First Band Gap Research Articles

Broadband inverted T-shaped seismic metamaterial

Seismic metamaterials (SMs) are expected to assist or replace traditional isolation systems owing to their strong attenuation of seismic waves. In this work, a one-dimensional inverted T-shaped SM (1D ITSM) composed of arrays of inverted T-shaped structures on a half space is proposed, which have an ultra-wide first bandgap (FBG) from 6.7 to 17.2 Hz. We find that the FBG is composed of two parts; part 1 with surface evanescent waves from 6.7 to 11.0 Hz and part 2 with no surface modes from 11.0 to 17.2 Hz by using the complex band structures. The propagation of seismic surface waves in the 1D ITSM is different in these two frequency ranges of the FBG. In part 1, the seismic surface waves are significantly attenuated in the 1D ITSM because of the surface evanescent waves, while in part 2, the surface waves are converted into bulk waves because surface waves cannot exist in the ITSM. Finally, the ultra-wide FBG is verified by using a kind of the two-dimensional ITSM in large-scale field experiments.

Acoustic characteristics of damped metamaterial plate with parallel attached resonators

An acoustic metamaterial consisting of a homogeneous damped plate with parallel attached resonators is presented. Theoretical analysis shows that the metamaterial plate can generate multiple resonant-type band gaps and the lower-bound frequency of each band gap coincides with the resonance frequencies of the resonators. The parallel arrangement of resonators, compared with the metamaterial plate with resonators attached in series reported by Peng et al. (2015), results in a wider second band gap with a lower edge, while the first band gap is almost the same, creating therefore an easier combination of the multiple band gaps into a wider one. It is noted that damping has a significant influence on the band gaps and the effective mass density (especially for the damping of resonators). Specifically, it can be concluded that damping cannot be neglected in practical engineering applications, damping in the material of the host plate can smooth and lower the responses in the whole frequency range, especially in the higher frequency range, and a high level of damping of resonators deactivates the effect of band gaps. Such weak/damped resonators actualise the metamaterial damping poorly, and rather tend only to contribute to the overall damping such as the damping of the host plate.

Research on the tunability of point defect modes in a two-dimensional magneto-elastic phononic crystal

Point defect modes in a 2D phononic crystal with giant magnetostrictive material tuned by a magnetic field and compressive stress are investigated theoretically in this study. The 3D magnetostrictive constitutive model proposed by Liu and Zheng (2005 Acta Mech. Sin. 21 278–85) is adopted to develop effective elastic, piezomagnetic, and magnetic permeability constants. The finite element method, in combination with a supercell technique, is then applied to obtain the band structures and transmission spectra of the point defect modes in a 2D phononic crystal composed of Terfenol-D rods of circular cross section embedded in a polymethyl methacrylate matrix with a square lattice. The magnetic field not only enlarges the first band gap (FBG) but also opens up a new band gap of XY modes. New point defect modes are simultaneously trapped in the band gaps. The width of the FBG and the frequencies of the point defects of the Z mode decrease as the magnetic field increases.

Propagation of Shear Horizontal Waves in Laminated Composites Based on Differently Orientated Poled 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 Single Crystals

The propagation characteristics of shear horizontal waves in [001]c, [011]c and [111]c direction polarized 0.72Pb (Mg1/3Nb2/3) O3-0.28PbTiO3 (PMN-0.28PT) piezoelectric single crystals/polymer periodic laminated composites are studied by using the global matrix method. The numerical results show that the piezoelectric effect has a significant influence on the bandgap width of the composite structure containing [011]c and [111]c poled PMN-0.28PT, but little effect on the band structure of the system containing [001]c poled single crystal. In addition, the first bandgap (FBG) width of the composite structure depends strongly on the poling directions when the filling fraction of PMN-0.28PT is larger than 0.5, and its FBG starting frequency displays no distinct difference among the three polarization directions at all filling fractions. The reported results provide valuable guidelines for designing filters and transducers made of composite structures containing relaxor-based ferroelectric single crystals.

Band gaps of lamb waves in one- dimensional piezoelectric composite plates: effect of substrate and boundary conditions

We theoretically study the band structures of Lamb waves in one-dimensional phononic crystal plates consisting of piezoelectric ceramics placed periodically in epoxy with epoxy or piezoelectric ceramic substrate by the virtual plane wave expansion method. The dependences of the widths and starting frequencies of first band gaps (FBG) on the substrate's thickness, the filling fraction, and the lattice spacing are calculated for different materials of substrate under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). The FBG width decreases gradually as the substrate's thickness increases and the FBG starting frequency increases progressively as the thickness increases on the whole. The FBG widths and starting frequencies with SC are always larger than with OC. Our research shows that it is possible to control the width and starting frequency of the FBG in the engineering according to need by choosing suitable values of the substrate's thickness, the filling fraction, and the lattice spacing.

Control of the elastic wave bandgaps in two-dimensional piezoelectric periodicstructures

Theoretical studies are presented for the band structures of bulk waves in a two-dimensionalcomposite structure consisting of rectangular piezoelectric ceramics placed periodically inan epoxy substrate. The dependences of the widths and starting frequencies of the firstbandgaps (FBGs) on the filling fraction and the ratio of length to width of theembedded section are calculated for different polarized directions of the piezoelectricceramics and different phononic structures. Our research shows that the FBG dependstrongly on the polarized directions, the phononic structures, the filling fraction andthe ratio of length to width, respectively. Therefore, one can control the FBGin engineering according to need by choosing these parameters of the system.

The Band Gaps of Plate-Mode Waves in One-Dimensional Piezoelectric Composite Plates: Polarizations and Boundary Conditions

Theoretical studies are presented for the band structures of plate-mode waves in a one-dimensional (1-D) phononic crystal plate consisting of piezoelectric ceramics placed periodically in an epoxy substrate. The dependences of the widths and starting frequencies of first band gaps (FBG) on the filling fraction and the thickness to lattice pitch ratio are calculated for different polarizations of piezoelectric ceramics under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). We found that the FBG always is broadened by polarizing piezoelectric ceramics, and the FBG widths with SC always are larger than that with OC for the same polarization. Our research shows that there are three critical parameters which determine the FBG: the polarized directions, the filling fraction, and the ratio of the plate thickness to the lattice pitch, respectively. Therefore, we can control the width and starting frequency of the FBG in the engineering according to need by choosing these parameters of the system.