Optimal Seismic Protection of Structures on Bearings With Bilinear Hysteretic Characteristic

The design of optimal seismic protection systems on bearings with hysteresis behavior leads to a conditional multidimensional global optimization problem with a nonlinear and non-differentiable objective function. In this paper, bearings with bilinear characteristic with hysteresis are considered, i.e. for each nonlinear bearing there are four parameters to optimize: ultimate elastic displacement and stiffness for the elastic mode and ultimate displacement and stiff-ness for the inelastic mode. We study the seismic response of an elastic beam on four nonlinear bearings under vertical seismic ground motion. The perturbation functional as an integral of the quadratic form of the state vector with a weight matrix formed from the stiffness and inertia matrices of the system on equivalent elastic supports is considered as the objective function. Minimization of the functional means the minimum of the total energy of the system on equivalent elastic bearings. Genetic algorithm is used to solve the optimization problem.