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In this paper, we study the free vibrations of the plate with metamaterial, i.e., with an arbitrary number of masses and springs. The free vibration frequencies and the mode shapes are determined as a prelude of studying forced and random vibrations. The comparison is made with previous studies devoted to a plate with a single mass, or with five resonators. Numerical results are reported for the plate supported with numerous resonators.

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Uncovering an Overlooked Natural Frequency in Free Vibrations of a Plate with Attached Resonators

  • 章节

  • 发表日期：

    2025年

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  • Isaac Elishakoff,
  • Matthieu Zawadzki

摘要

In this paper, we study the free vibrations of the plate with metamaterial, i.e., with an arbitrary number of masses and springs. The free vibration frequencies and the mode shapes are determined as a prelude of studying forced and random vibrations. The comparison is made with previous studies devoted to a plate with a single mass, or with five resonators. Numerical results are reported for the plate supported with numerous resonators.