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TIME‐DOMAIN ANALYSIS OF LINEAR HYSTERETIC DAMPING
Author(s) -
INAUDI J. A.,
MAKRIS N.
Publication year - 1996
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/(sici)1096-9845(199606)25:6<529::aid-eqe549>3.0.co;2-p
Subject(s) - mathematics , differential equation , mathematical analysis , time domain , dissipation , frequency domain , equations of motion , modal , physics , classical mechanics , computer science , chemistry , polymer chemistry , computer vision , thermodynamics
Two linear‐hysteretic‐damping models that provide energy dissipation independent of the deformation frequency, are studied in this paper: a hysteretic Kelvin element and a hysteretic Maxwell element. Both models use the Hilbert transform and yield integro–differential equations for the equations of motion of structures when real‐valued signals are utilized in the formulation. It is shown that the use of analytic (complex‐valued) signals allows the transformation of these integro–differential equations into differential equations with analytic input signals and complex‐valued coefficients. These differential equations show both stable and unstable poles. A technique for the solution of these differential equations is presented; it consists of a conventional modal decomposition of the state‐space equations and the integration of the differential equations forward in time for the modal co‐ordinates associated with stable poles, and backwards in time for the modal co‐ordinates associated with unstable poles. Some numerical examples are presented to illustrate the characteristics of the models and the proposed analysis technique.