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The paper studies the dynamics of a vibro-impact system consisting of a main (primary) structure and a vibro-impact damper coupled to it. A vibro-impact damper is a vibro-impact nonlinear energy sink (VI NES). The optimal damper design should provide the best vibration mitigation for the primary structure. The optimization procedures for finding the optimal NES design are carried out using standard MATLAB tools. We used different MATLAB programs, namely surf program, which graphically shows the ranges of parameter pairs to be optimized; fminsearch and fminconprograms, which search for local minima of the objective function. It is shown that the optimization procedure itself is ambiguous and contains a sufficient amount of arbitrariness. Its result is also ambiguous. It is due to the presence of the many possible sets of damper parameters that can provide maximum mitigation of the main structure vibrations. We do not use the genetic algorithm gabecause it selects random intermediate results and yields randomly selected parameter sets from the optimal parameters manifold. Setting the objective function and its parameters plays a crucial role in the optimization process. We have chosen the maximum total energy of the primary structure as the objective function. Each resulting variant of the damper parameter set should be carefully tested and analyzed. We compared the five obtained optimal designs for dampers with two different masses. When analyzing them, we observed different motion modes, namely periodic modes of different periodicity with different number of impacts per cycle, with different ratio of bodies motion periods: 1:1 resonance with resonance capture and 2:1 resonance; amulti-periodic mode with many impacts per cycle, which turned out to be an amplitude-modulated mode – Amplitude Modulated Signal . The final decision on the optimal damper design may be made taking into account various engineering considerations regarding its mass and other parameters. It should be based on the options obtained as a result of the optimization procedure.
Лізунов et al. (Wed,) studied this question.