Exact solution for free in-plane vibration analysis of an eccentric elliptical plate
Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by...
Ausführliche Beschreibung
Autor*in: |
Hasheminejad, Seyyed M. [verfasserIn] |
---|
Format: |
Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2013 |
---|
Schlagwörter: |
---|
Anmerkung: |
© Springer-Verlag Wien 2013 |
---|
Übergeordnetes Werk: |
Enthalten in: Acta mechanica - Springer Vienna, 1965, 224(2013), 8 vom: 03. März, Seite 1609-1624 |
---|---|
Übergeordnetes Werk: |
volume:224 ; year:2013 ; number:8 ; day:03 ; month:03 ; pages:1609-1624 |
Links: |
---|
DOI / URN: |
10.1007/s00707-013-0829-y |
---|
Katalog-ID: |
OLC2030138878 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | OLC2030138878 | ||
003 | DE-627 | ||
005 | 20230502143244.0 | ||
007 | tu | ||
008 | 200820s2013 xx ||||| 00| ||eng c | ||
024 | 7 | |a 10.1007/s00707-013-0829-y |2 doi | |
035 | |a (DE-627)OLC2030138878 | ||
035 | |a (DE-He213)s00707-013-0829-y-p | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
082 | 0 | 4 | |a 530 |q VZ |
100 | 1 | |a Hasheminejad, Seyyed M. |e verfasserin |4 aut | |
245 | 1 | 0 | |a Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
264 | 1 | |c 2013 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
338 | |a Band |b nc |2 rdacarrier | ||
500 | |a © Springer-Verlag Wien 2013 | ||
520 | |a Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. | ||
650 | 4 | |a Circular Plate | |
650 | 4 | |a Edge Condition | |
650 | 4 | |a Annular Plate | |
650 | 4 | |a Thin Elastic Plate | |
650 | 4 | |a Annular Disk | |
700 | 1 | |a Ghaheri, Ali |4 aut | |
700 | 1 | |a Vaezian, Sajjad |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Acta mechanica |d Springer Vienna, 1965 |g 224(2013), 8 vom: 03. März, Seite 1609-1624 |w (DE-627)129511676 |w (DE-600)210328-X |w (DE-576)014919141 |x 0001-5970 |7 nnns |
773 | 1 | 8 | |g volume:224 |g year:2013 |g number:8 |g day:03 |g month:03 |g pages:1609-1624 |
856 | 4 | 1 | |u https://doi.org/10.1007/s00707-013-0829-y |z lizenzpflichtig |3 Volltext |
912 | |a GBV_USEFLAG_A | ||
912 | |a SYSFLAG_A | ||
912 | |a GBV_OLC | ||
912 | |a SSG-OLC-TEC | ||
912 | |a SSG-OLC-PHY | ||
912 | |a GBV_ILN_22 | ||
912 | |a GBV_ILN_59 | ||
912 | |a GBV_ILN_70 | ||
912 | |a GBV_ILN_2020 | ||
912 | |a GBV_ILN_4700 | ||
951 | |a AR | ||
952 | |d 224 |j 2013 |e 8 |b 03 |c 03 |h 1609-1624 |
author_variant |
s m h sm smh a g ag s v sv |
---|---|
matchkey_str |
article:00015970:2013----::xcsltofrrenlnvbainnlssfncet |
hierarchy_sort_str |
2013 |
publishDate |
2013 |
allfields |
10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
spelling |
10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
allfields_unstemmed |
10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
allfieldsGer |
10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
allfieldsSound |
10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
language |
English |
source |
Enthalten in Acta mechanica 224(2013), 8 vom: 03. März, Seite 1609-1624 volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 |
sourceStr |
Enthalten in Acta mechanica 224(2013), 8 vom: 03. März, Seite 1609-1624 volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
topic_facet |
Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk |
dewey-raw |
530 |
isfreeaccess_bool |
false |
container_title |
Acta mechanica |
authorswithroles_txt_mv |
Hasheminejad, Seyyed M. @@aut@@ Ghaheri, Ali @@aut@@ Vaezian, Sajjad @@aut@@ |
publishDateDaySort_date |
2013-03-03T00:00:00Z |
hierarchy_top_id |
129511676 |
dewey-sort |
3530 |
id |
OLC2030138878 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2030138878</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502143244.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00707-013-0829-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2030138878</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00707-013-0829-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hasheminejad, Seyyed M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Exact solution for free in-plane vibration analysis of an eccentric elliptical plate</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Wien 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Circular Plate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Edge Condition</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Annular Plate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thin Elastic Plate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Annular Disk</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ghaheri, Ali</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vaezian, Sajjad</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Acta mechanica</subfield><subfield code="d">Springer Vienna, 1965</subfield><subfield code="g">224(2013), 8 vom: 03. März, Seite 1609-1624</subfield><subfield code="w">(DE-627)129511676</subfield><subfield code="w">(DE-600)210328-X</subfield><subfield code="w">(DE-576)014919141</subfield><subfield code="x">0001-5970</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:224</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:8</subfield><subfield code="g">day:03</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:1609-1624</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00707-013-0829-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_59</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">224</subfield><subfield code="j">2013</subfield><subfield code="e">8</subfield><subfield code="b">03</subfield><subfield code="c">03</subfield><subfield code="h">1609-1624</subfield></datafield></record></collection>
|
author |
Hasheminejad, Seyyed M. |
spellingShingle |
Hasheminejad, Seyyed M. ddc 530 misc Circular Plate misc Edge Condition misc Annular Plate misc Thin Elastic Plate misc Annular Disk Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
authorStr |
Hasheminejad, Seyyed M. |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)129511676 |
format |
Article |
dewey-ones |
530 - Physics |
delete_txt_mv |
keep |
author_role |
aut aut aut |
collection |
OLC |
remote_str |
false |
illustrated |
Not Illustrated |
issn |
0001-5970 |
topic_title |
530 VZ Exact solution for free in-plane vibration analysis of an eccentric elliptical plate Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk |
topic |
ddc 530 misc Circular Plate misc Edge Condition misc Annular Plate misc Thin Elastic Plate misc Annular Disk |
topic_unstemmed |
ddc 530 misc Circular Plate misc Edge Condition misc Annular Plate misc Thin Elastic Plate misc Annular Disk |
topic_browse |
ddc 530 misc Circular Plate misc Edge Condition misc Annular Plate misc Thin Elastic Plate misc Annular Disk |
format_facet |
Aufsätze Gedruckte Aufsätze |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
nc |
hierarchy_parent_title |
Acta mechanica |
hierarchy_parent_id |
129511676 |
dewey-tens |
530 - Physics |
hierarchy_top_title |
Acta mechanica |
isfreeaccess_txt |
false |
familylinks_str_mv |
(DE-627)129511676 (DE-600)210328-X (DE-576)014919141 |
title |
Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
ctrlnum |
(DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p |
title_full |
Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
author_sort |
Hasheminejad, Seyyed M. |
journal |
Acta mechanica |
journalStr |
Acta mechanica |
lang_code |
eng |
isOA_bool |
false |
dewey-hundreds |
500 - Science |
recordtype |
marc |
publishDateSort |
2013 |
contenttype_str_mv |
txt |
container_start_page |
1609 |
author_browse |
Hasheminejad, Seyyed M. Ghaheri, Ali Vaezian, Sajjad |
container_volume |
224 |
class |
530 VZ |
format_se |
Aufsätze |
author-letter |
Hasheminejad, Seyyed M. |
doi_str_mv |
10.1007/s00707-013-0829-y |
dewey-full |
530 |
title_sort |
exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
title_auth |
Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
abstract |
Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. © Springer-Verlag Wien 2013 |
abstractGer |
Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. © Springer-Verlag Wien 2013 |
abstract_unstemmed |
Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. © Springer-Verlag Wien 2013 |
collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 |
container_issue |
8 |
title_short |
Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
url |
https://doi.org/10.1007/s00707-013-0829-y |
remote_bool |
false |
author2 |
Ghaheri, Ali Vaezian, Sajjad |
author2Str |
Ghaheri, Ali Vaezian, Sajjad |
ppnlink |
129511676 |
mediatype_str_mv |
n |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1007/s00707-013-0829-y |
up_date |
2024-07-04T01:22:37.369Z |
_version_ |
1803609605272502272 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2030138878</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502143244.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00707-013-0829-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2030138878</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00707-013-0829-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hasheminejad, Seyyed M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Exact solution for free in-plane vibration analysis of an eccentric elliptical plate</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Wien 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Circular Plate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Edge Condition</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Annular Plate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thin Elastic Plate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Annular Disk</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ghaheri, Ali</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vaezian, Sajjad</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Acta mechanica</subfield><subfield code="d">Springer Vienna, 1965</subfield><subfield code="g">224(2013), 8 vom: 03. März, Seite 1609-1624</subfield><subfield code="w">(DE-627)129511676</subfield><subfield code="w">(DE-600)210328-X</subfield><subfield code="w">(DE-576)014919141</subfield><subfield code="x">0001-5970</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:224</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:8</subfield><subfield code="g">day:03</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:1609-1624</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00707-013-0829-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_59</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">224</subfield><subfield code="j">2013</subfield><subfield code="e">8</subfield><subfield code="b">03</subfield><subfield code="c">03</subfield><subfield code="h">1609-1624</subfield></datafield></record></collection>
|
score |
7.4006405 |