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Article: Precise integration methods based on the Chebyshev polynomial of the first kind
Title | Precise integration methods based on the Chebyshev polynomial of the first kind |
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Authors | |
Keywords | Chebyshev polynomial of the first kind Homogenized initial system method Integral formula method Structural dynamics The Crout decomposed method |
Issue Date | 2008 |
Publisher | Multidisciplinary Center for Earthquake Engineering Research. The Journal's web site is located at http://mceer.buffalo.edu/eeev |
Citation | Earthquake Engineering And Engineering Vibration, 2008, v. 7 n. 2, p. 207-216 How to Cite? |
Abstract | This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method (IFM) and the homogenized initial system method (HISM). In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods. © 2008 Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH. |
Persistent Identifier | http://hdl.handle.net/10722/71588 |
ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 0.426 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Wang, M | en_HK |
dc.contributor.author | Au, FTK | en_HK |
dc.date.accessioned | 2010-09-06T06:33:21Z | - |
dc.date.available | 2010-09-06T06:33:21Z | - |
dc.date.issued | 2008 | en_HK |
dc.identifier.citation | Earthquake Engineering And Engineering Vibration, 2008, v. 7 n. 2, p. 207-216 | en_HK |
dc.identifier.issn | 1671-3664 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/71588 | - |
dc.description.abstract | This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method (IFM) and the homogenized initial system method (HISM). In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods. © 2008 Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH. | en_HK |
dc.language | eng | en_HK |
dc.publisher | Multidisciplinary Center for Earthquake Engineering Research. The Journal's web site is located at http://mceer.buffalo.edu/eeev | en_HK |
dc.relation.ispartof | Earthquake Engineering and Engineering Vibration | en_HK |
dc.subject | Chebyshev polynomial of the first kind | en_HK |
dc.subject | Homogenized initial system method | en_HK |
dc.subject | Integral formula method | en_HK |
dc.subject | Structural dynamics | en_HK |
dc.subject | The Crout decomposed method | en_HK |
dc.title | Precise integration methods based on the Chebyshev polynomial of the first kind | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1671-3664&volume=7&issue=2&spage=207&epage=216&date=2008&atitle=Precise+integration+methods+based+on+the+Chebyshev+polynomial+of+the+first+kind | en_HK |
dc.identifier.email | Au, FTK:francis.au@hku.hk | en_HK |
dc.identifier.authority | Au, FTK=rp00083 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11803-008-0837-4 | en_HK |
dc.identifier.scopus | eid_2-s2.0-46449129474 | en_HK |
dc.identifier.hkuros | 147569 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-46449129474&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 7 | en_HK |
dc.identifier.issue | 2 | en_HK |
dc.identifier.spage | 207 | en_HK |
dc.identifier.epage | 216 | en_HK |
dc.identifier.isi | WOS:000257328100008 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Wang, M=7407801843 | en_HK |
dc.identifier.scopusauthorid | Au, FTK=7005204072 | en_HK |
dc.identifier.citeulike | 3638146 | - |
dc.identifier.issnl | 1671-3664 | - |