An event-driven time-domain sensitivity method for optimizing parameters of vibro-impact NES cells to suppress multi-mode vibration

Abstract

The effectiveness of Vibro-Impact Nonlinear Energy Sink cells (VI-NES cells) in suppressing multimode vibration is highly sensitive to contact stiffness, mass ratio, and impact gap, necessitating precise tuning of these parameters. This paper develops an event-driven sensitivity method to optimize a time-domain objective function, automatically obtaining cells' parameters with approximately global optimized vibration suppression efficiency. First, the vibro-impact process between VI-NES cells and a host structure is regularized as a Hertzian model with linear contact stiffness and damping, yielding explicitly piecewise linear forces governed by contact-separation phase transitions. Subsequently, an event-driven time integration algorithm is developed to analyze dynamic responses by detecting transition points. Before and after the contact-separation transition points, the sensitivity affine relation is derived in detail, resulting in the time-domain response sensitivity with respect to mass and impact gap. Ultimately, the acquired response sensitivities and Tikhonov regularization are applied to optimize a time-domain objective function about VI-NES parameters, minimizing the dynamic vibration responses of the host structure. Numerical studies validate that the proposed method enhances the multi-mode vibration suppression performance of VI-NES cells, and clarifies the energy dissipation, targeted energy transfer, and coupling mechanics of VI-NES cells, offering an essential framework toward large-scale simulations and optimization of the host structure with VI-NES cells.

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ORCID for Jie Yuan: orcid.org/0000-0002-2411-8789

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