Research on the vibration characteristics of an embedded elastic metamaterial plate

For a class of embedded elastic metamaterial plate, a general vibration analysis process is given based on the idea of equivalent analysis, which combines the equivalent medium theory and the classical thin plate vibration theory. The embedded elastic metamaterial plate is treated as an equivalent homogeneous plate with abnormal effective medium parameters by using the equivalent medium theory, and then the natural vibration characteristics and steady-state vibration characteristics are investigated. The results show that the semi-analytic form of the vibration analysis process is effective, which can obtain the vibration characteristics of such heterogeneous and complex structures quickly and accurately within the medium and low frequency regions. The results also reveal the plate’s anomalous behaviors that are quite different from the traditional homogeneous plates. For the natural vibration, there exists no natural frequency in the band gap and they can be formed only in the pass band. These modes tend to gather gradually when approaching the initial frequency of the band gap, and the closer to the lower band edge of the band gap, the smaller the distance between natural frequencies and the greater the modal density. Additionally, the modes of the corresponding orders before and after the band gap are identical on the macro level but completely different on the unit-cell level. For the steady-state vibration, there is no resonance peak in the band gap, the resonance peaks are distributed denser and denser when approaching the initial frequency of the band gap, and the distribution of the displacement field at corresponding order of resonance peaks before and after the band gap is also similar on the macro level. This work not only facilitates the design and analysis of elastic metamaterial plate structures, but also deepens the understanding of their extraordinary vibration characteristics and expands the design space of mode characteristics.