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Research Papers

Finite Element Analysis of the Seismic Response of Damped Structural Systems Including Fractional Derivative Models

[+] Author and Article Information
Fernando Cortés

Deusto Institute of Technology (DeustoTech),
Faculty of Engineering,
University of Deusto,
Avenida de las Universidades 24,
Bilbao 48007, Spain
e-mail: fernando.cortes@deusto.es

María Jesús Elejabarrieta

Department of Mechanical Engineering,
Mondragon Unibertsitatea,
Loramendi 4,
Mondragon 20500, Spain
e-mail: mjelejabarrieta@mondragon.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 17, 2013; final manuscript received April 11, 2014; published online July 25, 2014. Assoc. Editor: Thomas J. Royston.

J. Vib. Acoust 136(5), 050901 (Jul 25, 2014) (5 pages) Paper No: VIB-13-1111; doi: 10.1115/1.4027457 History: Received April 17, 2013; Revised April 11, 2014

This paper presents a finite element formulation for the seismic response of damped structural systems. Damping is obtained using a viscoelastic material, which is characterized by a constitutive law with fractional derivatives. The weighted residue method is applied resulting in a fractional motion equation, which is numerically integrated through an implicit scheme in combination with the constant acceleration Newmark method. An example of application is presented, in which the response of a cantilever beam with free layer damping is analyzed. The material properties are identified from the material experimental characterization, where the parameters of the fractional model were identified by curve fitting. The results of the simulation are compared with the experimental ones, concluding that the tendencies observed in the measurements are reproduced.

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References

Housner, G. W., Bergman, L. A., Caughey, T. K., Chassiakos, A. G., Claus, R. O., Masri, S. F., Skelton, S. E., Soong, T. T., Spencer, B. F., and Yao, J. T. P., 1997, “Structural Control: Past, Present and Future,” ASCE J. Eng. Mech., 123(9), pp. 897–971. [CrossRef]
Soong, T. T., and Constantinou, M. C., 1994, Passive and Active Structural Vibration Control in Civil Engineering, Springer, Berlin.
Soong, T. T., and Dargush, G. F., 1997, Passive Energy Dissipation Systems in Structural Engineering, Wiley, New York.
Ali, H. M., and Abdel-Ghaffar, A. M., 1995, “Modeling the Nonlinear Seismic Behaviour of Cable-Stayed Bridges With Passive Control Bearings,” Comput. Struct., 54(3), pp. 461–492. [CrossRef]
Zhu, H., Wen, Y., and Iemura, H., 2001, “A Study on Interaction Control for Seismic Response of Parallel Structures,” Comput. Struct., 79(2), pp. 231–242. [CrossRef]
Madsen, L. P. B., Thambiratnam, D. P., and Perera, N. J., 2003, “Seismic Response of Building Structures With Dampers in Shear Walls,” Comput. Struct., 81(4), pp. 239–253. [CrossRef]
Levy, R., and Lavan, O., 2006, “Fully Stressed Design of Passive Controllers in Framed Structures for Seismic Loadings,” Struct. Multidiscip. Optim., 32(6), pp. 485–498. [CrossRef]
Bagley, R. L., and Torvik, P. J., 1983, “Fractional Calculus—A Different Approach to the Analysis of Viscoelastically Damped Structures,” AIAA J., 23(6), pp. 918–925. [CrossRef]
Pritz, T., 1996, “Analysis of Four–Parameter Fractional Derivative Model of Real Solid Materials,” J. Sound Vib., 195(1), pp. 103–115. [CrossRef]
Lee, H. H., and Tsai, C. S., 1994, “Analytical Model of Viscoelastic Dampers for Seismic Mitigation of Structures,” Comput. Struct., 50(1), pp. 111–121. [CrossRef]
Hwang, J. S., and Ku, S. W., 1997, “Analytical Modeling of High Damping Rubber Bearings,” ASCE J. Struct. Eng., 123(8), pp. 1029–1036. [CrossRef]
Hwang, J. S., and Wang, J. C., 1998, “Seismic Response Prediction of HDR Bearings Using Fractional Derivative Maxwell Model,” Eng. Struct., 20(9), pp. 849–856. [CrossRef]
Hwang, J. S., and Hsu, T. Y., 2001, “A Fractional Derivative Model to Include the Effect of Ambient Temperature on HRD Bearings,” Comput. Struct., 23(5), pp. 484–490. [CrossRef]
Agrawal, O. P., 2001, “Stochastic Analysis of Dynamic Systems Containing Fractional Derivatives,” J. Sound Vib., 247(5), pp. 927–938. [CrossRef]
Rüdinger, F., 2006, “Tuned Mass Damper With Fractional Derivative Damping,” Eng. Struct., 28(13), pp. 1774–1779. [CrossRef]
Padovan, J., 1987, “Computational Algorithms for FE Formulations Involving Fractional Operators,” Comput. Mech., 2(4), pp. 271–287. [CrossRef]
Cortés, F., and Elejabarrieta, M. J., 2007, “Finite Element Formulations for Transient Dynamic Analysis in Structural Systems With Viscoelastic Treatments Containing Fractional Derivative Models,” Int. J. Numer. Methods Eng., 69(10), pp. 2173–2195. [CrossRef]
Cortés, F., and Elejabarrieta, M. J., 2007, “Homogenised Finite Element for Transient Dynamic Analysis of Unconstrained Layer Damping Beams Involving Fractional Derivative Models,” Comput. Mech., 40(2), pp. 313–324. [CrossRef]
Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, New York.
“Soundown—Peace and Quiet for Architectural, Marine, & Industrial Applications,” 2010, Soundown Corporation, Salem, MA, retrieved on Apr. 4, 2014, http://www.soundown.com
Kosloff, D., and Frazier, G. A., 1978, “Treatment of Hourglass Patterns in Low Order Finite Element Codes,” Int. J. Numer. Anal. Methods Geomech., 2(1), pp. 57–72. [CrossRef]
“ASM,” 2011, Aerospace Specification Metals, Pompano Beach, FL, retrieved on Apr. 4, 2014, http://asm.matweb.com
Cortés, F., and Elejabarrieta, M. J., 2007, “Viscoelastic Materials Characterisation Using the Seismic Response,” Mater. Des., 28(7), pp. 2054–2062. [CrossRef]
Cortés, F., Martinez, M., and Elejabarrieta, M. J., 2012, Viscoelastic Surface Treatments for Passive Control of Structural Vibration, Nova Publishers, Inc., New York.
ASTM E 756-05, 2010, Standard Test Method for Measuring Vibration-Damping Properties of Materials, American Society for Testing and Material, West Conshohocken, PA.

Figures

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Fig. 1

Photograph of the measurement system

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Fig. 2

Displacement of the base motion

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Fig. 3

Finite element model of the cantilever beam

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Fig. 4

Comparison between the fitted model and experimental data: (a) storage modulus and (b) loss modulus

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Fig. 5

Displacement of the free edge of the beam with base excitation obtained experimentally and numerically

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