Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders
In this paper, a semi-analytical solution for free vibration differential equations of curved girders is proposed based on their mathematical properties and vibration characteristics. The solutions of in-plane vibration differential equations are classified into two cases: one only considers variabl...
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doaj-37584af5abdf4b01ad1a91581e4eb1f92020-11-25T02:40:44ZengSciendoArchives of Civil Engineering1230-29452017-03-0163111513210.1515/ace-2017-0008ace-2017-0008Semi-Analytical Solution for Free Vibration Differential Equations of Curved GirdersSong Y.0Chai X.1Shanghai University of Engineering Science, Faculty of Urban Railway Transportation, 333 Longteng Rd, 201620 Shanghai, ChinaShanghai University of Engineering Science, Faculty of Urban Railway Transportation, 333 Longteng Rd, 201620 Shanghai, ChinaIn this paper, a semi-analytical solution for free vibration differential equations of curved girders is proposed based on their mathematical properties and vibration characteristics. The solutions of in-plane vibration differential equations are classified into two cases: one only considers variable separation of non-longitudinal vibration, while the other is a synthesis method addressing both longitudinal and non-longitudinal vibration using Rayleigh’s modal assumption and variable separation method. A similar approach is employed for the out of- plane vibration, but further mathematical operations are conducted to incorporate the coupling effect of bending and twisting. In this case study, the natural frequencies of a curved girder under different boundary conditions are obtained using the two proposed methods, respectively. The results are compared with those from the finite element analysis (FEA) and results show good convergence.http://www.degruyter.com/view/j/ace.2017.63.issue-1/ace-2017-0008/ace-2017-0008.xml?format=INTcurved girderfree vibrationnatural frequencysemi-analytical solutionvariable separation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Song Y. Chai X. |
spellingShingle |
Song Y. Chai X. Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders Archives of Civil Engineering curved girder free vibration natural frequency semi-analytical solution variable separation |
author_facet |
Song Y. Chai X. |
author_sort |
Song Y. |
title |
Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders |
title_short |
Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders |
title_full |
Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders |
title_fullStr |
Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders |
title_full_unstemmed |
Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders |
title_sort |
semi-analytical solution for free vibration differential equations of curved girders |
publisher |
Sciendo |
series |
Archives of Civil Engineering |
issn |
1230-2945 |
publishDate |
2017-03-01 |
description |
In this paper, a semi-analytical solution for free vibration differential equations of curved girders is proposed based on their mathematical properties and vibration characteristics. The solutions of in-plane vibration differential equations are classified into two cases: one only considers variable separation of non-longitudinal vibration, while the other is a synthesis method addressing both longitudinal and non-longitudinal vibration using Rayleigh’s modal assumption and variable separation method. A similar approach is employed for the out of- plane vibration, but further mathematical operations are conducted to incorporate the coupling effect of bending and twisting. In this case study, the natural frequencies of a curved girder under different boundary conditions are obtained using the two proposed methods, respectively. The results are compared with those from the finite element analysis (FEA) and results show good convergence. |
topic |
curved girder free vibration natural frequency semi-analytical solution variable separation |
url |
http://www.degruyter.com/view/j/ace.2017.63.issue-1/ace-2017-0008/ace-2017-0008.xml?format=INT |
work_keys_str_mv |
AT songy semianalyticalsolutionforfreevibrationdifferentialequationsofcurvedgirders AT chaix semianalyticalsolutionforfreevibrationdifferentialequationsofcurvedgirders |
_version_ |
1724780076773408768 |