Transmissibility functions for base isolation systems with nonlinear viscosity

Athanasios Markou, George D. Manolis

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


In this work, we suggest a physical process to explain the empirical formula introduced by J.M. Kelly in 1991, where the dissipated energy of a high damping rubber bearing (HDRB) under cyclic testing at constant frequency is proportional to the amplitude of the shear strain raised to a power of approximately n=1.50. The physical process is best described by non-Newtonian fluid behavior, originally developed by F.H. Norton in 1929 to describe creep in steel at high-temperatures. The constitutive model includes a viscous term that depends on the absolute value of the velocity raised to a non-integer power. An analytical solution for energy dissipation in a nonlinear viscous element is derived under cyclic testing and is subsequently compared with the one provided earlier by T.T. Soong and M.C. Constantinou in 1994. Identification of a three parameter Kelvin model, the simplest possible system with nonlinear viscosity, is also suggested here. Finally, a more advanced model with variable damping coefficient is implemented to further explain this complex mechanical process.
Original languageEnglish
Title of host publicationProceedings of the 11th HSTAM International Congress on Mechanics
Publication statusPublished - 2016
MoE publication typeA4 Article in a conference publication
EventHSTAM International Congress on Mechanics - Athens, Greece
Duration: 27 May 201630 May 2016
Conference number: 11


ConferenceHSTAM International Congress on Mechanics

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