Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model
Identifieur interne : 005248 ( Main/Merge ); précédent : 005247; suivant : 005249Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model
Auteurs : C. M. Wang [Singapour] ; Z. Zhang [Singapour] ; N. Challamel [France] ; W. H. Duan [Australie]Source :
- Journal of physics. D, Applied physics : (Print) [ 0022-3727 ] ; 2013.
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- Pascal (Inist)
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Abstract
In this paper, we calibrate Eringen's small length scale coefficient e0 for an initially stressed vibrating nonlocal Euler beam via a microstructured beam modelled by some repetitive cells comprising finite rigid segments and elastic rotational springs. By adopting the pseudo-differential operator and Padé's approximation, an analytical solution for the vibration frequency in terms of initial stress may be developed for the microstructured beam model. When comparing this analytical solution with the established exact vibration solution from the nonlocal beam theory, one finds that the calibrated Eringen's small length scale coefficient e0 is given by e0 = √(1/6) - (1/12)(σ0/σm) where σ0 is the initial stress and σm is the mth mode buckling stress of the corresponding local Euler beam. It is shown that e0 varies with respect to the initial axial stress, from 1/√12 ≃ 0.289 at the buckling compressive stress to 1/√6 ≃ 0.408 when the axial stress is zero and it monotonically increases with increasing initial tensile stress. The small length scale coefficient e0, however, does not depend on the vibration/buckling mode considered.
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model</title><author><name sortKey="Wang, C M" sort="Wang, C M" uniqKey="Wang C" first="C. M." last="Wang">C. M. Wang</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>Engineering Science Programme and Department of Civil and Environmental Engineering, National University of Singapore, Kent Ridge</s1><s2>Singapore 119260</s2><s3>SGP</s3><sZ>1 aut.</sZ></inist:fA14><country>Singapour</country><wicri:noRegion>Singapore 119260</wicri:noRegion><orgName type="university">Université nationale de Singapour</orgName></affiliation></author><author><name sortKey="Zhang, Z" sort="Zhang, Z" uniqKey="Zhang Z" first="Z." last="Zhang">Z. Zhang</name><affiliation wicri:level="4"><inist:fA14 i1="02"><s1>Department of Civil and Environmental Engineering, National University of Singapore, Kent Ridge</s1><s2>Singapore 119260</s2><s3>SGP</s3><sZ>2 aut.</sZ></inist:fA14><country>Singapour</country><wicri:noRegion>Singapore 119260</wicri:noRegion><orgName type="university">Université nationale de Singapour</orgName></affiliation></author><author><name sortKey="Challamel, N" sort="Challamel, N" uniqKey="Challamel N" first="N." last="Challamel">N. Challamel</name><affiliation wicri:level="3"><inist:fA14 i1="03"><s1>Université Européenne de Bretagne, University of South Brittany UBS, UBS-LIMATB, Centre de Recherche, Rue de Saint Maudé, BP92116</s1><s2>56321 Lorient</s2><s3>FRA</s3><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Région Bretagne</region><settlement type="city">Lorient</settlement></placeName></affiliation></author><author><name sortKey="Duan, W H" sort="Duan, W H" uniqKey="Duan W" first="W. H." last="Duan">W. H. Duan</name><affiliation wicri:level="1"><inist:fA14 i1="04"><s1>Department of Civil Engineering, Monash University</s1><s2>Clayton, Victoria 3800</s2><s3>AUS</s3><sZ>4 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Clayton, Victoria 3800</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">14-0221634</idno><date when="2013">2013</date><idno type="stanalyst">PASCAL 14-0221634 INIST</idno><idno type="RBID">Pascal:14-0221634</idno><idno type="wicri:Area/PascalFrancis/Corpus">000270</idno><idno type="wicri:Area/PascalFrancis/Curation">005B92</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000A74</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000A74</idno><idno type="wicri:doubleKey">0022-3727:2013:Wang C:calibration:of:eringen</idno><idno type="wicri:Area/Main/Merge">005248</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model</title><author><name sortKey="Wang, C M" sort="Wang, C M" uniqKey="Wang C" first="C. M." last="Wang">C. M. Wang</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>Engineering Science Programme and Department of Civil and Environmental Engineering, National University of Singapore, Kent Ridge</s1><s2>Singapore 119260</s2><s3>SGP</s3><sZ>1 aut.</sZ></inist:fA14><country>Singapour</country><wicri:noRegion>Singapore 119260</wicri:noRegion><orgName type="university">Université nationale de Singapour</orgName></affiliation></author><author><name sortKey="Zhang, Z" sort="Zhang, Z" uniqKey="Zhang Z" first="Z." last="Zhang">Z. Zhang</name><affiliation wicri:level="4"><inist:fA14 i1="02"><s1>Department of Civil and Environmental Engineering, National University of Singapore, Kent Ridge</s1><s2>Singapore 119260</s2><s3>SGP</s3><sZ>2 aut.</sZ></inist:fA14><country>Singapour</country><wicri:noRegion>Singapore 119260</wicri:noRegion><orgName type="university">Université nationale de Singapour</orgName></affiliation></author><author><name sortKey="Challamel, N" sort="Challamel, N" uniqKey="Challamel N" first="N." last="Challamel">N. Challamel</name><affiliation wicri:level="3"><inist:fA14 i1="03"><s1>Université Européenne de Bretagne, University of South Brittany UBS, UBS-LIMATB, Centre de Recherche, Rue de Saint Maudé, BP92116</s1><s2>56321 Lorient</s2><s3>FRA</s3><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Région Bretagne</region><settlement type="city">Lorient</settlement></placeName></affiliation></author><author><name sortKey="Duan, W H" sort="Duan, W H" uniqKey="Duan W" first="W. H." last="Duan">W. H. Duan</name><affiliation wicri:level="1"><inist:fA14 i1="04"><s1>Department of Civil Engineering, Monash University</s1><s2>Clayton, Victoria 3800</s2><s3>AUS</s3><sZ>4 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Clayton, Victoria 3800</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Journal of physics. D, Applied physics : (Print)</title><title level="j" type="abbreviated">J. phys., D. Appl. phys. : (Print)</title><idno type="ISSN">0022-3727</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Journal of physics. D, Applied physics : (Print)</title><title level="j" type="abbreviated">J. phys., D. Appl. phys. : (Print)</title><idno type="ISSN">0022-3727</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Axial stress</term><term>Beam(mechanics)</term><term>Buckling</term><term>Calibration</term><term>Critical load</term><term>Differential operator</term><term>Euler equation</term><term>Exact solution</term><term>Microstructure</term><term>Modeling</term><term>Non local theory</term><term>Padé approximation</term><term>Prestress</term><term>Vibration</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Précontrainte</term><term>Vibration</term><term>Charge critique</term><term>Contrainte axiale</term><term>Flambage</term><term>Etalonnage</term><term>Théorie non locale</term><term>Equation Euler</term><term>Poutre</term><term>Modélisation</term><term>Microstructure</term><term>Opérateur différentiel</term><term>Approximation Padé</term><term>Solution exacte</term><term>.</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this paper, we calibrate Eringen's small length scale coefficient e<sub>0</sub> for an initially stressed vibrating nonlocal Euler beam via a microstructured beam modelled by some repetitive cells comprising finite rigid segments and elastic rotational springs. By adopting the pseudo-differential operator and Padé's approximation, an analytical solution for the vibration frequency in terms of initial stress may be developed for the microstructured beam model. When comparing this analytical solution with the established exact vibration solution from the nonlocal beam theory, one finds that the calibrated Eringen's small length scale coefficient e<sub>0</sub> is given by e<sub>0</sub> = √(1/6) - (1/12)(σ<sub>0</sub>/σ<sub>m</sub>) where σ<sub>0</sub> is the initial stress and σ<sub>m</sub> is the mth mode buckling stress of the corresponding local Euler beam. It is shown that e<sub>0</sub> varies with respect to the initial axial stress, from 1/√12 ≃ 0.289 at the buckling compressive stress to 1/√6 ≃ 0.408 when the axial stress is zero and it monotonically increases with increasing initial tensile stress. The small length scale coefficient e<sub>0</sub>, however, does not depend on the vibration/buckling mode considered.</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li><li>Singapour</li></country><region><li>Région Bretagne</li></region><settlement><li>Lorient</li></settlement><orgName><li>Université nationale de Singapour</li></orgName></list><tree><country name="Singapour"><noRegion><name sortKey="Wang, C M" sort="Wang, C M" uniqKey="Wang C" first="C. M." last="Wang">C. M. Wang</name></noRegion><name sortKey="Zhang, Z" sort="Zhang, Z" uniqKey="Zhang Z" first="Z." last="Zhang">Z. Zhang</name></country><country name="France"><region name="Région Bretagne"><name sortKey="Challamel, N" sort="Challamel, N" uniqKey="Challamel N" first="N." last="Challamel">N. Challamel</name></region></country><country name="Australie"><noRegion><name sortKey="Duan, W H" sort="Duan, W H" uniqKey="Duan W" first="W. H." last="Duan">W. H. Duan</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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