This paper deals with the optimum design of vibration absorbers utilized to reduce undesirable vibrational effects which are originated in linear structures by seismic excitations. The single linear tuned mass dampers problem is treated and it is assumed that earthquake can be represented by a stationary filtered stochastic process. In the present problem, the objective is to minimize the maximum of the dimensionless peak of displacement of the protected system with respect to the unprotected one. Moreover, the constrained optimization problem is also analysed, in which a limitation of tuned probability of failure is imposed, where failure is related to threshold crossing probability by the maximum displacement over an admissible value. Examples are given to illustrate the efficiency of the proposed method. The variation of the optimum solution versus structural and input characteristics is analysed for the unconstrained and constrained optimization problems. A sensitivity analysis is carried out, and results are presented useful for the first design of the vibrations control strategy.
We study the optimal (minimum mass) problem for a prototypical self-similar tensegrity column. By considering both global and local instability, we obtain that mass minimization corresponds to the contemporary attainment of instability at all scales. The optimal tensegrity depends on a dimensionless main physical parameter χ 0 that decreases as the tensegrity span increases or as the carried load decreases. As we show, the optimal complexity (number of self-similar replication tensegrities) grows as χ 0 decreases with a fractal-like tensegrity limit.
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