TIME-DOMAIN ANALYSIS OF LINEAR HYSTERETIC DAMPING

✍ Scribed by INAUDI, J. A.; MAKRIS, N.

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 838 KB
• Volume: 25
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/(sici)1096-9845(199606)25:6<529::aid-eqe549>3.0.co;2-p

✦ Synopsis

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.