Study of the bending modes in circular quartz resonators
An experimental and theoretical study of bending modes in a partially electroded circular piezoelectric quartz (AT-cut) with free edge is presented. The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane dis...
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Veröffentlicht in: | IEEE transactions on ultrasonics, ferroelectrics, and frequency control ferroelectrics, and frequency control, 2006-10, Vol.53 (10), p.1934-1943 |
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container_title | IEEE transactions on ultrasonics, ferroelectrics, and frequency control |
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creator | Leclaire, P. Goossens, J. Martinez, L. Wilkie-Chancelier, N. Serfaty, S. Glorieux, C. |
description | An experimental and theoretical study of bending modes in a partially electroded circular piezoelectric quartz (AT-cut) with free edge is presented. The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane displacements. The classical theory of bending of thin disks is used to describe the flexural modes at frequencies lower than the first thickness shear resonance (6 MHz). A fairly good agreement is found between experimental and theoretical results for the forced mode shapes and for the resonance frequencies. However, it appears that the two springs used to maintain the disk in position introduce extra clamping conditions. Several source shapes were studied, among which a collection of an arbitrary number of forces is particularly useful. The two-dimensional wavenumber representation shows the presence of anisotropy related to the crystallographic axes at higher frequencies, which is not predicted by the model. The experimental phase velocities are compared to those given by the classical theory of disks and to those of Lamb A 0 mode. This study confirms the correspondence at low frequencies between the A 0 mode and the bending eigenmodes of a disk with finite size |
doi_str_mv | 10.1109/TUFFC.2006.126 |
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The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane displacements. The classical theory of bending of thin disks is used to describe the flexural modes at frequencies lower than the first thickness shear resonance (6 MHz). A fairly good agreement is found between experimental and theoretical results for the forced mode shapes and for the resonance frequencies. However, it appears that the two springs used to maintain the disk in position introduce extra clamping conditions. Several source shapes were studied, among which a collection of an arbitrary number of forces is particularly useful. The two-dimensional wavenumber representation shows the presence of anisotropy related to the crystallographic axes at higher frequencies, which is not predicted by the model. The experimental phase velocities are compared to those given by the classical theory of disks and to those of Lamb A 0 mode. This study confirms the correspondence at low frequencies between the A 0 mode and the bending eigenmodes of a disk with finite size</description><identifier>ISSN: 0885-3010</identifier><identifier>EISSN: 1525-8955</identifier><identifier>DOI: 10.1109/TUFFC.2006.126</identifier><identifier>PMID: 17036802</identifier><identifier>CODEN: ITUCER</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Acoustics ; Anisotropy ; Bending ; Disks ; Electrodes ; Engineering Sciences ; Exact sciences and technology ; Frequency ; Fundamental areas of phenomenology (including applications) ; General equipment and techniques ; Instruments, apparatus, components and techniques common to several branches of physics and astronomy ; Laser excitation ; Laser modes ; Mathematical models ; Measurement and testing methods ; Optical pulses ; Physics ; Pulse measurements ; Quartz ; Resonance ; Shape ; Shear ; Solid mechanics ; Structural and continuum mechanics ; Studies ; Surface emitting lasers ; Transducers ; Ultrasonics, quantum acoustics, and physical effects of sound ; Voltage ; Wavenumber</subject><ispartof>IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2006-10, Vol.53 (10), p.1934-1943</ispartof><rights>2006 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2006</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c445t-517073ede08841e642b3a2d3271f7187bc5c0e0cf4cc5d125ba2a864cb6d50a63</citedby><cites>FETCH-LOGICAL-c445t-517073ede08841e642b3a2d3271f7187bc5c0e0cf4cc5d125ba2a864cb6d50a63</cites><orcidid>0000-0001-7740-5215 ; 0000-0002-8598-6053 ; 0000-0003-4290-1336 ; 0000-0002-0273-4986</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4012878$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,314,776,780,792,881,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4012878$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18155968$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/17036802$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-01324416$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Leclaire, P.</creatorcontrib><creatorcontrib>Goossens, J.</creatorcontrib><creatorcontrib>Martinez, L.</creatorcontrib><creatorcontrib>Wilkie-Chancelier, N.</creatorcontrib><creatorcontrib>Serfaty, S.</creatorcontrib><creatorcontrib>Glorieux, C.</creatorcontrib><title>Study of the bending modes in circular quartz resonators</title><title>IEEE transactions on ultrasonics, ferroelectrics, and frequency control</title><addtitle>T-UFFC</addtitle><addtitle>IEEE Trans Ultrason Ferroelectr Freq Control</addtitle><description>An experimental and theoretical study of bending modes in a partially electroded circular piezoelectric quartz (AT-cut) with free edge is presented. The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane displacements. The classical theory of bending of thin disks is used to describe the flexural modes at frequencies lower than the first thickness shear resonance (6 MHz). A fairly good agreement is found between experimental and theoretical results for the forced mode shapes and for the resonance frequencies. However, it appears that the two springs used to maintain the disk in position introduce extra clamping conditions. Several source shapes were studied, among which a collection of an arbitrary number of forces is particularly useful. The two-dimensional wavenumber representation shows the presence of anisotropy related to the crystallographic axes at higher frequencies, which is not predicted by the model. The experimental phase velocities are compared to those given by the classical theory of disks and to those of Lamb A 0 mode. This study confirms the correspondence at low frequencies between the A 0 mode and the bending eigenmodes of a disk with finite size</description><subject>Acoustics</subject><subject>Anisotropy</subject><subject>Bending</subject><subject>Disks</subject><subject>Electrodes</subject><subject>Engineering Sciences</subject><subject>Exact sciences and technology</subject><subject>Frequency</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>General equipment and techniques</subject><subject>Instruments, apparatus, components and techniques common to several branches of physics and astronomy</subject><subject>Laser excitation</subject><subject>Laser modes</subject><subject>Mathematical models</subject><subject>Measurement and testing methods</subject><subject>Optical pulses</subject><subject>Physics</subject><subject>Pulse measurements</subject><subject>Quartz</subject><subject>Resonance</subject><subject>Shape</subject><subject>Shear</subject><subject>Solid mechanics</subject><subject>Structural and continuum mechanics</subject><subject>Studies</subject><subject>Surface emitting lasers</subject><subject>Transducers</subject><subject>Ultrasonics, quantum acoustics, and physical effects of sound</subject><subject>Voltage</subject><subject>Wavenumber</subject><issn>0885-3010</issn><issn>1525-8955</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpd0FFL5DAQB_AgHrqnvvoiSBGO4x66zqRJmj4uy-15sHAPp88hTada6TaatIJ-erO3i8I9BSa_mUn-jJ0jzBGhur69W62Wcw6g5sjVAZuh5DLXlZSHbAZay7wAhGP2NcZHABSi4kfsGEsolAY-Y_rvODWvmW-z8YGymoamG-6zjW8oZt2QuS64qbche55sGN-yQNEPdvQhnrIvre0jne3PE3a3-nm7vMnXf379Xi7WuRNCjrlMq8qCGkpvEUhK8LqwvCl4iW2JuqyddEDgWuGcbJDL2nKrlXC1aiRYVZywH7u5D7Y3T6Hb2PBqvO3MzWJttjXAgguB6gWT_b6zT8E_TxRHs-mio763A_kpGl0pDkopmeTVf_LRT2FIHzFaSa10JXhC8x1ywccYqP3Yj2C26Zt_6Ztt-ialnxou91OnekPNJ9_HncC3PbDR2b4NdnBd_HQapayUTu5i5zoi-rgWgFyXungHb0qSsw</recordid><startdate>20061001</startdate><enddate>20061001</enddate><creator>Leclaire, P.</creator><creator>Goossens, J.</creator><creator>Martinez, L.</creator><creator>Wilkie-Chancelier, N.</creator><creator>Serfaty, S.</creator><creator>Glorieux, C.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>L7M</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0001-7740-5215</orcidid><orcidid>https://orcid.org/0000-0002-8598-6053</orcidid><orcidid>https://orcid.org/0000-0003-4290-1336</orcidid><orcidid>https://orcid.org/0000-0002-0273-4986</orcidid></search><sort><creationdate>20061001</creationdate><title>Study of the bending modes in circular quartz resonators</title><author>Leclaire, P. ; Goossens, J. ; Martinez, L. ; Wilkie-Chancelier, N. ; Serfaty, S. ; Glorieux, C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c445t-517073ede08841e642b3a2d3271f7187bc5c0e0cf4cc5d125ba2a864cb6d50a63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Acoustics</topic><topic>Anisotropy</topic><topic>Bending</topic><topic>Disks</topic><topic>Electrodes</topic><topic>Engineering Sciences</topic><topic>Exact sciences and technology</topic><topic>Frequency</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>General equipment and techniques</topic><topic>Instruments, apparatus, components and techniques common to several branches of physics and astronomy</topic><topic>Laser excitation</topic><topic>Laser modes</topic><topic>Mathematical models</topic><topic>Measurement and testing methods</topic><topic>Optical pulses</topic><topic>Physics</topic><topic>Pulse measurements</topic><topic>Quartz</topic><topic>Resonance</topic><topic>Shape</topic><topic>Shear</topic><topic>Solid mechanics</topic><topic>Structural and continuum mechanics</topic><topic>Studies</topic><topic>Surface emitting lasers</topic><topic>Transducers</topic><topic>Ultrasonics, quantum acoustics, and physical effects of sound</topic><topic>Voltage</topic><topic>Wavenumber</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Leclaire, P.</creatorcontrib><creatorcontrib>Goossens, J.</creatorcontrib><creatorcontrib>Martinez, L.</creatorcontrib><creatorcontrib>Wilkie-Chancelier, N.</creatorcontrib><creatorcontrib>Serfaty, S.</creatorcontrib><creatorcontrib>Glorieux, C.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>IEEE transactions on ultrasonics, ferroelectrics, and frequency control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Leclaire, P.</au><au>Goossens, J.</au><au>Martinez, L.</au><au>Wilkie-Chancelier, N.</au><au>Serfaty, S.</au><au>Glorieux, C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Study of the bending modes in circular quartz resonators</atitle><jtitle>IEEE transactions on ultrasonics, ferroelectrics, and frequency control</jtitle><stitle>T-UFFC</stitle><addtitle>IEEE Trans Ultrason Ferroelectr Freq Control</addtitle><date>2006-10-01</date><risdate>2006</risdate><volume>53</volume><issue>10</issue><spage>1934</spage><epage>1943</epage><pages>1934-1943</pages><issn>0885-3010</issn><eissn>1525-8955</eissn><coden>ITUCER</coden><abstract>An experimental and theoretical study of bending modes in a partially electroded circular piezoelectric quartz (AT-cut) with free edge is presented. The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane displacements. The classical theory of bending of thin disks is used to describe the flexural modes at frequencies lower than the first thickness shear resonance (6 MHz). A fairly good agreement is found between experimental and theoretical results for the forced mode shapes and for the resonance frequencies. However, it appears that the two springs used to maintain the disk in position introduce extra clamping conditions. Several source shapes were studied, among which a collection of an arbitrary number of forces is particularly useful. The two-dimensional wavenumber representation shows the presence of anisotropy related to the crystallographic axes at higher frequencies, which is not predicted by the model. The experimental phase velocities are compared to those given by the classical theory of disks and to those of Lamb A 0 mode. This study confirms the correspondence at low frequencies between the A 0 mode and the bending eigenmodes of a disk with finite size</abstract><cop>New York, NY</cop><pub>IEEE</pub><pmid>17036802</pmid><doi>10.1109/TUFFC.2006.126</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0001-7740-5215</orcidid><orcidid>https://orcid.org/0000-0002-8598-6053</orcidid><orcidid>https://orcid.org/0000-0003-4290-1336</orcidid><orcidid>https://orcid.org/0000-0002-0273-4986</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Acoustics Anisotropy Bending Disks Electrodes Engineering Sciences Exact sciences and technology Frequency Fundamental areas of phenomenology (including applications) General equipment and techniques Instruments, apparatus, components and techniques common to several branches of physics and astronomy Laser excitation Laser modes Mathematical models Measurement and testing methods Optical pulses Physics Pulse measurements Quartz Resonance Shape Shear Solid mechanics Structural and continuum mechanics Studies Surface emitting lasers Transducers Ultrasonics, quantum acoustics, and physical effects of sound Voltage Wavenumber |
title | Study of the bending modes in circular quartz resonators |
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