Natural vibrations of clamped curved nano-beams and nano-arches
Numerical solution of the clamped-clamped (C-C) nanoarches based on the non-local theory of elasticity is analysed. The present study is helpful to understand the mechanical behaviour of the nanostructures. The nanoarch under consideration has constant thickness and dimension of the cross-section an...
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| creator | Lellep, Jaan Mubasshar, Shahid |
| description | Numerical solution of the clamped-clamped (C-C) nanoarches based on the
non-local theory of elasticity is analysed. The present study is helpful to
understand the mechanical behaviour of the nanostructures. The nanoarch under
consideration has constant thickness and dimension of the cross-section and is
weakened by crack-like defects. It is assumed that the crack is stationary and
the mechanical behaviour of the nanoarch can be modelled by the Eringens
non-local theory of elasticity. The influence of cracks on the natural
vibration is prescribed with the aid of additional local compliance at the
weakened cross-section. An algorithm to determine the eigen frequencies of
nanoarches is developed. Present study reveals that there are significant
effects of crack length non-local paremeters and radius of the arch on eigen
frequency of the nanoarches. The final results are obtained numerically with
the help of computer and presented graphically. The results are also compared
with those presented by other researchers in the form of a table. |
| doi_str_mv | 10.48550/arxiv.2208.09303 |
| format | Article |
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non-local theory of elasticity is analysed. The present study is helpful to
understand the mechanical behaviour of the nanostructures. The nanoarch under
consideration has constant thickness and dimension of the cross-section and is
weakened by crack-like defects. It is assumed that the crack is stationary and
the mechanical behaviour of the nanoarch can be modelled by the Eringens
non-local theory of elasticity. The influence of cracks on the natural
vibration is prescribed with the aid of additional local compliance at the
weakened cross-section. An algorithm to determine the eigen frequencies of
nanoarches is developed. Present study reveals that there are significant
effects of crack length non-local paremeters and radius of the arch on eigen
frequency of the nanoarches. The final results are obtained numerically with
the help of computer and presented graphically. The results are also compared
with those presented by other researchers in the form of a table.</description><identifier>DOI: 10.48550/arxiv.2208.09303</identifier><language>eng</language><subject>Mathematics - Dynamical Systems</subject><creationdate>2022-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2208.09303$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2208.09303$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Lellep, Jaan</creatorcontrib><creatorcontrib>Mubasshar, Shahid</creatorcontrib><title>Natural vibrations of clamped curved nano-beams and nano-arches</title><description>Numerical solution of the clamped-clamped (C-C) nanoarches based on the
non-local theory of elasticity is analysed. The present study is helpful to
understand the mechanical behaviour of the nanostructures. The nanoarch under
consideration has constant thickness and dimension of the cross-section and is
weakened by crack-like defects. It is assumed that the crack is stationary and
the mechanical behaviour of the nanoarch can be modelled by the Eringens
non-local theory of elasticity. The influence of cracks on the natural
vibration is prescribed with the aid of additional local compliance at the
weakened cross-section. An algorithm to determine the eigen frequencies of
nanoarches is developed. Present study reveals that there are significant
effects of crack length non-local paremeters and radius of the arch on eigen
frequency of the nanoarches. The final results are obtained numerically with
the help of computer and presented graphically. The results are also compared
with those presented by other researchers in the form of a table.</description><subject>Mathematics - Dynamical Systems</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAUhmEvHVDLBTDhG0g48bEde0KoooBUlaV7dHxqi0j5qZw2oncPlE6vvuWTHiEeKii1MwaeKH-3c6kUuBI8At6J5x2dzpk6Obch06kdh0mOSXJH_TEeJJ_z_JuBhrEIkfpJ0nCblPkrTiuxSNRN8f7WpdhvXvfr92L7-faxftkWZGssajCWoq7ZR_TWcxUOaJx1WGkLlpxCSsAp6NoBmRgUmOTBGVI6MgPjUjz-314FzTG3PeVL8ydprhL8AZonQus</recordid><startdate>20220819</startdate><enddate>20220819</enddate><creator>Lellep, Jaan</creator><creator>Mubasshar, Shahid</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220819</creationdate><title>Natural vibrations of clamped curved nano-beams and nano-arches</title><author>Lellep, Jaan ; Mubasshar, Shahid</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-7056ae47c9e3969c1bd35868314606a823af0cfb4780a5eb205f9085a24ecc0c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Dynamical Systems</topic><toplevel>online_resources</toplevel><creatorcontrib>Lellep, Jaan</creatorcontrib><creatorcontrib>Mubasshar, Shahid</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Lellep, Jaan</au><au>Mubasshar, Shahid</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Natural vibrations of clamped curved nano-beams and nano-arches</atitle><date>2022-08-19</date><risdate>2022</risdate><abstract>Numerical solution of the clamped-clamped (C-C) nanoarches based on the
non-local theory of elasticity is analysed. The present study is helpful to
understand the mechanical behaviour of the nanostructures. The nanoarch under
consideration has constant thickness and dimension of the cross-section and is
weakened by crack-like defects. It is assumed that the crack is stationary and
the mechanical behaviour of the nanoarch can be modelled by the Eringens
non-local theory of elasticity. The influence of cracks on the natural
vibration is prescribed with the aid of additional local compliance at the
weakened cross-section. An algorithm to determine the eigen frequencies of
nanoarches is developed. Present study reveals that there are significant
effects of crack length non-local paremeters and radius of the arch on eigen
frequency of the nanoarches. The final results are obtained numerically with
the help of computer and presented graphically. The results are also compared
with those presented by other researchers in the form of a table.</abstract><doi>10.48550/arxiv.2208.09303</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems |
| title | Natural vibrations of clamped curved nano-beams and nano-arches |
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