The Modeling of Acoustic Fluidic Sensors Using Spectral Methods
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In this thesis, the modeling of liquid sensors consisting of layered structures, which are suitable to measure mass density and shear viscosity, is presented. Two types of sensors are considered. The Double Diaphragm Cell Sensor (invented by Erwin K.~Reichel et al.) is analyzed in detail. For this purpose a semi-numerical model is presented, which is based on a temporal and spatial Fourier transform of the governing equations. Compared to the original problem, the complexity of the thus formulated model is reduced considerably. The presented spectral approach is adapted to layered problems and features superior numerical efficiency and accuracy compared to finite element approaches.
The second sensor type examined, is a piezoelectric disc sensor with a one-sided electrode structure for lateral field excitation. In contrast to conventional sensors with double-sided metalization, the electrical fields expand into the sample liquid. This interaction has a profound effect, such that adaptions of the standard one-dimensional models are inaccurate. For this type of sensor, a semi-numeric two- and three-dimensional model is proposed which fully includes the effects of piezoelectric anisotropy, liquid conductivity and permittivity. The obtained fields and frequency responses consider all excitable modes and are in agreement with results presented in literature.
In addition to the modeling of these two sensors, the concept of acoustic impedance matrices is discussed. These matrices can be interpreted as generalized acoustic transmission line models, which naturally include the mode coupling for non-zero wavenumbers. The calculation of impedance matrices and their application to selected examples illustrate the efficiency of the method for the modeling of elastic and electroacoustic layered systems.