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.
Reliability analysis of the hysteretic nonlinear energy sink in shock mitigation considering uncertainties
The reliability of the hysteretic nonlinear energy sink in shock mitigation is investigated herein. The hysteretic nonlinear energy sink is a passive vibration control device which is coupled to a primary linear oscillator. Apart from its small mass and a nonlinear elastic spring of the Duffing oscillator, it also comprises a purely hysteretic and a linear elastic spring of potentially negative stiffness. The Bouc–Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. The hysteretic nonlinear energy sink protects the primary system through the energy pumping mechanism which transfers energy from the primary system and dissipates it in the hysteretic nonlinear energy sink. Three nonlinear equations of motion describe the resulting two-degree-of-freedom system response. The parameters of the system to be considered as uncertain are the natural frequency of the primary system and the hysteretic nonlinear energy sink linear elastic spring, which follow a normal distribution. A reliability analysis is then performed to evaluate the robustness of the coupled system in the presence of uncertainty. Specifically, the reliability index is calculated based on first passage probabilities of distinct dissipation energy level crossings using the Monte Carlo method. Several examples are examined considering various levels of initial input energy, and useful conclusions are drawn concerning the influence of uncertainty in the system robustness.
Modeling of chemical reactors—XXIX mixing-cell model for packed bed reactors. Steady state considerations. Problems of multiplicity
Abstract The axial heat and mass transfer in tubular catalytic reactors may be described by mixing-cell model and diffusion model as well. The diffusion description yields for a strong exothermic reaction and adiabatic conditions three steady state profiles, on the other hand the mixing-cell model gives rise to more than three steady states. A simple numerical and graphical analysis for mixing-cell model is presented.