Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals

Based on a better understanding of the lattice vibration modes, two simple spring-mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.

Directional Propagation Characteristics of Flexural Waves in Two-Dimensional Thin-Plate Phononic Crystals

The propagation characteristics of flexural waves in two-dimensional thin-plate phononic crystals （PCs） are analysed with the plane wave expansion （PWE） method to yield phase constant surfaces, which predict high directivity of flexural wave propagation for certain frequencies outside the band gap. The prediction is validated through the computation of the harmonic responses of a finite structure with 9 × 9 unit cells. The results indicate that directional propagation of flexural waves is an while specific effects of the directional propagation in inherent characteristic of two-dimensional thin-plate PCs a finite structure vary with the positions of excitations.

Band gap control of phononic beam with negative capacitance piezoelectric shunt

Periodic arrays of negative capacitance shunted piezoelectric patches are employed to control the band gaps of phononic beams. The location and the extent of induced band gap depend on the mismatch in impedance generated by each patch. The total impedance mismatch is determined by the added mass and stiffness of each patch as well as the shunting electrical impedance. Therefore, the band gap of the shunted phononic beam can be actively tuned by appropriately selecting the value of negative capacitance. The control of the band gap of phononic beam with negative capacitive shunt is demonstrated numerically by employing transfer matrix method. The result reveals that using negative capacitive shunt to tune the band gap is effective.

Theoretical and experimental investigations of flexural wave propagation in periodic grid structures designed with the idea of phononic crystals

The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.

Sound Absorption of Locally Resonant Sonic Materials

The acoustic properties of locally resonant sonic materials with viscosity are theoretically investigated by using the multiple-scattering approach. We find that the absorption of a two-layer slab dominates the wave attenuation in the resonant frequency region under the condition of moderate or high viscous level. The fundamental mechanism operating in local resonance for absorption is investigated for the viability by the mode translation in the scattering process of a single scatterer. Finally the absorption performance in a multi-layer system is discussed.

Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals

The low-frequency band gap and the corresponding vibration modes in two-dimensional ternary locally resonant phononic crystals are restudied successfully with the lumped-mass method. Compared with the work of C. Goffaux and J. Sánchez-Dehesa （Phys. Rev. B 67 14 4301（2003））, it is shown that there exists an error of about 50% in their calculated results of the band structure, and one band is missing in their results. Moreover, the in-plane modes shown in their paper are improper, which results in the wrong conclusion on the mechanism of the ternary locally resonant phononic crystals. Based on the lumped-mass method and better description of the vibration modes according to the band gaps, the locally resonant mechanism in forming the subfrequency gaps is thoroughly analysed. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap is also verified in this ternary case.

Theoretical and Experimental Investigation of Flexural Wave Propagating in a Periodic Pipe with Fluid-Filled Loading

Based on the Bragg scattering mechanism of phononic crystals （PCs）, a periodic composite material pipe with fluid loading is designed and studied. The band structure of the flexural wave in the periodic pipe is calculated with the transfer matrix （TM） method. A periodic piping experimental system is designed, and the vibration experiment is performed to validate the attenuation ability of the periodic pipe structure. Finally, a finite-element pipe model is constructed using the MSC-Actran software, and the calculated results match well with the vibration experiment. The errors between the theoretical calculation results and the vibration experimental results are analyzed.

Broadband Attenuation in Phononic Beams Induced by Periodic Arrays of Feedback Shunted Piezoelectric Patches

The effect of periodic arrays of feedback shunted piezoelectric patches in the flexural wave attenuation of phononic beams is analyzed theoretically and experimentally.A numerical model based on transfer matrix methodology is developed to predict the transmission of vibration and the frequency ranges of the band gaps.Broadband vibration attenuations are observed in or out of the band gaps.The proposed concept is validated on a suspended epoxy beam driven by a shaker,and the experimental results are presented in terms of the vibration transmissions recorded using two accelerometers placed on both sides of the beam.

Comparison of the mechanism of gap formation for tri- and bi-component phononic crystal

Using an exact Mie scattering solution, this paper investigates the mode conversions during the Mie scattering of a single bi- or one-component sphere in unbounded epoxy. Then the formation mechanism of the first complete gap in the corresponding tri- or bi-component phononic crystal is investigated by the multiple-scattering method. It is shown that the heavy density of the scatterer plays an essential role in the Mie resonance and the formation of the gaps for both types of the phononic crystals. For the tri-component phononic crystal, the gap is mainly induced by the Mie resonance of the single scatterer. For the bi-component phononic crystal, the transverse wave （by mode-conversion during the Mie scattering under a longitudinal wave incidence） is modulated by the periodicity and governed by the Bloch theory, which induces the gap cooperatively.

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases, The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Coupled flexural-torsional vibration band gap in periodic beam including warping effect

The propagation of coupled flexural-torsional vibration in the periodic beam including warping effect is investigated with the transfer matrix theory. The band structures of the periodic beam, both including warping effect and ignoring warping effect, are obtained. The frequency response function of the finite periodic beams is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The effect of warping stiffness on the band structure is studied and it is concluded that substantial error can be produced in high frequency range if the effect is ignored. The result including warping effect agrees quite well with the simulated result.