Developments in Ceramic Materials Research

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224 R. Ramesh, H. Kara, Ron Stevens and C. R. Bowen characteristics of piezocomposite hydrophones. 3-dimensional FEM studies on 1-3 piezocomposites [23] and 3-3 piezocomposites [39] have demonstrated the importance of real-sized models. Before attempting to model the complicated structures of porous piezoceramics, it is worthwhile to model a dense piezoceramic element of simple geometry and validate the results with analytical or experimental data. Then, it can be extended to more complicated geometrical shapes of 3-3 piezocomposites. Several specialised finite element packages are available to model piezoelectric systems. Some of the popular and commonly used packages are, ATILA, ANSYS, PAFEC, and PZFLEX. Each one has its advantages and disadvantages. The multi physics module of ANSYS offers a convenient way of generating complicated structures and is well suited for porous piezoceramic systems. 4.1. Model of Dense PZT Discs Due to the simplicity in geometry, the dense PZT disc hydrophones are modelled by using 2-dimensional axisymmetric harmonic analysis. Consider a PZT disc of length L and radius a as shown in Figure 8. Uniform electrodes are coated on the top and bottom flat surfaces and it is poled in the axial direction. The hydrophone is encapsulated by an acoustically transparent rubber and is surrounded by water medium. The details of the axisymmetric model and the finite element mesh are shown in Figure 9. Axisymmetric coupled-field elements are used for the active material. The model includes the PZT hydrophone and the surrounding fluid (water) medium. Figure 8. Geometry of piezoceramic disc modeled. V is the voltage across the electrodes and F 1, F 2 and F3 are the forces acting on the surfaces.
Progress in Porous Piezoceramics 225 A small section of the fluid medium, which is in contact with the solid elements is assigned with acoustic elements capable of handling fluid-structure interactions. In all other fluid elements, the displacement degree of freedom (d.o.f) has been suppressed. This significantly reduces the memory requirement and the computing time. The outer boundary of the fluid mesh contains infinite acoustic damping elements. This ensures that the acoustic waves are not reflected at the boundary, simulating the infinite extent of the fluid medium. In order to obtain better numerical accuracy, the size of the mesh has been kept small compared to the dominant wavelength of the sound waves in PZT as well as in water in the vicinity of the hydrophone. That means, the mesh size has been maintained to be less than or equal to λ/5 of the highest frequency (100 kHz) studied. The nodes lying on the top and bottom electrode surfaces of the PZT disc are coupled individually and voltage d.o.f is activated. Nodes on all outer surfaces are coupled and pressure d.o.f is activated. Two different boundary conditions are applied for the present studies. In the case of the receiving sensitivity measurement, an acoustic wave of known pressure P excites the transducer from the fluid medium and the voltage generated at the electrodes is determined. For electrical impedance measurement, the outer surfaces of the transducer are stress-free and a known voltage is applied between the electrodes. Impedance is calculated from the charge collected at the electrodes. Harmonic analysis with no damping is performed in the frequency range 10 kHz-100 kHz. The electrical impedance spectrum for the dense piezoceramic hydrophone in the frequency range 10-100 kHz obtained by analytical [40], FEM and experimental studies are shown in Figure 10a. The specimen used in the experimental study is made up of PZT5H with the geometry described in Figure 8. It is seen from Figure 10a that the FEM results agree well with the analytical and experimental results. The resonance peaks observed at around 50 kHz correspond to the fundamental radial-mode of vibrations. Figure 9. The axisymmetric (2D) Finite Element Model of a dense piezoceramic disc.
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DEVELOPMENTS IN CERAMIC MATERIALS R
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Copyright © 2007 by Nova Science P
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PREFACE Ceramics are refractory, in
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Preface ix crystals is discussed. A
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Preface xi spectra and the directio
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2 Leslie G. Cecil comprehensive dat
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6 Leslie G. Cecil The main architec
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10 Leslie G. Cecil Middleton et al.
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12 Leslie G. Cecil The laser ablate
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18 Leslie G. Cecil second group (Fi
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24 Leslie G. Cecil Ixlú and Ch’i
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