FE Dynamic Analysis Using Moving Support Element on Multi-Span Beams Subjected to Support Motions
ABSTRACT
In the present study, finite element dynamic analysis or time history analysis of two-span beams subjected to asynchronous multi-support motions is carried out by using the moving support finite element. The elemental equation of the element is based on total displacements and is derived under the concept of the quasi-static displacement decomposition. The use of moving support element shows that the element is very simple and convenient to represent continuous beam moving, deforming and vibrating simultaneously due to support motions. The comparison between the numerical results and analytical solutions indicates that the FE result agrees with the analytical solution.
In the present study, finite element dynamic analysis or time history analysis of two-span beams subjected to asynchronous multi-support motions is carried out by using the moving support finite element. The elemental equation of the element is based on total displacements and is derived under the concept of the quasi-static displacement decomposition. The use of moving support element shows that the element is very simple and convenient to represent continuous beam moving, deforming and vibrating simultaneously due to support motions. The comparison between the numerical results and analytical solutions indicates that the FE result agrees with the analytical solution.
KEYWORDS
Moving Support Element, Support Motions, Rayleigh-Damped Bernoulli-Euler Beam, Multi-Span Beam, Time History Analysis, Finite Element Method
Moving Support Element, Support Motions, Rayleigh-Damped Bernoulli-Euler Beam, Multi-Span Beam, Time History Analysis, Finite Element Method
Cite this paper
Kim, Y. and Lee, S. (2015) FE Dynamic Analysis Using Moving Support Element on Multi-Span Beams Subjected to Support Motions. Modern Mechanical Engineering, 5, 112-121. doi: 10.4236/mme.2015.54011.
Kim, Y. and Lee, S. (2015) FE Dynamic Analysis Using Moving Support Element on Multi-Span Beams Subjected to Support Motions. Modern Mechanical Engineering, 5, 112-121. doi: 10.4236/mme.2015.54011.
References
[1] Abdel-Ghaffar, A.M. and Rood, J.D. (1982) Simplified Earthquake Analysis of Suspension Bridge Towers. Journal of the Engineering Mechanics Division, ASCE, 108, EM2, 291-308. [2] Harichandran, R. and Wang, W.J. (1990) Response of Indeterminate Two-Span Beam to Spatially Varying Seismic Excitation. Earthquake Engineering and Structural Dynamics, 19, 173-187.
http://dx.doi.org/10.1002/eqe.4290190203 [3] Chen, J.T., Hong, H.-K., Yeh, C.S. and Chyuan, S.W. (1996) Integral Representations and Regularizations for a Divergent Series Solution of a Beam Subjected to Support Motions. Earthquake Engineering and Structural Dynamics, 25, 909-925.
http://dx.doi.org/10.1002/(SICI)1096-9845(199609)25:9<909::AID-EQE591>3.0.CO;2-M [4] Yau, J.D. and Fryba, L. (2007) Response of Suspended Beams Due to Moving Loads and Vertical Seismic Ground Excitations. Engineering Structures, 29, 3255-3262.
http://dx.doi.org/10.1016/j.engstruct.2007.10.001 [5] Fryba, L. and Yau, J.-D. (2009) Suspended Bridges Subjected to Moving Loads and Support Motions Due to Earthquake. Journal of Sound and Vibration, 319, 218-227.
http://dx.doi.org/10.1016/j.jsv.2008.05.012 [6] Liu, M.-F., Chang, T.-P. and Zeng, D.-Y. (2011) The Interactive Vibration in a Suspension Bridge System under Moving Vehicle Loads and Vertical Seismic Excitations. Applied Mathematical Modelling, 35, 398-411.
http://dx.doi.org/10.1016/j.apm.2010.07.005 [7] Yau, J.D. (2009) Dynamic Response Analysis of Suspended Beams Subjected to Moving Vehicles and Multiple Support Excitations. Journal of Sound and Vibration, 325, 907-922.
http://dx.doi.org/10.1016/j.jsv.2009.04.013 [8] Lin, J.H., Zhang, Y.H., Li, Q.S. and Williams, F.W. (2004) Seismic Spatial Effects for Long-Span Bridges, Using the Pseudo Excitation Method. Engineering Structures, 26, 1207-1216.
http://dx.doi.org/10.1016/j.engstruct.2004.03.019 [9] Zhang, Y.H., Li, Q.S., Lin, J.H. and Williams, F.W. (2009) Random Vibration Analysis of Long-Span Structures Subjected to Spatially Varying Ground Motions. Soil Dynamics and Earthquake Engineering, 29, 620-629.
http://dx.doi.org/10.1016/j.soildyn.2008.06.007 [10] Mindlin, R.D. and Goodman, L.E. (1950) Beam Vibrations with Time-Dependent Boundary Conditions. Journal of Applied Mechanics, ASME, 17, 377-380. [11] Datta, T.K. (2010) Seismic Analysis of Structures. John Wiley & Sons (Asia) Pte Ltd., Singapore.
http://dx.doi.org/10.1002/9780470824634 [12] Kim, Y.-W. and Jhung, M.J. (2013) Moving Support Elements for Dynamic Finite Element Analysis of Statically Determinate Beams Subjected to Support Motions. Transactions of the Korean Society of Mechanical Engineers A, 37, 555-567.
http://dx.doi.org/10.3795/KSME-A.2013.37.4.555 [13] Kim, Y.-W. (2015) Finite Element Formulation for Earthquake Analysis of Single-Span Beams Involving Forced Deformation Caused by Multi-Support Motions. Journal of Mechanical Science and Technology, 29, 461-469.
http://dx.doi.org/10.1007/s12206-015-0106-1
[1] Abdel-Ghaffar, A.M. and Rood, J.D. (1982) Simplified Earthquake Analysis of Suspension Bridge Towers. Journal of the Engineering Mechanics Division, ASCE, 108, EM2, 291-308. [2] Harichandran, R. and Wang, W.J. (1990) Response of Indeterminate Two-Span Beam to Spatially Varying Seismic Excitation. Earthquake Engineering and Structural Dynamics, 19, 173-187.
http://dx.doi.org/10.1002/eqe.4290190203 [3] Chen, J.T., Hong, H.-K., Yeh, C.S. and Chyuan, S.W. (1996) Integral Representations and Regularizations for a Divergent Series Solution of a Beam Subjected to Support Motions. Earthquake Engineering and Structural Dynamics, 25, 909-925.
http://dx.doi.org/10.1002/(SICI)1096-9845(199609)25:9<909::AID-EQE591>3.0.CO;2-M [4] Yau, J.D. and Fryba, L. (2007) Response of Suspended Beams Due to Moving Loads and Vertical Seismic Ground Excitations. Engineering Structures, 29, 3255-3262.
http://dx.doi.org/10.1016/j.engstruct.2007.10.001 [5] Fryba, L. and Yau, J.-D. (2009) Suspended Bridges Subjected to Moving Loads and Support Motions Due to Earthquake. Journal of Sound and Vibration, 319, 218-227.
http://dx.doi.org/10.1016/j.jsv.2008.05.012 [6] Liu, M.-F., Chang, T.-P. and Zeng, D.-Y. (2011) The Interactive Vibration in a Suspension Bridge System under Moving Vehicle Loads and Vertical Seismic Excitations. Applied Mathematical Modelling, 35, 398-411.
http://dx.doi.org/10.1016/j.apm.2010.07.005 [7] Yau, J.D. (2009) Dynamic Response Analysis of Suspended Beams Subjected to Moving Vehicles and Multiple Support Excitations. Journal of Sound and Vibration, 325, 907-922.
http://dx.doi.org/10.1016/j.jsv.2009.04.013 [8] Lin, J.H., Zhang, Y.H., Li, Q.S. and Williams, F.W. (2004) Seismic Spatial Effects for Long-Span Bridges, Using the Pseudo Excitation Method. Engineering Structures, 26, 1207-1216.
http://dx.doi.org/10.1016/j.engstruct.2004.03.019 [9] Zhang, Y.H., Li, Q.S., Lin, J.H. and Williams, F.W. (2009) Random Vibration Analysis of Long-Span Structures Subjected to Spatially Varying Ground Motions. Soil Dynamics and Earthquake Engineering, 29, 620-629.
http://dx.doi.org/10.1016/j.soildyn.2008.06.007 [10] Mindlin, R.D. and Goodman, L.E. (1950) Beam Vibrations with Time-Dependent Boundary Conditions. Journal of Applied Mechanics, ASME, 17, 377-380. [11] Datta, T.K. (2010) Seismic Analysis of Structures. John Wiley & Sons (Asia) Pte Ltd., Singapore.
http://dx.doi.org/10.1002/9780470824634 [12] Kim, Y.-W. and Jhung, M.J. (2013) Moving Support Elements for Dynamic Finite Element Analysis of Statically Determinate Beams Subjected to Support Motions. Transactions of the Korean Society of Mechanical Engineers A, 37, 555-567.
http://dx.doi.org/10.3795/KSME-A.2013.37.4.555 [13] Kim, Y.-W. (2015) Finite Element Formulation for Earthquake Analysis of Single-Span Beams Involving Forced Deformation Caused by Multi-Support Motions. Journal of Mechanical Science and Technology, 29, 461-469.
http://dx.doi.org/10.1007/s12206-015-0106-1