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Finite Element Modeling of Ultrasonic
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Interactive figures and animationsSome interactive figures and animations which have been made during the dr. scient. work of Jan Kocbach, are presented here. These interactive figures and animations have been made using the simulation tool FEMP (Finite Element Modeling of Piezoelectric structures), which has been developed during the dr. scient work.The interactive figures and animations have been an important supplement in the interpretation of the analysis results during the dr. scient. work, and are also very useful for the reader of the dr. scient. thesis. They are therefore provided here as a service to the reader of the dr. scient. thesis and other interested people. The following material is available here
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Vibration of piezoelectric disksIn a piezoelectric disk with finite diameter (D) and thickness (T), there is no vibrational mode for which the disk vibrates like a plane piston, as is assumed in the 1D models. Instead, there is a complicated spectrum of different vibrational modes, and the vibrational characteristics of the piezoelectric disk varies strongly with the D/T ratio Using resonance frequency spectra of piezoelectric disks, in which the variation of the resonance frequencies of piezoelectric disks is shown as a function of the D/T ratio of the disks, it is possible to study the transition from one mode type to another when the D/T ratio of the disk changes, including the strong mode coupling which may occur.Below, interactive resonance frequency spectra for circular piezoelectric disks of three different materials, PZT-5A, BaTiO3 and PbTiO3 are presented. When clicking on the resonance frequency spectrum along the lines corresponding to the resonance frequencies, the corresponding eigenmode is shown.
- Mode shapes of PZT-5A disks |
Radiated sound field from piezoelectric disksThe radiated sound field from a PZT-5A disk in water with D/T ratio of 5 and the vibration of the disk is shown for selected frequencies corresponding to different vibrational modes in the PZT-5A disk.R1 modeFor the first radial mode, there are large vibrations in both radial and axial direction, because the disk expands in the thickness direction when it contracts in the radial direction, and conversely. Thus, sound waves are radiated in both the axial direction and in the radial direction, 180 degrees out of phase. The interference of these field components leads to high sidelobes, with approximately the same height as the main lobe.- MPEG file of vibration for R1 mode. (see also AVI-file)
R2 modeAt the frequency corresponding to the R2 mode for the disk with D/T=5, the middle part of the front surface of the disk is vibrating in phase with the circular edge of the disk, and out of phase with the outer part of the front surface of the disk. The radiated sound field close to the piezoelectric disk has three distinct maxima, closely related to the vibration of the disk; one at the middle of the front surface of the disk, one at the sides of the front surface of the disk, and one at the circular edge of the disk. There are strong interference effects between these field components.- MPEG file of vibration for R2 mode. (see also AVI-file)
R3/E modeFor the peak in the source sensitivity response of the PZT-5A disk with D/T=5 at around 610 kHz, corresponding to the R3/E mode, similar observations may be made as for the peak corresponding to the R2 mode. The central and outer part of the front surface of the disk vibrate out of phase with the rest of the front surface of the disk, and therefore there are maxima in the pressure amplitude of the radiated sound field corresponding to these three areas close to the piezoelectric disk, in addition to a maximum corresponding to the vibration of the circular edge of the disk. The directivity pattern is similar to the directivity pattern for the frequency of the R2 mode, except for a sidelobe at approximately 15 degrees, which is therefore assigned to the edge vibration for the edge mode.- MPEG file of vibration for R3/E mode. (see also AVI-file)
A2+ modeThe vibration at this frequency shows more similarity to the plane piston than the R modes considered above. This leads to a directivity pattern with more similarities with the directivity pattern for the plane piston radiator. The width of the main lobe is approximately the same as for the plane piston radiator, and the level of the first sidelobe is down 16 dB, whereas it is down 17.5 dB for the plane piston. There is however another sidelobe at 50 degrees which is only 14 dB down compared to the main lobe. This sidelobe is assigned to the influence from the R5 mode on the vibration for this frequency.- MPEG file of vibration for A2+ mode. (see also AVI-file)
TE1 modeThe TE1 mode is the mode which is most often used in transducer applications, and this is also the mode for which the deformation of the disk most closely resembles the vibration of a plane piston radiator. The sound pressure field close to the piezoelectric disk exhibits complicated interference effects, as for a plane piston radiator with this ka-value (ka=21.6). However, whereas the interference effects for the plane piston radiator are due to the interference between a plane wave component and a component from the edge of the radiator, the interference effects for the PZT-5A disk is k at the frequency of the TE1 mode, and is in agreement with earlier observations.- MPEG file of vibration for TE1 mode. (see also AVI-file)
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Vibration of piezoelectric disk with a front layerDue to the high characteristic acoustic impedance of most piezoceramic materials compared to the acoustic impedance of water and air, one or several front layers is often used for acoustic matching to the fluid medium in piezoelectric transducers. In the figure below, it is shown how the vibration of a PZT-5A disk with a cork front layer, in vacuum, varies when the front layer thickness is varied. |
Other publications by Jan Kocbach are to be found at this location.