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 open-circuit sensitivity and the diaphragm collapse voltage.

Traditional condenser microphones based on precision mechanics and silicon condenser microphones based on micro-mechanics 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 open-circuit sensitivity of two B & K Type 4190 microphones present good agreements. The optimization of the backplate dimension according to the open-circuit 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 open-circuit 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 open-circuit 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 open-circuit 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

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. 543-546.
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 double-shielded 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 MIL-STD-11268. 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 IEEE-P1451.4 standard, which is a smart transducer interface for sensors including mixed-mode 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: 23-26, 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.