**Acknowledgements**

*Photonic Crystals - A Glimpse of the Current Research Trends*

In this chapter, metal-matrix embedded phononic crystals consisting of double-sided stubs (single stubs and composite stubs), which are deposited on a two-dimensional locally resonant phononic crystal plate that consists of an array of rubber fillers embedded in a steel plate, are introduced. The following summaries

*The evolution of the first bandgap in the proposed phononic-crystal plate with "hard" stubs as a function of* 

*steel-stub height with D = 8 mm, d = 7.5 mm, e = 1 mm, and a = 10 mm, respectively.*

The spring-mass system of the resonator can be decoupled by introducing the rubber filler, and then the out-of-plane bandgap and the in-plane bandgap can be adjusted into the same lowest frequency range. The out-of-plane bandgap and the in-plane bandgap can be overlapped with each other. As a result, a lower frequency complete bandgap which ranges from 59 to 93 Hz is obtained in the metal-matrix

Both the out-of-plane and the in-plane phononic bandgap increase after introducing single "hard" cylinder stubs. When introducing the rubber filler and the single "hard" stub simultaneously, two new kinds of resonance modes are produced: an in-plane analogous-rigid modes, where the whole stub vibrates in-plane with the plate, and the other new resonance mode is the out-of-plane analogous-rigid mode, where the whole stub vibrates out-of-plane with respect to the plate. The out-of-plane bandgap increases for the out-of-plane analogous-rigid mode, and the in-plane bandgap increases for the in-plane analogous-rigid mode. Both the out-ofplane and the in-plane analogous-rigid modes are mainly formed due to introducing the single "hard" cylinder stub. The in-plane and out-of-plane bandgaps overlap and produce a broad complete bandgap in the metal-matrix embedded phononic crystals. Within this broad complete bandgap, both the in-plane and out-of-plane Lamb waves are prohibited. The absolute bandwidth of the bandgap for the proposed structure is five times higher than for the classic double-sided stubbed

The effect of the stub on the bandgaps is investigated. Results show that the location of the bandgaps can be modulated in a significant lower frequency range, and the bandwidth can be expanded in a considerable large frequency range by introducing different composite taper stubs, and the bandwidth can be expanded to

The proposed structure provides an effective way for phononic crystals to obtain wide complete bandgaps and lower frequency complete bandgaps (below 100 Hz), which have a potential application in the low-frequency vibration reduction in a

a larger frequency range by introducing different "hard" stubs.

**6. Conclusions**

**Figure 15.**

were drawn [14, 18]:

embedded phononic crystals.

metal-matrix phononic-crystal plate.

**46**

practical case.

This chapter was supported by the Project of the National Science Foundation of China (No. 51674199).
