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The active support of a large-scale structure, made up of two elements was designed and manufactured. The first of them - piezoelectric actuator, enables the simulations of vibrations transferred from the ground to the structure. In order to minimize vibrations transmitted through the ground to the construction, the second element of the active support - a system based on magnetorheological dampers was used. The active support enables the simulations of vibrations from the ground using a piezoelectric stack controlled in a reverse feedback loop. Control signals of the feedback loop are: the volume of deformation and vibrations in the selected structures node.

We consider a variational problem in which the minimized functional is convex but non-differentiable. In the static case, the variational problem serves to describe the mechanical system’s equilibrium position. In the rheological case it is employed to determine the velocities, and in the dynamical case it can be used to determine the accelerations of the body.

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