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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Fig. 1

Photograph of the measurement system

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Fig. 2

Displacement of the base motion

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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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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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