beyond mesh 

domain) is shown below 

One can determine how 

focused the acoustic signal 

is from this plot, which can 

help evaluate speaker 

performance. 

New in 14.0!

17 

Perform Frequency Sweep 


2011 

While a frequency sweep can be specified within a 

Harmonic Response analysis, one can also use 

Workbench Parameters to specify the sweep 

Note that “Frequency” is a 

Workbench Parameter. 

The frequency for the analysis 

is made as a parameter equal 

to this value. 

The benefit to this approach is 

that users can add frequencies 

to the solution after solving 

without having the re-solve 

the entire frequency range

18 

Perform Frequency Sweep with RSM 


2011 

By using this approach, users can also take 

advantage of Remote Solve Manager (RSM) to 

submit jobs on a cluster 

• Instead of solving each frequency sequentially, if a user 

has more than one ANSYS Mechanical license, the jobs 

can be submitted through RSM 

• Whether solving locally, on two machines, or on a 

cluster, multiple frequencies can then be solved 

simultaneously, thus decreasing overall solution time!

19 

Review Frequency Sweep Results 


2011 

After the solution is complete, one can plot results 

within the Workbench Parameters page 

An output of SPL in front of 

the speaker, designated 

earlier, is tracked in this 

example. 

In speaker design, a constant 

response is sought within the 

frequency range of interest. 

This example shows that 

structural resonance around 

800 Hz is causing undesirable 

behavior.

New in 14.0! 

20 

New Symmetric Option in 14.0 


2011 

In the past, ANSYS Mechanical solved these two 

physics simultaneously with unsymmetric matrices, 

which required double the memory and more CPU 

time. In ANSYS 14.0, symmetric option is introduced 

to cut memory requirements in half and significantly 

decreasing CPU time. 

The table on the right compares 

the overall solution time speed-up 

for 275k DOF solved on dual quadcore 

Intel Xeon E5530. 

Note that the symmetric option is 

about 1.5 times faster for this 

model on this model on this 

particular hardware. 

Cores Solver Option Speed-up 

1 Sparse Unsym 1.00 

1 Sparse Sym 1.64 


2 Sparse Sym 1.56 


4 Sparse Sym 1.50

21 

Using GPU Accelerator 


2011 

The GPU Accelerator can also help decrease solution 

time for vibroacoustic problems. GPU Accelerator 

performs the solver computation on the graphics 

card cores. 

The table on the right compares 

the overall solution time speed-up 

for 275k DOF solved on dual quadcore 

Intel Xeon E5530. 

Note that the GPU Accelerator 

provides noticeable speed-up for 

this model on this model on this 

particular hardware. 

Cores Solver GPU Speed-up 

1 Sparse off 1.00 



1 Sparse on 2.24 

2 Sparse on 2.68 

4 Sparse on 3.00

22 

Other New 14.0 Features in Acoustics 


2011 

There are a myriad of other new acoustics features 

not covered in this presentation: 

• Non-uniform acoustic medium, which can be a function 

of temperature or static pressure 

• Acoustic scattering capability and ability to output total 

or scattered pressure 

• Ability to input bulk viscosity to model viscous losses 

• Mass sources, impedance sheet, normal velocity b.c. 

• Near-field postprocessing 

• Ability to define external 

planar wave, monopole, 

dipole sources

Acoustics Analysis of Speaker

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