An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters
Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the convergence of the Neumann series to obtain the bounds of eigenvalues of structure...
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| Vydáno v: | Computers & structures Ročník 87; číslo 9; s. 582 - 590 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Kidlington
Elsevier Ltd
01.05.2009
Elsevier |
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| ISSN: | 0045-7949, 1879-2243 |
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| Abstract | Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the convergence of the Neumann series to obtain the bounds of eigenvalues of structures with single interval parameter, thus increasing the computing accuracy and reducing the computational effort. Finally, the effect of uncertain parameters on natural frequencies is evaluated. Two engineering examples show that the proposed method can give better results than those obtained by the first-order approximation, even if the uncertainties of parameters are fairly large. |
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| AbstractList | Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the convergence of the Neumann series to obtain the bounds of eigenvalues of structures with single interval parameter, thus increasing the computing accuracy and reducing the computational effort. Finally, the effect of uncertain parameters on natural frequencies is evaluated. Two engineering examples show that the proposed method can give better results than those obtained by the first-order approximation, even if the uncertainties of parameters are fairly large. |
| Author | Ma, Liang Meng, Guang Wei Guo, Rui Chen, Su Huan |
| Author_xml | – sequence: 1 givenname: Su Huan surname: Chen fullname: Chen, Su Huan email: chensh@jlu.edu.cn – sequence: 2 givenname: Liang surname: Ma fullname: Ma, Liang – sequence: 3 givenname: Guang Wei surname: Meng fullname: Meng, Guang Wei – sequence: 4 givenname: Rui surname: Guo fullname: Guo, Rui |
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| Cites_doi | 10.1016/0045-7949(90)90002-J 10.1016/j.compstruc.2005.08.004 10.1007/BF01390336 10.1115/1.2897690 10.1016/0377-0427(95)00133-6 10.1016/0045-7949(94)90026-4 10.1006/jath.1996.0053 10.1002/nme.1612 10.1061/(ASCE)0733-9399(1996)122:6(521) 10.12989/sem.2001.12.6.669 10.2514/3.10182 10.1016/0263-8231(96)00009-2 10.1016/S0045-7949(99)00047-4 10.1016/S0377-0427(00)00355-1 10.1016/S0045-7949(99)00077-2 |
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| Keywords | Efficient method Uncertain-but-bounded parameters Epsilon-algorithm Natural frequencies Natural frequency Uncertain system Vibration Taylor series Eigenvalue problem Modeling Interval arithmetic Neumann series |
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| SubjectTerms | Computational techniques Efficient method Epsilon-algorithm Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical methods in physics Natural frequencies Physics Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Uncertain-but-bounded parameters Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) |
| Title | An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters |
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