Effects of Hysteresis and Negative Stiffness on Seismic Response Reduction: A Case Study Based on the 1999 Athens, Greece Earthquake
The aim of this paper is to investigate the effects of hysteresis and negative stiffness on seismic response reduction. For this reason, the novel Hysteretic Nonlinear Energy Sink (HNES) is used as a passive vibration control device for seismic response mitigation. So far, HNES performance has been tested in shock mitigation and has proved to exhibit exceptional robustness and energy dissipation merits. Apart from a small mass and a nonlinear elastic spring of the Duffing oscillator (type-I NES), HNES is also comprised of a purely hysteretic and a linear elastic spring of potentially negative stiffness, connected in parallel. The Bouc-Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. In this investigation, the response reduction of a primary two-degree-of-freedom model of a shear building is studied against a strong ground motion which is based on the 1999 Athens, Greece earthquake. The response reduction is achieved by using three optimized passive vibration control devices, i.e. an HNES, a type-I NES, and a traditional Tuned Mass Damper (TMD). The optimum configuration of each device is determined using Differential Evolution, a robust metaheuristic algorithm, using the maximum absolute displacement of the top floor as the objective function. Example problems are presented in order to assert that HNES behavior is vastly superior over both NES and TMD. Furthermore, the key advantage of HNES is its inherent insensitivity to drastic changes in the structural characteristics. In particular, it maintains a significant level of performance even if the column stiffness is reduced by half.
A comparative study of linear and nonlinear mass damping systems under seismic excitation
Abstract A comparative study of the seismic response of structures equipped with linear and nonlinear mass damping systems is presented herein. Three optimized mass damping systems mounted at the top of a linearly elastic two-degree-of-freedom building are tested under an artificial seismic motion to assess their response. The artificial seismic motion is generated using the SIMQKE software and matching a specific response spectrum. The mass damping systems consist of (i) a Linear Mass Damper (LMD), (ii) a type-I Nonlinear Energy Sink (NES) with a nonlinear elastic spring of the cubic oscillator, and (iii) a Friction Nonlinear Energy Sink (FNES) which extends the NES with a friction element and a linear elastic spring of potentially negative stiffness. The results for each configuration are validated with a set of real scaled ground motion time histories matching the same specific spectrum, and a quantification of the response variability in relation to the input variability is attempted. An interesting observation is that the artificially generated excitation consistently underestimates critical design/response quantities, as compared to the average response of the set of real ground motions.
Mathematical Time and Physical Time in the Theory Of Relativity
In the Theory of Relativity time is an imaginary quantity that can not be observed; it is a multiplication of a number that indicates duration of material change and number i that is an imaginary number. i on the square is -1. Time i⁄t is a mathematical time that describes the speed and the duration of material change. In the Universe one can observe physical time only as a stream of material change. It is not that change run in physical time, change itself is physical time.. Distinction between imaginary mathematical time and visible physical time opens some new perspectives into interpretation of Theory of Relativity. c