Please use this identifier to cite or link to this item:
https://repository.cihe.edu.hk/jspui/handle/cihe/2955
DC Field | Value | Language |
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dc.contributor.author | Leung, Andrew Yee Tak | en_US |
dc.date.accessioned | 2022-04-07T09:10:09Z | - |
dc.date.available | 2022-04-07T09:10:09Z | - |
dc.date.issued | 2001 | - |
dc.identifier.uri | https://repository.cihe.edu.hk/jspui/handle/cihe/2955 | - |
dc.description.abstract | The solution of <i>ż=Az</i> is <i>z(t)</i>=exp(<i>At</i>)z<sub>0</sub>=E<sub>t</sub>z<sub>0</sub>, z<sub>0</sub>=z(0)</i>. Since <i>z</i>(<i>2t</i>)=E<sub>2t</sub>z<sub>0</sub>=E<sup>t</sup><sub>2</sub>z<sub>0</sub></i>, <i>z</i>(<i>4t</i>)=E<sub>4t</sub>z<sub>0</sub>=E<sup>2t</sup><sub>2</sub>z<sub>0</sub></i>, etc., one function evaluation can double the time step. For an <i>n</i>-degree-of-freedoms system, A is a 2<i>n</i> matrix of the <i>n</i>th-order mass, damping and stiffness matrices <i>M</i>, <i>C</i> and <i>K</i>. If the forcing term is given as piecewise combinations of the elementary functions, the force response can be obtained analytically. The mean-square response <i>P</i> to a white noise random force with intensity W(<i>t</i>) is governed by the Lyapunov differential equation: <i>Ṗ=AP+PA<sup>T</sup>+W</i>. The solution of the homogeneous Lyapunov equation is <i>P</i>(<i>t</i>)=exp(<i>At</i>) <i>P</i><sub>0</sub></i> exp(<i>A</i><sup>T</sup><i>t</i>), <i>P</i><sub>0</sub>=<i>P</i>(0). One function evaluation can also double the time step. If <i>W(t)</i> is given as piecewise polynomials, the mean-square response can also be obtained analytically. In fact, exp(<i>At</i>) consists of the impulsive- and step-response functions and requires no special treatment. The method is extended further to coloured noise. In particular, for a linear system initially at rest under white noise excitation, the classical non-stationary response is resulted immediately without integration. The method is further extended to modulated noise excitations. The method gives analytical mean-square response matrices for lightly damped or heavily damped systems without using modal expansion. No integration over the frequency is required for the mean-square response. Four examples are given. The first one shows that the method include the result of Caughy and Stumpf as a particular case. The second one deals with non-white excitation. The third finds the transient stress intensity factor of a gun barrel and the fourth finds the means-square response matrix of a simply supported beam by finite element method. | en_US |
dc.language.iso | en | en_US |
dc.publisher | John Wiley & Sons | en_US |
dc.relation.ispartof | International Journal for Numerical Methods in Engineering | en_US |
dc.title | Fast matrix exponent for deterministic or random excitations | en_US |
dc.type | journal article | en_US |
dc.identifier.doi | 10.1002/1097-0207(20010120)50:2<377::AID-NME29>3.0.CO;2-E | - |
dc.contributor.affiliation | School of Computing and Information Sciences | en_US |
dc.relation.issn | 1097-0207 | en_US |
dc.description.volume | 50 | en_US |
dc.description.issue | 2 | en_US |
dc.description.startpage | 377 | en_US |
dc.description.endpage | 394 | en_US |
dc.cihe.affiliated | No | - |
item.cerifentitytype | Publications | - |
item.fulltext | No Fulltext | - |
item.languageiso639-1 | en | - |
item.openairecristype | http://purl.org/coar/resource_type/c_6501 | - |
item.grantfulltext | none | - |
item.openairetype | journal article | - |
crisitem.author.dept | Yam Pak Charitable Foundation School of Computing and Information Sciences | - |
Appears in Collections: | CIS Publication |
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