Supercell Plane Wave Expansion Method Research Articles

Study on Lamb Waves in a Composite Phononic Crystal Plate

In the paper, a phononic crystal plate composed of a magnetorheological elastomer with adjustable band gaps in the low frequency range is constructed. The dispersion relations of Lamb waves are studied by the supercell plane wave expansion method. The transmission responses as well as the displacement fields of Lamb waves are calculated by the finite element method. The influence of geometric parameters on the band gaps, the regulation effect of the volume ratio of Fe particles and the bias magnetic field on the band gaps are analyzed. Based on the numerical results, we find that the volume ratio of Fe particles and the magnetic field affect the band gap effectively. The location and width of the band gaps can be adjusted within a broad frequency range by varying the geometric parameters and magnetic field. We can control the band gap, achieve an appropriate and wide low band gap by selecting proper geometric parameters and applying an external contactless magnetic field to deal with complicated and changeable engineering environment. The results are useful for understanding and optimizing the design of composite vibration isolation plates.

Band gap tunability in deformable dielectric composite plates

Subject to voltage, dielectric elastomers deform and stiffen. We show that harmonic excitations at certain frequencies cannot propagate in incompressible dielectric elastomer fiber composite films. Importantly, we demonstrate that these band gaps are tunable by the voltage. To show this, we formulate the equations governing small-amplitude waves in a deformed film, taking into consideration its surfaces. We develop a scheme to numerically solve the resultant equations, based on the supercell plane wave expansion method. To arrive at the findings above, we apply our scheme to a composite with circular fibers, and parametrically study the propagation dependency on the phase properties, film thickness, and voltage. Our results are another step towards the use of soft dielectric films as active wave manipulators.

Phononic thin plates with embedded acoustic black holes

We introduce a class of two-dimensional nonresonant single-phase phononic materials and investigate its peculiar dispersion characteristics. The material consists of a thin platelike structure with an embedded periodic lattice of acoustic black holes. The use of these periodic tapers allows achieving remarkable dispersion properties such as zero group velocity in the fundamental modes, negative group refraction index, birefraction, Dirac-like cones, and mode anisotropy. The dispersion properties are numerically investigated using both a three-dimensional supercell plane wave expansion method and finite element analysis. The effect on the dispersion and propagation characteristics of key geometric parameters of the black hole, such as the taper profile and the residual thickness, are also explored.

Low-frequency band gaps in one-dimensional thin phononic crystal plate with periodic stubbed surface

Using supercell plane wave expansion method, the Lamb wave band structure of one-dimensional thin plate with periodic stubs is investigated. The numerical results show that flat bands will appear and band gap can exist in a low-frequency domain. The position of the flat bands and width of the low-frequency Lamb wave band gap can be tuned by the stub height, plate thickness and filling fraction. The band gap is obtained by opening the folding points of the same plate modes not the crossing point of different plate mode when the stub height is small.

Flexural Vibration in a Ternary Locally Resonant Phononic Crystal Thin Plate with Defects

The improved supercell plane wave expansion method is applied to theoretically study the propagation of flexural waves in a ternary locally resonant phononic crystal thin plate with a point defect and linear defects. The thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps in low frequency are obtained. For the point defect, the defect mode is localized around the defect, and the magnitude of the resonant defect mode is strongly dependent on the defect filling fraction, mass density and Young’s modulus of the defect cylinder. For the straight linear defects, several resonant linear defect bands appear inside the absolute band gap. And the displacement distributions show that the flexural waves could well propagate along the linear defects.

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.

Lamb waves in phononic crystal slabs with square or rectangular symmetries

We report on both numerical and experimental results showing the occurrence of band gaps for Lamb waves propagating in phononic crystal plates. The structures are made of centered rectangular and square arrays of holes drilled in a silicon plate. A supercell plane wave expansion method is used to calculate the band structures and to predict the position and the magnitude of the gaps. The band structures of phononic crystal slabs are then measured using a laser ultrasonic technique. Lamb waves in the megahertz range and with wave vectors ranging over more than the first two reduced Brillouin zones are investigated.

Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates

We introduce a supercell plane wave expansion (SC-PWE) method for the calculation of elastic band structures of two-dimensional phononic crystal plates. We compute the band structure of solid-solid and air-solid two-dimensional phononic crystal plates. The air is modeled as a low impedance medium (LIM) with very low density and very high velocities of sound. We investigate the influence of the constituent materials, of the plate thickness, and of the geometry of the array on the band structure. We establish the range of validity of the SC-PWE method in terms of the rate of convergence with respect to the number of plane waves and contrast in physical properties of the matrix and inclusion materials. We show that for high contrast solid-solid phononic crystal plates, our SC-PWE method, as other PWE-based methods introduced to date, suffers from convergence difficulties. In the case of air (modeled as the LIM) holes-solid plates, we demonstrate that the SC-PWE method leads to fast convergence for a wide range of values of solid physical properties. With these constituent materials, we find that the largest absolute forbidden bands occur in the band structure of the phononic crystal plate provided the thickness of the plate is of the order of magnitude of the periodicity of the array of inclusions. We demonstrate the existence of guided modes in an air-silicon phononic crystal plate containing a linear defect.