Global loss factor in steel structures with viscoelastic dampers through state equations
Keywords:
Viscoelastic dampers, viscoelastic materials, energy dissipation, loss factor
Abstract
In this work, is presented a method based on use complex eigenvalues to determine factors of overall loss and equivalent natural frequencies in a steel frame with viscoelastic dampers in the bracing bars. The complex eigenvalues are obtained to solve the eigenvalue problem associated with the equations of motion written as state equations of first order. A study using three-dimensional finite element models developed in ABAQUS program including variations with frequency of materials was also made. The estimations at the global loss factors was achieved from an analysis of the frames subjected to a harmonic load in regime using the half power method. The study allows to check the effectiveness of the technique on the level of additional damping can be achieved.Downloads
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References
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[2] W. Flugge, “Viscoelasticity,” Waltham, Massachusetts: Blaisdell Publishing Company, 1967.
[3] R. Lewandowski y B. Chorazyczewski, “Identification of the parameters of the Kelvin–Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers,” Computers & Structures , vol. 88, pp. 1-17, 2010.
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[19] A. de Lima, D. Rade and F. Le´poreNeto, “An efficient modeling methodology of structural systems containing viscoelastic dampers based on frequency response function substructuring,” Mechanical Systems and Signal Processing, vol. 23, p. 1272-1281, 2009.
[20] I. Saidi, E. F. Gad, J. L. Wilson y N. Haritos, “Development of passive viscoelastic damper to attenuate excessive floor vibrations,” Engineering Structures, vol. 33, pp. 3317-3328, 2011.
[21] E. Moliner, P. Museros y M. Martínez-Rodrigo, “Retrofit of existing railway bridges of short to medium spans for high-speed traffic using viscoelastic dampers,” Engineering Structures, vol. 40, pp. 519-528, 2012.
[22] M. Rijnen, F. Pasteuning, R. Fey, G. vanSchothorst y H. Nijmeijer, “A numerical and experimental study on viscoelastic damping of a 3D structure,” Journal of Sound and Vibration, vol. 349, pp. 80-98, 2015.
[23] J. J. Gil Peláez, “Disertación. Amortiguamiento en estructuras de acero utilizando materiales viscoelásticos,” Mayaguez: Departamento de Ingeniería Civil y Agrimensura, UPRM, 2008.
[24] J. J. Gil Peláez y L. E. Suarez, “Amortiguamiento de estructuras de acero mediante tratamiento a cortante,” Iteckne, vol. 7, nº 1, pp. 34-45, 2010.
[25] L.-Y. Lu, G.-L. Lin y M.-H. Shih, “An experimental study on a generalized Maxwell model for nonlinear viscoelastic dampers used in seismic isolation,” Engineering Structures, vol. 34, p. 111-123, 2012.
[26] K. C. Chang, S. J. Chen y M. L. Lai, “Inelastic Behavior of Steel Frames with Added Viscoelastic Dampers,” vol. 122, nº 10, pp. 1178-1186, 1996.
[27] K.-W. Min, J. Kim y S.-H. Lee, “Vibration Test of 5-Storey Steel Frame with Viscoelastic Dampers,” vol. 26, pp. 831-839, 2004.
[28] R. Lewandowski and Z. Pawlak, “Dynamic analysis of frames with viscoelastic dampers modelled by rheological models with fractional derivatives,” Journal of Soundand Vibration, vol. 330, pp. 923-936, 2011.
[29] Z. Pawlak y R. Lewandowski, “The continuation method for the eigenvalue problem of structures with viscoelastic dampers,” Computers and Structures, vol. 125, p. 53-61, 2013.
[30] D. M. Bergman y R. D. Hanson, “Viscoelastic Mechanical Damping Devices Tested at Real Eathquake Displacements,” vol. 9, nº 3, pp. 389-417, 1993.
[31] L. Meirovitch, “Elements of Vibration Analysis,” New York: McGraw-Hill, 1986.
[32] F. Hejazi, A. Zabihi y M. Jaafar, “Development of elasto-plastic viscous damper finite element model for reinforced concrete frames,” Soil Dynamics and Earthquake Engineering, vol. 65, pp. 284-293, 2014.
[2] W. Flugge, “Viscoelasticity,” Waltham, Massachusetts: Blaisdell Publishing Company, 1967.
[3] R. Lewandowski y B. Chorazyczewski, “Identification of the parameters of the Kelvin–Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers,” Computers & Structures , vol. 88, pp. 1-17, 2010.
[4] T. T. Soong y G. F. Dargush, “Passive Energy Dissipation Systems in Structural Engineering,” Chichester: John Wiley & Sons, 1997.
[5] A. D. Nashif, D. I. G. Jones y J. Henderson, “Vibration Damping,” New York: John Wiley & Sons, 1985.
[6] C. T. Sun y Y. P. Lu, “Vibration Damping of Structural Elements,” Englewood Cliffs, New Jersey: Prentice Hall PRT, 1995.
[7] G. Luca Ghiringhellia y M. Terraneob, “Analytically driven experimental characterisation of damping in viscoelastic materials,” Aerospace Science and Technology, vol. 40, pp. 75-85, 2015.
[8] T. Karavasilis, T. Blakeborough y M. Williams, “Development of nonlinear analytical model and seismic analyses of a steel frame with self-centering devices and viscoelastic dampers,” Computers and Structures, vol. 89, p. 1232-1240, 2011.
[9] J. Kim, J. Ryu and L. Chung, “Seismic performance of structures connected by viscoelastic dampers,” Engineering Structures, vol. 28, pp. 183-195, 2006.
[10] K. C. Chang y Y. Y. Lin, “Seismic Response of Full-Scale Structure with Added Viscoelastic Dampers,” vol. 130, nº 4, pp. 600-608, 2004.
[11] K. C. Chang, T. T. Soong, S.-T. Oh y M. Lai, “Seismic Behavior of Steel Frame with Added Viscoelastic Dampers,” vol. 121, nº 10, pp. 1418-1426, 1995.
[12] I. D. Aiken, J. M. Kelly y P. Mahmoodi, “The Application of Viscoelastic Dampers to Seismically Resistant Struture,” vol. 3, pp. 459-468, 1990.
[13] R. F. Lobo, J. M. Bracci, K. L. Shen, A. M. Reinhorn y T. T. Soong, “Inelastic Response of R/C Structures with Viscoelastic Braces,” vol. 9, nº 3, pp. 419-446, 1993.
[14] C. Constantin, A. Filiatrault y V. Bertero, “Principles of passive supplemental damping and seismic isolation,” Pavia: IUSS Press, 2006.
[15] P. Mahmoodi, L. E. Robertson, M. Yontar, C. Moy y L. Feld, “Performance of Viscoelastic Dampers in World Trade-Center Towers. Dynamics of Structures,” pp. 632-644, August 1987.
[16] P. Mahmoodi y C. J. Keel, “Performance of Viscoelastic Structural Dampers for the Columbia Center Building, Building motion in wind,” pp. 83-106, 1986.
[17] Z.-D. Xu, H.-T. Zhao y A.-Q. Li, “Optimal analysis and experimental study on structures with viscoelastic dampers,” Journal of Sound and Vibration, vol. 273, pp. 607-618, 2004.
[18] A. Bilbao, R. Avilés, J. Agirrebeitia y G. Ajuria, “Proportional damping approximation for structures with added viscoelastic dampers,” Finite Elements in Analysis and Design, vol. 42, pp. 492-502, 2006.
[19] A. de Lima, D. Rade and F. Le´poreNeto, “An efficient modeling methodology of structural systems containing viscoelastic dampers based on frequency response function substructuring,” Mechanical Systems and Signal Processing, vol. 23, p. 1272-1281, 2009.
[20] I. Saidi, E. F. Gad, J. L. Wilson y N. Haritos, “Development of passive viscoelastic damper to attenuate excessive floor vibrations,” Engineering Structures, vol. 33, pp. 3317-3328, 2011.
[21] E. Moliner, P. Museros y M. Martínez-Rodrigo, “Retrofit of existing railway bridges of short to medium spans for high-speed traffic using viscoelastic dampers,” Engineering Structures, vol. 40, pp. 519-528, 2012.
[22] M. Rijnen, F. Pasteuning, R. Fey, G. vanSchothorst y H. Nijmeijer, “A numerical and experimental study on viscoelastic damping of a 3D structure,” Journal of Sound and Vibration, vol. 349, pp. 80-98, 2015.
[23] J. J. Gil Peláez, “Disertación. Amortiguamiento en estructuras de acero utilizando materiales viscoelásticos,” Mayaguez: Departamento de Ingeniería Civil y Agrimensura, UPRM, 2008.
[24] J. J. Gil Peláez y L. E. Suarez, “Amortiguamiento de estructuras de acero mediante tratamiento a cortante,” Iteckne, vol. 7, nº 1, pp. 34-45, 2010.
[25] L.-Y. Lu, G.-L. Lin y M.-H. Shih, “An experimental study on a generalized Maxwell model for nonlinear viscoelastic dampers used in seismic isolation,” Engineering Structures, vol. 34, p. 111-123, 2012.
[26] K. C. Chang, S. J. Chen y M. L. Lai, “Inelastic Behavior of Steel Frames with Added Viscoelastic Dampers,” vol. 122, nº 10, pp. 1178-1186, 1996.
[27] K.-W. Min, J. Kim y S.-H. Lee, “Vibration Test of 5-Storey Steel Frame with Viscoelastic Dampers,” vol. 26, pp. 831-839, 2004.
[28] R. Lewandowski and Z. Pawlak, “Dynamic analysis of frames with viscoelastic dampers modelled by rheological models with fractional derivatives,” Journal of Soundand Vibration, vol. 330, pp. 923-936, 2011.
[29] Z. Pawlak y R. Lewandowski, “The continuation method for the eigenvalue problem of structures with viscoelastic dampers,” Computers and Structures, vol. 125, p. 53-61, 2013.
[30] D. M. Bergman y R. D. Hanson, “Viscoelastic Mechanical Damping Devices Tested at Real Eathquake Displacements,” vol. 9, nº 3, pp. 389-417, 1993.
[31] L. Meirovitch, “Elements of Vibration Analysis,” New York: McGraw-Hill, 1986.
[32] F. Hejazi, A. Zabihi y M. Jaafar, “Development of elasto-plastic viscous damper finite element model for reinforced concrete frames,” Soil Dynamics and Earthquake Engineering, vol. 65, pp. 284-293, 2014.
Published
2016-09-22
How to Cite
Gil-Peláez, J., & Suárez, L. (2016). Global loss factor in steel structures with viscoelastic dampers through state equations. ITECKNE, 13(2), 146-156. https://doi.org/https://doi.org/10.15332/iteckne.v13i2.1479
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Section
Research and Innovation Articles
