Equivalent bilinear elastic single degree of freedom system of multi-degree of freedom structure with negative stiffness

Abstract The advantage of negative stiffness (NS) is to reduce the structural internal force, especially base shear, which is necessary to be considered during structural design. During design procedures, the structural response should be estimated. For the purpose of estimating the response of the structure with NS, this paper presents an innovative approximate method to transfer a multi degree of freedom (MDOF) structure with NS in the 1st story (MNS1) to an approximate single degree of freedom (SDOF) bilinear elastic system (ASBS). The accuracy of approximation from the MNS1 to the ASBS is studied by the sensitivity method of mode shapes in which the relative changes in structural mode shapes are related to the variation of stiffness. An eight-story numerical example is employed to illustrate the accuracy of approximation by the proposed method. The results show that the accuracy of approach is acceptable, and ASBS can estimate the response of the MNS1.

[1]  V. Spitas,et al.  Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element , 2015 .

[2]  Zhiyi Zhang,et al.  Shock isolation performance of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: Theoretical and experimental study , 2015 .

[3]  Enrique Hernández-Montes,et al.  Estimates of peak roof displacement using equivalent single degree of freedom systems , 2005 .

[4]  Jun Zhao,et al.  Sensitivity Study for Vibrational Parameters Used in Damage Detection , 1999 .

[5]  Satish Nagarajaiah,et al.  Nonlinear elastic and inelastic spectra with inherent and supplemental damping , 2013 .

[6]  A. G. Tsonos.  An innovative solution for strengthening of old R/C structures and for improving the FRP strengthening method , 2014 .

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

[8]  T. Makarios.  Equivalent non‐linear single‐degree‐of‐freedom system of spatial asymmetric multi‐storey buildings in pushover procedure: theory and applications , 2009 .

[9]  A. G. Tsonos,et al.  Effectiveness of R/C jacketing of substandard R/C columns with short lap splices , 2014 .

[10]  Gang Li,et al.  Displacement estimation of nonlinear structures using the force analogy method , 2015 .

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

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

[13]  Anil K. Chopra,et al.  A modal pushover analysis procedure for estimating seismic demands for buildings , 2002 .

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

[15]  Yeping Xiong,et al.  Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism , 2013 .

[16]  Dimitrios Vamvatsikos,et al.  Direct estimation of the seismic demand and capacity of oscillators with multi‐linear static pushovers through IDA , 2006 .

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

[18]  Satish Nagarajaiah,et al.  Study of a piecewise linear dynamic system with negative and positive stiffness , 2015, Commun. Nonlinear Sci. Numer. Simul..

[19]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[20]  Wenjiang Wu,et al.  Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness , 2014 .