Optimal design of eccentricity for seismic applications

Making either mass or stiffness eccentric mitigates the translational vibration of systems subjected to base excitation. The level of mitigation depends not only on the amount of eccentricity but also on the frequency ratio (the ration of translational frequency to rotational frequency). This paper proposes a systematic approach for finding the values of eccentricity and frequency ratio that lead to the maximum reduction in translational vibrations. First an optimization problem in frequency domain is formulated. The mean square value of response is selected as the performance index. Two types of constraints including limitations on rotations and eccentricity are imposed. Kanai-Tajimi power spectral density function is used to model the ground motion. After formulating the optimization problem two structural models are studied numerically: a single story building model and a multistory building model. It is observed that using the proposed approach the performance index can be reduced by up to 50%. The time history analyses also indicate significant reductions in displacements. Finally a case study is conducted to compare the performance of the proposed strategy with that of other established passive control methods. The results of the case study show that the proposed method can be as effective as other strategies, as far as displacement control is concerned.