多年來在 PACSYS 公司的 PAFEC VibroAcoustics
軟體是一種聲音分析軟體基於有限元方法累積），這是邊界元法 (BEM)
技術開發。此軟體可以選擇的組合有限元或邊界僅有限元和邊界元法分析方法通過分析。對應于考慮結構振動的結構和聲學雜訊分析與設計的揚聲器等聲學分析的互動關係的耦合分析。 
PAFECVibroAcoustics  Application Areas
Audio
Air is a light medium and hence will generally have a lesser
effect on a vibrating structure than in underwater acoustics.
However the cone, dustcap and surround of a loudspeaker drive unit
are also light, and hence to obtain accurate results a fully coupled
analysis is necessary.
Application Areas
cone breakup
cabinet cavity modes
radiation from drive unit
diffraction from edges
placement of speakers in a small room
radiation from panels
horn design
load/displacement computation for spiders and surrounds
compression
driver design
Underwater Acoustics
For structures vibrating underwater a fully coupled vibroacoustic
solution is almost always essential. The density of fluid ensures
that the pressure field generated by the vibrating surface applies
significant loading to the structure and it vibrates differently in
fluid from in vacuo. Generally speaking modes/resonances will occur
at lower frequencies due to an added mass effect. Radiation damping
generally reduces the amplitude at resonance.
Application Areas
SONAR transducer design
array design
SONAR domes
radiation from submerged structures
scattering from submerged structures
tile design
Medical Ultrasonics
Physiotherapy transducer based on the model created by Martin
Hughes, during his PhD at the University of Bath under the
supervision of Professor Victor Humphrey, assisted by funding from
the National Physical Laboratory.
A more complete description of the transducer can be found in
"Finite Element and Boundary Element Modelling of a Medical
Ultrasound Transducer and its Generated NearField" , University of
Bath 2001.
Architectural
Acoustic finite and boundary elements solve the Helmholtz equations
exactly, within the discretization error. Thus effects such as
defraction are naturally modelled. It is also possible to model
interactions with structural objects such as windows. However, the
element size required is proportional to the wavelength, therefore
as the number of elements increases the problem becomes
computationally larger. Thus FE and BE techniques can be used to
analyse 'small rooms'
Areas of localised design, such as diffusers or apertures can
benefit from finite and boundary element analyses.
Axisymmetic analysis of a cylindrical aperature in a rigid baffle
connecting two half spaces. Each half space is bounded by an
infinite rigid baffle, with the aperature at the centre. A plane
wave is incident on the baffle in the right hand space. A
combination of acoustic finite and boundary elements are used to
model this problem.
Barriers
Finite and boundary element techniques can be used to analyse
barriers. It is relatively straightforward to predict results for
'ideal conditions'. However the effectiveness of the barrier will
change with wind conditions, and variations in temperature in the
surrounding air space will also be difficult to incorporate into the
model. A boundary element approach could be used to compare between
a number of different designs under 'ideal conditions', with the
assumption that the best design might also be best in other
circumstances.
Automotive
In automotive acoustics it is usually possible to use uncoupled
acoustic analysis. Surface vibration data may be taken from a
previous structural FE analysis or from experimental measurement.
For interior cavity problems the sound field is set up by a number
of vibrating panels. For a particular point of interest, e.g. the
driver's outside ear, a contribution to the pressure at this point
can be computed from each panel. These sum in the complex plane to
give the resultant pressure. Panels which have a positive(negative)
contribution relative to the resultant pressure are sources(sinks).
Reducing vibration at a sink will actually make the problem worse!
Application Areas
interior cavity resonances
panel contributions
source/sink identification
driveby noise
air intake/exhaust analysis
Ultrasonic Cleaning
The example below illustrates the action of an ultrasonic cleaning
device. A cermic block is attached to a steel plate at the base of
the tank containing water. The ceramic is excited by a voltage
applied across the electrodes on the upper/lower surfaces. The
vibration of the plate radiates acoustic energy into the water. The
surface at the top of the tank is defined as free. Cavitation
affects the properties of the acoustic medium, and in particular the
fluid becomes becomes lossy. The example is a simple plain strain
model.
