Surface acoustic wave band gaps in micro-machined air/silicon phononic structures — theoretical calculation and experiment

Wu, Tsung‐Tsong; Huang, Zi-Gui; Liu, Shih-Yang

doi:10.1524/zkri.2005.220.9-10.841

Cited by 20 publications

(5 citation statements)

References 39 publications

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Section: Reflective Grating For Saws Using Phononic Crystalsmentioning

confidence: 99%

“…For an air/Si PC with square lattice, propagation of SAWs was analyzed in previous studies [56,41]. With a filling fraction F D 0.283, there is a partial band gap for SAW along the X direction [56]. Further, the band gap enlarges with the increase of filling fraction, and reaches the widest gap for the case of F D 0.48 [41].…”

Section: Reflective Grating For Saws Using Phononic Crystalsmentioning

confidence: 99%

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Surface Acoustic Waves in Phononic Crystals

Hsu

Sun

et al. 2016

Phononic Crystals

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Over the past two decades, propagation of acoustic waves in periodic structures comprised of multi-components has received much attention because of renewed physical properties and potential applications in a variety of fields, such as noise and vibration isolation, frequency filters in wireless communication, super lens design, etc. These composite materials, called phononic crystals (PCs) [1,2], give rise to forbidden gaps for acoustic waves which are analogous to the band gaps for electromagnetic waves in photonic crystals. Major mechanisms leading to the forbidden gaps are Bragg scattering and localized resonances (LR) [3]. The former opens up the Bragg gap at the Brillouin-zone boundaries, and the band-gap frequency corresponds to the wavelength in the order of the structural period, i.e. of the lattice constant, and relates to the lattice symmetry. On the other hand, localized

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Section: Reflective Grating For Saws Using Phononic Crystalsmentioning

confidence: 99%

Section: Reflective Grating For Saws Using Phononic Crystalsmentioning

confidence: 99%

Surface Acoustic Waves in Phononic Crystals

Hsu

Sun

et al. 2016

Phononic Crystals

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“…If S fs vanishes, no coupling effect will exist between the solid and fluid. For the present acoustic fluid-solid interaction problem under the conditions (6)-(9), a key step is to obtain the finite element formulation for one unit cell by imposing (6) and (7) to (10). 35,36 To describe the derivation process explicitly without loss of generality, we consider a fluid-solid system consisting of N identical substructures (i.e.…”

Section: Finite Element Formulationmentioning

confidence: 99%

Dispersion Relations of a Periodic Array of Fluid-Filled Holes Embedded in an Elastic Solid

Wang

Zhang

2012

J. Comp. Acous.

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Dispersive properties of elastic waves in a periodic composite with an array of fluid-filled holes are studied in this paper. A finite element method taking into account of the fluid-solid interaction is developed to calculate the dispersion curves. The finite element formulation is presented for one unit cell by taking advantage of the periodicity of the structures and the Bloch theorem. After dividing the equations in the real and imaginary parts, the numerical computation is performed by using the standard finite element code ABAQUS. As numerical examples, some typical twoand three-dimensional systems with circular or spherical holes filled with air, water or mercury are considered in detail. The method can yield precise results with fast convergence for all cases from very low-density fluids to very high-density fluids.applications such as acoustic filters, control of vibration isolation, noise suppression and design of new transducers, etc.Bandgaps can be characterized by the dispersion relations (i.e., band structures), that is, the frequency intervals where there is no dispersion curve are complete bandgaps. Therefore the calculation of the band structures or dispersion relations is one of the main tasks in studying phononic crystals. So far, several methods have been developed, among which, the transfer matrix (TM) method, 6 the plane wave expansion (PWE) method, 7−13 the finite difference time-domain (FDTD) method, 14−18 the multiple scattering theory (MST) method 19−24 and the wavelet method 25−27 are often used. Except the TM method, the other methods are applicable to one-, two-and three-dimensional (1D, 2D, and 3D) systems; and many of results based on these methods have been reported about the perfectly phononic crystals or those with defects. 28−31 However, most of them encounter difficulties when dealing with the systems with fluid-filled holes (fluid/solid systems). As well known, different wave modes propagate in solids and fluids, respectively -the mixed longitudinal and transverse elastic waves in solids and the purely longitudinal acoustic wave in fluids. Proper fluid-solid interface conditions, which are different from those between two solids or two fluids, should be considered to match the wave solutions in solids and fluids. The PWE method cannot yield correct results for fluid/solid systems. Unphysical flat bands appear randomly in the calculated band structures according to the number of plane waves used in calculation. The origin of the failure of the PWE method is that the Bloch theorem is singular in some areas of the systems. 32 To overcome this difficulty, Goffaux and Vigneron 8 introduced an artificial transverse wave velocity in the fluid. Although this assumption seems to work reasonably well, 8,10 the choice of the artificial transverse wave velocity in the fluid is not straightforward. Besides, this technique is only justified in a low-density fluid (e.g. air) and is not valid for the high-density fluid (e.g. water or mercury). The wavelet method 26,27 can eliminate these unph...

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“…At present, a certain degree of interests is being generated on the PCs with periodic holes (vacuum [6] or filled with air [7]) with their bandgaps mainly determined by the geometric parameters. Most of the reports are focused on the systems with convex holes (circular or regular polygon holes) [3][4][5][6][7]. In a recent paper [8], we proposed a kind of PCs with the cross-like (a kind of non-convex) holes.…”

Section: Motivation and Backgroundmentioning

confidence: 99%

Complete bandgaps in three-dimensional holey phononic crystals with helmholtz resonators

Wang

2012

2012 IEEE International Ultrasonics Symposium

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In this paper, the bandgap properties of three-dimensional holey phononic crystals with Helmholtz resonators are investigated by using the finite element method. The resonators are periodically arranged cubic lumps in the cubic holes connected to the matrix by one narrow connector. In contrast to a system with cubic or spherical holes, which has no bandgaps, systems with Helmholtz resonators can exhibit complete bandgap, which is lower by an order of magnitude than the Bragg bandgap can be obtained. The vibration modes at the band edges of the lowest bandgap are analyzed in order to understand the mechanism of the bandgap generation. It is found that the emergence of the bandgap is due to the local resonance of the resonators. Spring-mass/ pendulum models are developed in order to evaluate the frequencies of the bandgap edges. The study in this paper is relevant to the optimal design of the bandgaps in light porous materials.

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Surface acoustic wave band gaps in micro-machined air/silicon phononic structures — theoretical calculation and experiment

Cited by 20 publications

References 39 publications

Surface Acoustic Waves in Phononic Crystals

Surface Acoustic Waves in Phononic Crystals

Dispersion Relations of a Periodic Array of Fluid-Filled Holes Embedded in an Elastic Solid

Complete bandgaps in three-dimensional holey phononic crystals with helmholtz resonators

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