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Article: Gibbs-phenomenon-free Fourier series for vibration and stability of complex beams

TitleGibbs-phenomenon-free Fourier series for vibration and stability of complex beams
Authors
Issue Date2001
Citation
Aiaa Journal, 2001, v. 39 n. 10, p. 1977-1984 How to Cite?
AbstractThe Gibbs phenomenon in Fourier series has long been recognized as a drawback in its applications, in particular when it is used to represent a function having discontinuities. One category, namely, intrinsic discontinuities, could be derived from the nature of the physical problems. Another, namely, inherent discontinuities, is created undesirably through the employment of Fourier series. To alleviate these drawbacks, two techniques are developed. The first aims at eliminating the inherent discontinuities. The size of the original domain [0, l] is first doubled with a virtual function φ0 defined over the neighboring domain [-l, 0]. The augmented domain [-l, l] is then further extended periodically. The virtual function φ0(y) is chosen so that continuities are achieved at y=0, ±l, ±2l, .... Consequently, no Gibbs phenomena will occur at the boundaries. The second aims at reproducing the intrinsic discontinuities in the representation function by incorporating piecewise cubic polynomials into the Fourier base function. The enlarged basis function, namely, the Gibbs-phenomenon-free-Fourier-series function, is able to represent accurately any specific boundary conditions and interior intrinsic discontinuous conditions. Examples of vibration and buckling analysis of complex beams show that the present method is versatile, accurate, and efficient.
Persistent Identifierhttp://hdl.handle.net/10722/150193
ISSN
2015 Impact Factor: 1.326
2015 SCImago Journal Rankings: 0.970
References

 

DC FieldValueLanguage
dc.contributor.authorFan, SCen_US
dc.contributor.authorZheng, DYen_US
dc.contributor.authorAu, FTKen_US
dc.date.accessioned2012-06-26T06:02:08Z-
dc.date.available2012-06-26T06:02:08Z-
dc.date.issued2001en_US
dc.identifier.citationAiaa Journal, 2001, v. 39 n. 10, p. 1977-1984en_US
dc.identifier.issn0001-1452en_US
dc.identifier.urihttp://hdl.handle.net/10722/150193-
dc.description.abstractThe Gibbs phenomenon in Fourier series has long been recognized as a drawback in its applications, in particular when it is used to represent a function having discontinuities. One category, namely, intrinsic discontinuities, could be derived from the nature of the physical problems. Another, namely, inherent discontinuities, is created undesirably through the employment of Fourier series. To alleviate these drawbacks, two techniques are developed. The first aims at eliminating the inherent discontinuities. The size of the original domain [0, l] is first doubled with a virtual function φ0 defined over the neighboring domain [-l, 0]. The augmented domain [-l, l] is then further extended periodically. The virtual function φ0(y) is chosen so that continuities are achieved at y=0, ±l, ±2l, .... Consequently, no Gibbs phenomena will occur at the boundaries. The second aims at reproducing the intrinsic discontinuities in the representation function by incorporating piecewise cubic polynomials into the Fourier base function. The enlarged basis function, namely, the Gibbs-phenomenon-free-Fourier-series function, is able to represent accurately any specific boundary conditions and interior intrinsic discontinuous conditions. Examples of vibration and buckling analysis of complex beams show that the present method is versatile, accurate, and efficient.en_US
dc.languageengen_US
dc.relation.ispartofAIAA Journalen_US
dc.titleGibbs-phenomenon-free Fourier series for vibration and stability of complex beamsen_US
dc.typeArticleen_US
dc.identifier.emailAu, FTK:francis.au@hku.hken_US
dc.identifier.authorityAu, FTK=rp00083en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0035474973en_US
dc.identifier.hkuros65476-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0035474973&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume39en_US
dc.identifier.issue10en_US
dc.identifier.spage1977en_US
dc.identifier.epage1984en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridFan, SC=7402678113en_US
dc.identifier.scopusauthoridZheng, DY=7202567275en_US
dc.identifier.scopusauthoridAu, FTK=7005204072en_US

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