Dimensional Analysis of Inelastic Structures with Negative Stiffness and Supplemental Damping Devices

AbstractA negative stiffness device (NSD) has been proposed as an innovative way for seismic protection of structures. It was shown both numerically and experimentally to improve the performance of inelastic structures when it is appropriately designed for the given application. In order to systematically evaluate the effects of a NSD, dimensional analysis is used in this study to quantify the structural responses as the function of input ground motion characteristics, model parameters of structure and NSD, as well as supplemental damping. To facilitate this, a simplified yet parameterized numerical model is first proposed to mimic the observed responses of the tested prototype NSD. The dimensional analysis is then conducted on a single degree of freedom (SDOF) system equipped with both a NSD and a nonlinear damper. By comparing the dimensionless structural responses for the cases of (1) inelastic structure only, (2) inelastic structure with nonlinear damper, and (3) inelastic structure with both nonlinea...

[1]  Michael C. Constantinou,et al.  Apparent Weakening in SDOF Yielding Structures Using a Negative Stiffness Device: Experimental and Analytical Study , 2015 .

[2]  Michael C. Constantinou,et al.  Adaptive Negative Stiffness: New Structural Modification Approach for Seismic Protection , 2013 .

[3]  Andrew S. Whittaker,et al.  Energy dissipation systems for seismic applications: Current practice and recent developments , 2008 .

[4]  Hirokazu Iemura,et al.  Negative stiffness friction damping for seismically isolated structures , 2006 .

[5]  J. Florentin.  Optimal Control of Continuous Time, Markov, Stochastic Systems† , 1961 .

[6]  C.-M. Lee,et al.  Design of springs with “negative” stiffness to improve vehicle driver vibration isolation , 2007 .

[7]  Michael C. Constantinou,et al.  Adaptive Negative Stiffness: A New Structural Modification Approach for Seismic Protection , 2013 .

[8]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[9]  Michael C. Constantinou,et al.  Numerical simulations of a highway bridge structure employing passive negative stiffness device for seismic protection , 2015 .

[10]  N. Abrahamson,et al.  Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity , 1997 .

[11]  Nicos Makris,et al.  A half-century of rocking isolation , 2014 .

[12]  Shih-Po Chang,et al.  Effect of viscous, viscoplastic and friction damping on the response of seismic isolated structures , 2000 .

[13]  Michael C. Constantinou,et al.  Simulated Bilinear-Elastic Behavior in a SDOF Elastic Structure Using Negative Stiffness Device: Experimental and Analytical Study , 2014 .

[14]  Jann N. Yang,et al.  Application of Optimal Control Theory to Civil Engineering Structures , 1975 .

[15]  Gian Paolo Cimellaro,et al.  Retrofit of a hospital through strength reduction and enhanced damping , 2006 .

[16]  Michael C. Constantinou,et al.  Negative Stiffness Device for Seismic Protection of Structures , 2013 .

[17]  Nicos Makris,et al.  Dimensional analysis of bilinear oscillators under pulse-type excitations , 2004 .

[18]  Jian Zhang,et al.  DIMENSIONAL ANALYSIS OF STRUCTURES WITH TRANSLATING AND ROCKING FOUNDATIONS , 2009 .

[19]  Gian Paolo Cimellaro,et al.  Retrofit of Structures: Strength Reduction with Damping Enhancement , 2005 .

[20]  Nicos Makris,et al.  Evaluation of Peak Ground Velocity as a “Good” Intensity Measure for Near-Source Ground Motions , 2004 .

[21]  T. T. Soong,et al.  Supplemental energy dissipation: state-of-the-art and state-of-the- practice , 2002 .

[22]  Jian Zhang,et al.  Optimal Nonlinear Damping for Inelastic Structures Using Dimensional Analysis , 2012 .

[23]  Marvin W. Halling,et al.  Near-Source Ground Motion and its Effects on Flexible Buildings , 1995 .

[24]  B. F. Spencer,et al.  STATE OF THE ART OF STRUCTURAL CONTROL , 2003 .

[25]  Babak Alavi,et al.  Behavior of moment‐resisting frame structures subjected to near‐fault ground motions , 2004 .

[26]  Farzad Naeim,et al.  Design of seismic isolated structures : from theory to practice , 1999 .

[27]  Jian Zhang,et al.  Inelastic displacement demand of bridge columns considering shear–flexure interaction , 2011 .

[28]  George P. Mavroeidis,et al.  A Mathematical Representation of Near-Fault Ground Motions , 2003 .