An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates

A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Xing, Yufeng [verfasserIn] Wang, Zekun [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Closed-form solution Free vibrations Orthotropic rectangular thin plate Separation-of-variable method

Übergeordnetes Werk:	Enthalten in: Composite structures - Amsterdam : Elsevier, 1983, 252
Übergeordnetes Werk:	volume:252

DOI / URN:	10.1016/j.compstruct.2020.112664

Katalog-ID:	ELV004647343

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245	1	0	\|a An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates
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520			\|a A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling.
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author_variant	y x yx z w zw
matchkey_str	article:02638223:2020----::nmrvdeaainfaibeehdotereirtoootorp
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publishDate	2020
allfields	10.1016/j.compstruct.2020.112664 doi (DE-627)ELV004647343 (ELSEVIER)S0263-8223(20)32590-3 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Xing, Yufeng verfasserin aut An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling. Closed-form solution Free vibrations Orthotropic rectangular thin plate Separation-of-variable method Wang, Zekun verfasserin aut Enthalten in Composite structures Amsterdam : Elsevier, 1983 252 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:252 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 252
spelling	10.1016/j.compstruct.2020.112664 doi (DE-627)ELV004647343 (ELSEVIER)S0263-8223(20)32590-3 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Xing, Yufeng verfasserin aut An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling. Closed-form solution Free vibrations Orthotropic rectangular thin plate Separation-of-variable method Wang, Zekun verfasserin aut Enthalten in Composite structures Amsterdam : Elsevier, 1983 252 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:252 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 252
allfields_unstemmed	10.1016/j.compstruct.2020.112664 doi (DE-627)ELV004647343 (ELSEVIER)S0263-8223(20)32590-3 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Xing, Yufeng verfasserin aut An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling. Closed-form solution Free vibrations Orthotropic rectangular thin plate Separation-of-variable method Wang, Zekun verfasserin aut Enthalten in Composite structures Amsterdam : Elsevier, 1983 252 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:252 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 252
allfieldsGer	10.1016/j.compstruct.2020.112664 doi (DE-627)ELV004647343 (ELSEVIER)S0263-8223(20)32590-3 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Xing, Yufeng verfasserin aut An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling. Closed-form solution Free vibrations Orthotropic rectangular thin plate Separation-of-variable method Wang, Zekun verfasserin aut Enthalten in Composite structures Amsterdam : Elsevier, 1983 252 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:252 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 252
allfieldsSound	10.1016/j.compstruct.2020.112664 doi (DE-627)ELV004647343 (ELSEVIER)S0263-8223(20)32590-3 DE-627 ger DE-627 rda eng 670 DE-600 51.75 bkl Xing, Yufeng verfasserin aut An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling. Closed-form solution Free vibrations Orthotropic rectangular thin plate Separation-of-variable method Wang, Zekun verfasserin aut Enthalten in Composite structures Amsterdam : Elsevier, 1983 252 (DE-627)320509044 (DE-600)2013177-X (DE-576)094531447 0263-8223 nnns volume:252 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 51.75 Verbundwerkstoffe Schichtstoffe AR 252
language	English
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authorswithroles_txt_mv	Xing, Yufeng @@aut@@ Wang, Zekun @@aut@@
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author	Xing, Yufeng
spellingShingle	Xing, Yufeng ddc 670 bkl 51.75 misc Closed-form solution misc Free vibrations misc Orthotropic rectangular thin plate misc Separation-of-variable method An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates
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topic_title	670 DE-600 51.75 bkl An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates Closed-form solution Free vibrations Orthotropic rectangular thin plate Separation-of-variable method
topic	ddc 670 bkl 51.75 misc Closed-form solution misc Free vibrations misc Orthotropic rectangular thin plate misc Separation-of-variable method
topic_unstemmed	ddc 670 bkl 51.75 misc Closed-form solution misc Free vibrations misc Orthotropic rectangular thin plate misc Separation-of-variable method
topic_browse	ddc 670 bkl 51.75 misc Closed-form solution misc Free vibrations misc Orthotropic rectangular thin plate misc Separation-of-variable method
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title	An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates
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title_full	An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates
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title_sort	an improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates
title_auth	An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates
abstract	A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling.
abstractGer	A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling.
abstract_unstemmed	A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling.
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title_short	An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates
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doi_str	10.1016/j.compstruct.2020.112664
up_date	2024-07-06T23:41:41.408Z
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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">ELV004647343</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230524144534.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230503s2020 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.compstruct.2020.112664</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV004647343</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0263-8223(20)32590-3</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">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">670</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">51.75</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Xing, Yufeng</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. 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An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates

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