On the problem of optimizing vibration protection systems based on the bilinear hysteresis elements

The paper presents a problem statement of the multidimensional optimization of a nonlinear mechanical system based on elements with the bilinear hysteresis deformation diagram. This approach is illustrated using the example of an asymmetric continuous beam on four rubber-metal shock absorbers; each of them is having four optimized parameters. A synthesized accelerogram of the base vertical acceleration is used to determine the external influence The beam model on shock absorbers was obtained using the finite element method. The model seismic response was determined by the method of direct integration of the motion equations in the MATLAB environment. The objective function was accepted as the quadratic functional of disturbances of the state vector with a weight matrix formed from the system rigidity and inertia matrices on the equivalent elastic supports. The multidimensional problem of optimizing the shock absorbers parameters was solved using a genetic algorithm in the MATLAB environment. The paper shows that the resulting solution perfectly tunes the system against the prevailing frequencies of a given accelerogram, but it is not reliable, if the random nature of seismic ground displacement is taken into account.
EDN: GIXXBH, https://elibrary/ gixxbh

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