Standing and propagating waves in cubically nonlinear media

Standing and propagating waves in cubically nonlinear media

The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonli...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Enflo, Bengt O, Hedberg, Claes M, Rudenko, Oleg V
Format: Tagungsbericht
Sprache:eng
Schlagworte:
cubic nonlinear media
cubic resonator
N-wave propagation
nonlinear acoustic resonator
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 195
container_issue
container_start_page 187
container_title
container_volume 834
creator Enflo, Bengt O
Hedberg, Claes M
Rudenko, Oleg V
description The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonlinear medium results in functional equations. The frequency response shows the dependence of the amplitude of the resonance on the difference between one of the resonator's eigenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and differ very much for quadratic and cubic nonlinearities. In the third part a propagating N-wave is studied, which fulfils a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for new parts of the wave profile.
doi_str_mv 10.1063/1.2205802
format Conference Proceeding
fullrecord <record><control><sourceid>proquest_swepu</sourceid><recordid>TN_cdi_proquest_miscellaneous_29662285</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>29662285</sourcerecordid><originalsourceid>FETCH-LOGICAL-p258t-ec8977fb4b2acfdaaaef313f902f80825bef266181f2965668c64883ab9c3c473</originalsourceid><addsrcrecordid>eNotj8tOwzAURC0BEqV0wR9kxYoU-_oRW6wq3lIlFjzEzrpx7WJIkxAnVP17gspqNNLRHA0hZ4zOGVX8ks0BqNQUDsjMFJoWXArKQfJDMqHUiBwEfz8mJyl9UgqmKPSEXD33WK9ivc7GyNquaXGN_V_f4o9PWawzN5TRYVXtsrqpq1h77LKNX0U8JUcBq-Rn_zklr3e3L9cP-fLp_vF6scxbkLrPvdOjK5SiBHRhhYg-cMaDoRA01SBLH0ApplkAo6RS2imhNcfSOO5EwafkYr-btr4dStt2cYPdzjYY7U18W9imW9uv_sMKZqQc8fM9Pr75Hnzq7SYm56sKa98MyY4SBaAl_wUlCFrO</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>conference_proceeding</recordtype><pqid>29662285</pqid></control><display><type>conference_proceeding</type><title>Standing and propagating waves in cubically nonlinear media</title><source>AIP Journals Complete</source><creator>Enflo, Bengt O ; Hedberg, Claes M ; Rudenko, Oleg V</creator><creatorcontrib>Enflo, Bengt O ; Hedberg, Claes M ; Rudenko, Oleg V</creatorcontrib><description>The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonlinear medium results in functional equations. The frequency response shows the dependence of the amplitude of the resonance on the difference between one of the resonator's eigenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and differ very much for quadratic and cubic nonlinearities. In the third part a propagating N-wave is studied, which fulfils a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for new parts of the wave profile.</description><identifier>ISSN: 0094-243X</identifier><identifier>ISBN: 9780735403253</identifier><identifier>ISBN: 0735403252</identifier><identifier>DOI: 10.1063/1.2205802</identifier><language>eng</language><subject>cubic nonlinear media ; cubic resonator ; N-wave propagation ; nonlinear acoustic resonator</subject><ispartof>Mathematical Modelling of Wave Phenomena, 2006, Vol.834, p.187-195</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>309,310,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-41955$$DView record from Swedish Publication Index$$Hfree_for_read</backlink></links><search><creatorcontrib>Enflo, Bengt O</creatorcontrib><creatorcontrib>Hedberg, Claes M</creatorcontrib><creatorcontrib>Rudenko, Oleg V</creatorcontrib><title>Standing and propagating waves in cubically nonlinear media</title><title>Mathematical Modelling of Wave Phenomena</title><description>The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonlinear medium results in functional equations. The frequency response shows the dependence of the amplitude of the resonance on the difference between one of the resonator's eigenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and differ very much for quadratic and cubic nonlinearities. In the third part a propagating N-wave is studied, which fulfils a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for new parts of the wave profile.</description><subject>cubic nonlinear media</subject><subject>cubic resonator</subject><subject>N-wave propagation</subject><subject>nonlinear acoustic resonator</subject><issn>0094-243X</issn><isbn>9780735403253</isbn><isbn>0735403252</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2006</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNotj8tOwzAURC0BEqV0wR9kxYoU-_oRW6wq3lIlFjzEzrpx7WJIkxAnVP17gspqNNLRHA0hZ4zOGVX8ks0BqNQUDsjMFJoWXArKQfJDMqHUiBwEfz8mJyl9UgqmKPSEXD33WK9ivc7GyNquaXGN_V_f4o9PWawzN5TRYVXtsrqpq1h77LKNX0U8JUcBq-Rn_zklr3e3L9cP-fLp_vF6scxbkLrPvdOjK5SiBHRhhYg-cMaDoRA01SBLH0ApplkAo6RS2imhNcfSOO5EwafkYr-btr4dStt2cYPdzjYY7U18W9imW9uv_sMKZqQc8fM9Pr75Hnzq7SYm56sKa98MyY4SBaAl_wUlCFrO</recordid><startdate>20060101</startdate><enddate>20060101</enddate><creator>Enflo, Bengt O</creator><creator>Hedberg, Claes M</creator><creator>Rudenko, Oleg V</creator><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope><scope>ADTPV</scope><scope>BNKNJ</scope><scope>D8V</scope></search><sort><creationdate>20060101</creationdate><title>Standing and propagating waves in cubically nonlinear media</title><author>Enflo, Bengt O ; Hedberg, Claes M ; Rudenko, Oleg V</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p258t-ec8977fb4b2acfdaaaef313f902f80825bef266181f2965668c64883ab9c3c473</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2006</creationdate><topic>cubic nonlinear media</topic><topic>cubic resonator</topic><topic>N-wave propagation</topic><topic>nonlinear acoustic resonator</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Enflo, Bengt O</creatorcontrib><creatorcontrib>Hedberg, Claes M</creatorcontrib><creatorcontrib>Rudenko, Oleg V</creatorcontrib><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>SwePub</collection><collection>SwePub Conference</collection><collection>SWEPUB Kungliga Tekniska Högskolan</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Enflo, Bengt O</au><au>Hedberg, Claes M</au><au>Rudenko, Oleg V</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Standing and propagating waves in cubically nonlinear media</atitle><btitle>Mathematical Modelling of Wave Phenomena</btitle><date>2006-01-01</date><risdate>2006</risdate><volume>834</volume><spage>187</spage><epage>195</epage><pages>187-195</pages><issn>0094-243X</issn><isbn>9780735403253</isbn><isbn>0735403252</isbn><abstract>The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonlinear medium results in functional equations. The frequency response shows the dependence of the amplitude of the resonance on the difference between one of the resonator's eigenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and differ very much for quadratic and cubic nonlinearities. In the third part a propagating N-wave is studied, which fulfils a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for new parts of the wave profile.</abstract><doi>10.1063/1.2205802</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0094-243X
ispartof Mathematical Modelling of Wave Phenomena, 2006, Vol.834, p.187-195
issn 0094-243X
language eng
recordid cdi_proquest_miscellaneous_29662285
source AIP Journals Complete
subjects cubic nonlinear media
cubic resonator
N-wave propagation
nonlinear acoustic resonator
title Standing and propagating waves in cubically nonlinear media
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T04%3A03%3A17IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_swepu&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=proceeding&rft.atitle=Standing%20and%20propagating%20waves%20in%20cubically%20nonlinear%20media&rft.btitle=Mathematical%20Modelling%20of%20Wave%20Phenomena&rft.au=Enflo,%20Bengt%20O&rft.date=2006-01-01&rft.volume=834&rft.spage=187&rft.epage=195&rft.pages=187-195&rft.issn=0094-243X&rft.isbn=9780735403253&rft.isbn_list=0735403252&rft_id=info:doi/10.1063/1.2205802&rft_dat=%3Cproquest_swepu%3E29662285%3C/proquest_swepu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=29662285&rft_id=info:pmid/&rfr_iscdi=true