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Modeling the high-frequency complex modulus of a silicone rubber using standing lamb waves and an inverse finite element method
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. Umeå University, Faculty of Science and Technology, Centre for Biomedical Engineering and Physics (CMTF).
Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics. Umeå University, Faculty of Science and Technology, Centre for Biomedical Engineering and Physics (CMTF). Dept. of Engineering Sciences and Mathematics, Luleå University of Technology, Sweden.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. Umeå University, Faculty of Science and Technology, Centre for Biomedical Engineering and Physics (CMTF).
2014 (English)In: IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, ISSN 0885-3010, E-ISSN 1525-8955, Vol. 61, no 12, 2106-2120 p.Article in journal (Refereed) Published
Abstract [en]

To gain an understanding of the high-frequency elastic properties of silicone rubber, a finite element model of a cylindrical piezoelectric element, in contact with a silicone rubber disk, was constructed. The frequency dependent elastic modulus of the silicone rubber was modeled by a four parameter fractional derivative viscoelastic model in the 100 kHz to 250 kHz frequency range. The calculations were carried out in the range of the first radial resonance frequency of the sensor. At the resonance, the hyperelastic effect of the silicone rubber was modeled by a hyperelastic compensating function. The calculated response was matched to the measured response by using the transitional peaks in the impedance spectrum that originates from the switching of standing Lamb wave modes in the silicone rubber. To validate the results, the impedance responses of three 5 mm thick silicone rubber disks, with different radial lengths, were measured. The calculated and measured transitional frequencies have been compared in detail. The comparison showed very good agreement, with average relative differences of 0.7 %, 0.6 %, and 0.7 % for the silicone rubber samples with radial lengths of 38.0 mm, 21.4 mm, and 11.0 mm, respectively. The average, complex, elastic modulus of the samples were: (0.97 + 0.009i) GPa at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz.

Place, publisher, year, edition, pages
IEEE Press, 2014. Vol. 61, no 12, 2106-2120 p.
Keyword [en]
piezoelectric, silicone rubber, impedance, resonance, lamb waves, phantom
National Category
Medical Laboratory and Measurements Technologies Electrical Engineering, Electronic Engineering, Information Engineering Fluid Mechanics and Acoustics
Research subject
Electronics
Identifiers
URN: urn:nbn:se:umu:diva-88214DOI: 10.1109/TUFFC.2014.006471ISI: 000345944300017OAI: oai:DiVA.org:umu-88214DiVA: diva2:714397
Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2017-04-22Bibliographically approved
In thesis
1. Detecting Inclusions in a Silicone Rubber Phantom Using Standing Lamb Waves and Multiple Frequency Footprints
Open this publication in new window or tab >>Detecting Inclusions in a Silicone Rubber Phantom Using Standing Lamb Waves and Multiple Frequency Footprints
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The thesis deals with one major question: is it possible, using one piezoelectric sensor/vibrator, to detect a hard inclusion in a silicone rubber phantom? The question was approached with an open mind and the task was subdivided into three clearly identifiable parts: characterization of the piezoelectric sensor/vibrator (paper I), creating a model of the visco-elastic properties of a tissue-like material (phantom) in contact with the sensor/vibrator (paper II), and to detect the presence of a hard inclusion in the phantom (paper III). All vibrations of the sensor/vibrator and phantom was modeled using a finite element method (FEM). To minimize the computational time and to maximize the FEM model's ability to correctly reproduce the vibrations, a two-dimensional model system consisting of a cylindrical piezoelectric sensor/vibrator, emitting radial elastic waves in to a cylindrical disk-shaped phantom, was chosen. The piezoelectric sensor/vibrator was characterized using a parameter tuning procedure using harmonic overtones. The procedure enables tuning of the electro-elastic parameters of the sensor/vibrator so that the measured and calculated impedance frequency responses match. Silicone rubber was chosen as a phantom to mimic soft tissue. The properties of the phantom was modeled using a fractional derivative visco-elastic model. The hyperelastic effect at the first radial resonance of the sensor vibrator was corrected for by a compensating function. The high frequency complex visco-elastic modulus of the silicone rubber was determined using the transitions of standing Lamb waves in the phantom. The presence of a ring-shaped inclusion in the phantom, of polyamide, was detected using the change of the transitional Lamb wave patterns in the phantom. The tuning of the PZT5A1 sensor/vibrator parameters yielded a match between the calculated and the measured impedance spectra better than 0.54%. The average, complex, elastic modulus of three silicone rubber, Silgel 612, samples were: (0.97 + 0.009i) GPa  at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz. The presence of a polyamide inclusion, PA6GPE, was detected in the phantom using multiple frequency footprints.

Abstract [sv]

Denna avhandling berör frågan: är det möjligt, med en piezoelektrisk sensor/vibrator, att detektera ett hårt objekt inneslutet i en fantom av silikongummi? Frågan närmades utan begränsningar och uppgiften delades upp i tre tydliga delar: karaktäriseringen av den piezoelektriska sensorn/vibratorn (paper I), skapa en modell av det viskoelastiska uppförandet hos ett vävnadsliknande material (fantom) som står i kontakt med sensorn-/vibratorn (paper II) och att detektera förekomsten av ett hårt objekt inneslutet i fantomen (paper III). En finit element modell (FEM) skapades för att beräkna vibrationerna hos sensorn/vibratorn och fantomen. För att minimera beräkningstiden och maximera modellens förmåga att återge vibrationer på ett korrekt sätt, så skapades ett tvådimensionellt modellsystem bestående av en cylindrisk piezoelektrisk sensor/vibrator i kontakt med en cylindrisk fantom av silikongummi. Sensorn/vibratorn skickar radiella elastiska vågor in i fantomen. Den piezoelektriska sensorn/vibratorn karakteriserades med hjälp av en procedur som anpassar parametervärden med hjälp av övertoner. Proceduren möjliggör en justering av parametervärdena så att uppmätta och beräknade impedansspektra överensstämmer. En 'fractional derivative' modell av de viskoelastiska egenskaperna hos silikongummit skapades. De hyperelastiska egenskaperna vid första radiella resonansen blev kompenserade med hjälp av en sigmoidformad funktion. Den komplexa viskoelastiska modulen bestämdes för höga frekvenser med hjälp av transitioner hos stående Lambvågor i fantomen. Närvaron av ett hårt ringformat objekt i fantomen detekterades med hjälp av förändringar i mönstret hos de stående Lambvågorna. Justeringen av de piezoelektriska parametrarna hos elementet PZT5A1 gav som mest en skillnad på 0.54% mellan uppmätta och beräknade impedansspektra. Medelvärdet hos tre prov av silikongummit Silgel 612 av den komplexa elastiska modulen uppmättes till (0.97 + 0.009i) GPa  vid 100 kHz och (0.97 + 0.005i) GPa vid 250 kHz. Närvaron av ett hårt objekt, gjort av polyaramid (PA6GPE), detekterades i fantomen med hjälp av multifrekvensiella fotavtryck.

Place, publisher, year, edition, pages
Umeå: Umeå Universitet, 2014. 65 p.
Series
Resonance Sensor Lab, ISSN 1653-6789 ; 7
Keyword
Piezoelectric, Silicone rubber, Impedance, Resonance, Lamb waves, Phantom
National Category
Medical Laboratory and Measurements Technologies
Research subject
Electronics
Identifiers
urn:nbn:se:umu:diva-88220 (URN)978-91-7601-055-6 (ISBN)
Public defence
2014-05-27, Naturvetarhuset, plan 4, N460, Umeå universitet, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2014-05-06 Created: 2014-04-28 Last updated: 2015-08-11Bibliographically approved

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Jonsson, Ulf GLindahl, Olof AAndersson, Britt M
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IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control
Medical Laboratory and Measurements TechnologiesElectrical Engineering, Electronic Engineering, Information EngineeringFluid Mechanics and Acoustics

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