Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative
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Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.
Keywordsfractional derivative viscoelastic damper stochastic seismic response
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- Agrawal OP (1999), “An Analytical Scheme for Stochastic Dynamic Systems Contain Fractional Derivative,”Proceedings of the American Society of Mechanical Engineers Design Engineering Technical Conferences Las Vegas, NV, September 12–15, Paper No: DETC99/BIV-8238.Google Scholar
- Bagley RL and Torvik PJ (1985), “Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures,”AIAA of Journal,23(6): 918–925.Google Scholar
- Bagley RL and Calico RA (1991), “Fractional Order State Equations for the Control of Viscoelastically Damped structures,”Journal of Guidance, Control and Dynamics,14 (2): 304–311.Google Scholar
- Mainardi F (1997),Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics, Springer-Verlag, New York.Google Scholar
- Miller KS and Ross B (1993),An Introduction to the Fractional Calculus and Fractional Differential Equations, New York; John Wiley and Sons, Inc.Google Scholar
- Nigam NC (1983),Introduction to Random Vibration, MIT Press, Cambridge.Google Scholar
- Oldham KB and Spanier J (1974),The Fractional Calculus, Acdemic Press, New York.Google Scholar