Please use this identifier to cite or link to this item: https://repository.cihe.edu.hk/jspui/handle/cihe/3267
DC FieldValueLanguage
dc.contributor.authorLeung, Andrew Yee Taken_US
dc.contributor.otherFung, T. C.-
dc.date.accessioned2022-05-20T10:04:27Z-
dc.date.available2022-05-20T10:04:27Z-
dc.date.issued1989-
dc.identifier.urihttps://repository.cihe.edu.hk/jspui/handle/cihe/3267-
dc.description.abstractA finite element method based on the virtual work principle to determine the steady state response of frams in free or forced periodic vibration is introduced. The axial and flexural deformations are coupled by mean of the induced axial force along the element. The spatial discretization of the deformations is achieved by the usual finite element method and the time discretization by Fourier coefficients of the nodal displacements. No unconventional element matrices are needed. After applying the harmonic balance method, a set of non-linear algebraic equations of the Fourier coefficients is obtained. These equations are solved by the Newtonian iteration method in terms of the Fourier coefficient increments. Nodal damping can easily be included by a diagonal damping matrix. The direct numerical determination of the Fourier coefficient increments is difficult owing to the presence of peaks, loops and discontinuities of slope along the amplitude-frequency response curves. Parametric construction of the response curves using the phase difference between the response and excitation is recommended to provide more points during the rapid change of the phase (i.e. at resonance). For undamped natural vibration, the method of selective coefficients adopted. Numerical examples on the Duffing equation, a hinged–hinged beam, a clamped–hinged beam, a ring and a frame are given. For reasonably accurate results, it is shown that the number of finite elements must be sufficient to predict at least the linear mode at the frequency of interest and the number of harmones considered must satisfy the conditions of completeness and balanceability, which are discussed in detail.en_US
dc.language.isoenen_US
dc.publisherJohn Wiley & Sonsen_US
dc.relation.ispartofInternational Journal for Numerical Methods in Engineeringen_US
dc.titleNon-linear steady state vibration of frames by finite element methoden_US
dc.typejournal articleen_US
dc.identifier.doi10.1002/nme.1620280710-
dc.contributor.affiliationSchool of Computing and Information Sciencesen_US
dc.relation.issn1097-0207en_US
dc.description.volume28en_US
dc.description.issue7en_US
dc.description.startpage1599en_US
dc.description.endpage1618en_US
dc.cihe.affiliatedNo-
item.languageiso639-1en-
item.fulltextNo Fulltext-
item.openairetypejournal article-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
crisitem.author.deptYam Pak Charitable Foundation School of Computing and Information Sciences-
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