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Energy and transmissibility in nonlinear viscous base isolators. (English) Zbl 1397.70020
Summary: High damping rubber bearings (HDRB) are the most commonly used base isolators in buildings and are often combined with other systems, such as sliding bearings. Their mechanical behaviour is highly nonlinear and dependent on a number of factors. At first, a physical process is suggested here to explain the empirical formula introduced by J. M. Kelly in 1991, where the dissipated energy of a HDRB under cyclic testing, at constant frequency, is proportional to the amplitude of the shear strain, raised to a power of approximately 1.50. This physical process is best described by non-Newtonian fluid behaviour, originally developed by F. H. Norton in 1929 to describe creep in steel at high-temperatures. The constitutive model used includes a viscous term, that depends on the absolute value of the velocity, raised to a non-integer power. The identification of a three parameter Kelvin model, the simplest possible system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i.e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under time-harmonic loads.
70F25 Nonholonomic systems related to the dynamics of a system of particles
Full Text: DOI
[1] Bhuiyan, A. K., Y. Okui, H. Mitamura, T. Imai. A Rheology Model of High Damping Rubber Bearings for Seismic Analysis: Identification of Nonlinear Viscosity. International Journal of Solids and Structures, 46 (2009), 1778-1792. · Zbl 1217.74022
[2] Markou, A. A., G. Oliveto, A. Mossucca, F. C. Ponzo. Laboratory Experimental Tests on Elastomeric Bearing from the Solarino Project, Progetto di Ricerca, Report DPC - RELUIS, Italy, Potenza, University of Basilicata, 2014.
[3] Norton, F. H. The Creep of Steels at High Temperatures, New York, McGraw- Hill, 1929.
[4] Irgens, F. Rheology and Non-Newtonian Fluids, Heidelberg, Springer-Verlag, 2014. · Zbl 1270.76001
[5] Besson, J., G. Cailletaud, J. L. Chaboche, S. Forest, M. Bletry. Non- Linear Mechanics of Materials, Heidelberg, Springer-Verlag, 2010.
[6] DalľAsta A., L. Ragni. Experimental Tests and Analytical Model of High Damping Rubber Dissipating Devices. Engineering Structures, 28 (2006), 1874-1884.
[7] Kelly, J. M. Dynamic and Failure Characteristics of Bridgestone Isolation Bearings. Report No. UCB/EERC 91/04, CA, Berkley, Earthquake Engineering Re- search Center, 1991.
[8] Kelly, J. M., E. Quiroz. Mechanical Characteristics of Neoprene Isolation Bearings, Report No. UCB/EERC 92/11, CA, Berkley, Earthquake Engineering Research Center, 1992.
[9] Kelly, J. M. Earthquake-Resistant Design with Rubber, Heidelberg, Springer-Verlag, 1997.
[10] Naeim, F., J. M. Kelly. Design of Seismic Isolated Structures, from Theory to Practice, New York, John Wiley, 1999.
[11] Weisstein, E. W. Wallis Cosine Formula, From MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/WallisCosineFormula.html, 2003.
[12] Soong, T. T., M. C. Constantinou. Passive and Active Structural Vibration Control in Civil Engineering, Vienna, Springer-Verlag, 1994.
[13] Hansen, N. The CMA-Evolution Strategy: A Tutorial, https://www.lri.fr/ hansen/cmatutorial.pdf, 2011.
[14] MATLAB, The MathWorks, Inc., Natick, Massachusetts, 2009.
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