The project: 
The design of transducers
for sound and vibration based on the Finite Element Method (FEM) is described
in this thesis. Here transducers for sound and vibration are condenser
microphones and piezoelectric accelerometers.
According to the study of piezoelectric accelerometers specifications,
Chapter 2 presents the design considerations from a theoretical point
of view. Besides these design considerations, in order to obtain better
and faster design an efficient design method is needed as well. A comparison
between the available development methods made in Chapter 3 shows that
among the methods mentioned the FEM can make more accurate estimations
of the design performances, simulate more detailed specifications, visualize
simulated results, and improve the scientific understanding.
In order to demonstrate how to realize these advantages, Chapter 4 describes
the detailed simulation procedure by simulating an existing piezoelectric
accelerometer. The results substantiate that the FEM can be used to simulate
the piezoelectric accelerometers to the degree of precision required for
R&D for existing accelerometers and the FEM can improve the scientific
understanding of piezoelectric accelerometers.
Based on the FE method described in Chapter 4, detailed analyses are made
for different piezoelectric accelerometer designs in Chapter 5. The results
show that with same seismic mass: (1) DeltaShear design has the highest
sensitivity due to the contribution from the other components to the active
seismic mass; (2) Annular Shear design has the highest mounted resonance
frequency; (3) the Upright compression design has the biggest base bending
effect; (4) the Planar shear design is the lightest.
Chapter 6 presents the design procedures of two new designs. Good agreements
are achieved between the specifications of the physical and virtual prototypes.
The results substantiate that the FEM can simulate the piezoelectric accelerometers
to the degree of precision required for R&D for prevision accelerometers.
Besides, detailed analyses such as the analysis of the thickness of the
thick film, the analysis of the glue influence, etc. are made. All these
works improve the scientific understanding of piezoelectric accelerometers.
After the description of the successful FEM implementation to the piezoelectric
accelerometer design, the thesis describes the FEM application to the
condenser microphone design. It has to be stated that the work behind
this part is not aiming to simulate all detailed microphone specifications
since we for example cannot calculate on the microphone acoustics due
to the iii fact that the strong point of the commercial code used for
this project is structure analysis. The main purpose is to simulate the
opencircuit sensitivity and the diaphragm collapse voltage.
Traditional condenser microphones based on precision mechanics and silicon
condenser microphones based on micromechanics are discussed in this part.
As presented in Chapter 7, the main construction difference between the
two kinds of microphones related with the work done in this thesis is
the shape of the diaphragm and the backplate. The traditional one has
a circular diaphragm and a circular backplate while the silicon one has
an octagonal diaphragm and a quadratic backplate.
The modeling of circular condenser microphones is described in Chapter
8. Good agreements are achieved between the simulated and analytical static
deflection profile, fundamental resonance frequency, and collapse voltage.
Comparisons between the simulated and measured capacitance and opencircuit
sensitivity of two B & K Type 4190 microphones present good agreements.
The optimization of the backplate dimension according to the opencircuit
sensitivity is presented at last.
Chapter 9 presents the modeling of silicon condenser microphones. Due
to the special shape of the diaphragm and the backplate, there is not
any analytical model for these microphones. The FE simulation result is
the only available reference for the fundamental resonance frequency,
static deflection profile, collapse voltage and the opencircuit sensitivity.
An experimental verification is made with three B & K silicon condenser
microphones. Good agreements are achieved. At the end, the optimization
of the backplate dimension according to the opencircuit sensitivity is
made.
The work presented in Chapter 8 and 9 show: (1) the FEM can be used to
simulate traditional and silicon condenser microphones to the degree of
precision required for R&D for existing products; (2) the virtual prototype
improves the scientific understanding of traditional and silicon condenser
microphones; (3) the FE simulation gives designers the opportunity to
go to the limits of what is physically possible with traditional and silicon
condenser microphones to achieve the best design concerning the opencircuit
sensitivity.
Finally, in Chapter 10 the most important conclusions of this thesis are
summarized and some suggestions for the future work are given.
The project period was 1998 to 2001.
Supervisor was Ass.
Professor Torben Lenau

Publications: 
B. Liu,
Q. Yao and B. Kriegbaum: Finite Element Based Design and Optimization
for Piezoelectric Accelerometers, InterNoise
98', Christchurch, New Zealand, 1998, 4 pages.
A systematic Finite Element design and optimisation procedure
is implemented for the development of piezoelectric accelerometers. Most
of the specifications of accelerometers can be obtained using the Finite
Element simulations. The deviations between the simulated and calibrated
sensitivities and resonance are proved to be within 8%. The computerised
design and optimisation makes it possible to minimise the development time
and cost to a maximum extent. As examples, the Finite Element simulations
for standard Brüel & Kjær OrthoShear accelerometer 4506 and
ThetaShear accelerometer 4507 are given.
Bin Liu: Piezoelectric Accelerometers
Development, International Congress on Sound and Vibration ICSV,
Lyngby, 1999.
The paper describes the development of piezoelectric accelerometers
using Finite Element (FE) approach. Brüel & Kjær Accelerometer
Type 8325 is chosen as an example to illustrate the advanced accelerometer
development procedure. The deviation between simulated results and measured
results of Type 8325 are below 6%. It is proved that the specifications
of the accelerometer can be effectively predicted using the FE method,
especially when modifications of the accelerometer are required. The development
process of piezoelectric accelerometers in Brüel & Kjær
is becoming more efficient.
B. Liu, Q. Yao and B. Kriegbaum:
The Development of Piezoelectric Accelerometers Using Finite Element
Analysis, 17th International Modal Analysis Conference IMAC,
Kissimme, Orlando Florida, USA, 1999, p. 543546.
This paper describes the application of Finite Element (FE)
approach for the development of piezoelectric accelerometers. An accelerometer
is simulated using the FE approach as an example. Good agreement is achieved
between simulated results and calibrated results. It is proved that the
FE modeling can be effectively used to predict the specifications of the
accelerometer, especially when modification of the accelerometer is required.
The FE developing technology forms the bases of fast responsiveness and
flexible customized design of piezoelectric accelerometers.
B. Liu & B. Kriegbaum:
A New Annular Shear Piezoelectric Accelerometer, 18th International
Modal Analysis Conference IMAC,
San Antonio, USA, 2000, 4 pages.
This paper describes the construction and performance of
a recently introduced Annular Shear piezoelectric accelerometer, Type
4511. The design has insulated and doubleshielded case. The accelerometer
housing is made of stainless steel, AISI 316L. Piezoceramic PZ23 is used.
The seismic mass is made of tungsten. All processes and materials comply
with MILSTD11268. The mounted resonance frequency exceeds 40kHz. The
sensitivity is 10mV/g ±5%. During the design process, the new design
is evaluated and sufficiently optimized by using the Finite Element (FE)
simulation before making actual prototype. Reasonable agreement between
the experimental results of the physical prototype and the simulation
results is achieved. The design becomes more efficient. In addition, Type
4511 has a built in DeltaTronâ charge amplifier with ID and complies
with IEEEP1451.4 standard, which is a smart transducer interface for
sensors including mixedmode communication protocols and transducer electronic
data sheet (TEDS).
B. Liu and B. Kriegbaum: Piezoelectric
Accelerometers Modification Based on the Finite Element Method, International
Journal of Acoustics and Vibration, March 2000, Volume 5, Number 1, Page:
2326, printed in St. Petersburg, Russia.
The paper describes the modification of piezoelectric accelerometers
using a Finite Element (FE) method. Brüel & Kjær Accelerometer
Type 8325 is chosen as an example to illustrate the advanced accelerometer
development procedure. The deviation between the measurement and FE simulation
results of Type 8325 is below 6%. It is proved that the specifications
of the accelerometer can be effectively predicted using the FE method,
especially when modifications of the accelerometer are required.
B. Liu & B. Kriegbaum:
A new annular shear piezoelectric accelerometer, Brüel &
Kjær Technical Review, 2000 (accepted for publication), 7 pages.
Bin Liu: Piezoelectric Accelerometers
Development Based on the Finite Element Method, halfway report, Department
of Manufacturing Engineering, DTU, February 2000, 71 pages.
