On the Vibrations of a Rigid Solid Hung by Kinematic Chains

In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using...
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Autor*in:	Alin-Florentin Stan [verfasserIn] Nicolae Pandrea [verfasserIn] Nicolae-Doru Stănescu [verfasserIn] Ligia Munteanu [verfasserIn] Veturia Chiroiu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 14(2022), 4, p 770
Übergeordnetes Werk:	volume:14 ; year:2022 ; number:4, p 770

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym14040770

Katalog-ID:	DOAJ079295169

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520			\|a In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical.
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allfields	10.3390/sym14040770 doi (DE-627)DOAJ079295169 (DE-599)DOAJ57fe4d0eaebf459fbe929d1272abe8be DE-627 ger DE-627 rakwb eng QA1-939 Alin-Florentin Stan verfasserin aut On the Vibrations of a Rigid Solid Hung by Kinematic Chains 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical. rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain Mathematics Nicolae Pandrea verfasserin aut Nicolae-Doru Stănescu verfasserin aut Ligia Munteanu verfasserin aut Veturia Chiroiu verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 4, p 770 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:4, p 770 https://doi.org/10.3390/sym14040770 kostenfrei https://doaj.org/article/57fe4d0eaebf459fbe929d1272abe8be kostenfrei https://www.mdpi.com/2073-8994/14/4/770 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 4, p 770
spelling	10.3390/sym14040770 doi (DE-627)DOAJ079295169 (DE-599)DOAJ57fe4d0eaebf459fbe929d1272abe8be DE-627 ger DE-627 rakwb eng QA1-939 Alin-Florentin Stan verfasserin aut On the Vibrations of a Rigid Solid Hung by Kinematic Chains 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical. rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain Mathematics Nicolae Pandrea verfasserin aut Nicolae-Doru Stănescu verfasserin aut Ligia Munteanu verfasserin aut Veturia Chiroiu verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 4, p 770 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:4, p 770 https://doi.org/10.3390/sym14040770 kostenfrei https://doaj.org/article/57fe4d0eaebf459fbe929d1272abe8be kostenfrei https://www.mdpi.com/2073-8994/14/4/770 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 4, p 770
allfields_unstemmed	10.3390/sym14040770 doi (DE-627)DOAJ079295169 (DE-599)DOAJ57fe4d0eaebf459fbe929d1272abe8be DE-627 ger DE-627 rakwb eng QA1-939 Alin-Florentin Stan verfasserin aut On the Vibrations of a Rigid Solid Hung by Kinematic Chains 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical. rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain Mathematics Nicolae Pandrea verfasserin aut Nicolae-Doru Stănescu verfasserin aut Ligia Munteanu verfasserin aut Veturia Chiroiu verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 4, p 770 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:4, p 770 https://doi.org/10.3390/sym14040770 kostenfrei https://doaj.org/article/57fe4d0eaebf459fbe929d1272abe8be kostenfrei https://www.mdpi.com/2073-8994/14/4/770 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 4, p 770
allfieldsGer	10.3390/sym14040770 doi (DE-627)DOAJ079295169 (DE-599)DOAJ57fe4d0eaebf459fbe929d1272abe8be DE-627 ger DE-627 rakwb eng QA1-939 Alin-Florentin Stan verfasserin aut On the Vibrations of a Rigid Solid Hung by Kinematic Chains 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical. rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain Mathematics Nicolae Pandrea verfasserin aut Nicolae-Doru Stănescu verfasserin aut Ligia Munteanu verfasserin aut Veturia Chiroiu verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 4, p 770 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:4, p 770 https://doi.org/10.3390/sym14040770 kostenfrei https://doaj.org/article/57fe4d0eaebf459fbe929d1272abe8be kostenfrei https://www.mdpi.com/2073-8994/14/4/770 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 4, p 770
allfieldsSound	10.3390/sym14040770 doi (DE-627)DOAJ079295169 (DE-599)DOAJ57fe4d0eaebf459fbe929d1272abe8be DE-627 ger DE-627 rakwb eng QA1-939 Alin-Florentin Stan verfasserin aut On the Vibrations of a Rigid Solid Hung by Kinematic Chains 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical. rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain Mathematics Nicolae Pandrea verfasserin aut Nicolae-Doru Stănescu verfasserin aut Ligia Munteanu verfasserin aut Veturia Chiroiu verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 4, p 770 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:4, p 770 https://doi.org/10.3390/sym14040770 kostenfrei https://doaj.org/article/57fe4d0eaebf459fbe929d1272abe8be kostenfrei https://www.mdpi.com/2073-8994/14/4/770 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 4, p 770
language	English
source	In Symmetry 14(2022), 4, p 770 volume:14 year:2022 number:4, p 770
sourceStr	In Symmetry 14(2022), 4, p 770 volume:14 year:2022 number:4, p 770
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain Mathematics
isfreeaccess_bool	true
container_title	Symmetry
authorswithroles_txt_mv	Alin-Florentin Stan @@aut@@ Nicolae Pandrea @@aut@@ Nicolae-Doru Stănescu @@aut@@ Ligia Munteanu @@aut@@ Veturia Chiroiu @@aut@@
publishDateDaySort_date	2022-01-01T00:00:00Z
hierarchy_top_id	610604112
id	DOAJ079295169
language_de	englisch
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In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. 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callnumber-first	Q - Science
author	Alin-Florentin Stan
spellingShingle	Alin-Florentin Stan misc QA1-939 misc rigidity matrix misc screw coordinates misc free and forced vibrations misc elastic kinematic chains misc rigid kinematic chain misc Mathematics On the Vibrations of a Rigid Solid Hung by Kinematic Chains
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topic_title	QA1-939 On the Vibrations of a Rigid Solid Hung by Kinematic Chains rigidity matrix screw coordinates free and forced vibrations elastic kinematic chains rigid kinematic chain
topic	misc QA1-939 misc rigidity matrix misc screw coordinates misc free and forced vibrations misc elastic kinematic chains misc rigid kinematic chain misc Mathematics
topic_unstemmed	misc QA1-939 misc rigidity matrix misc screw coordinates misc free and forced vibrations misc elastic kinematic chains misc rigid kinematic chain misc Mathematics
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title	On the Vibrations of a Rigid Solid Hung by Kinematic Chains
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title_sort	on the vibrations of a rigid solid hung by kinematic chains
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title_auth	On the Vibrations of a Rigid Solid Hung by Kinematic Chains
abstract	In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical.
abstractGer	In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical.
abstract_unstemmed	In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical.
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title_short	On the Vibrations of a Rigid Solid Hung by Kinematic Chains
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