Acoustic Band Gap Materials Research Articles

Improving the functionality of biosensors through the use of periodic and quasi-periodic one-dimensional phononic crystals

Abstract Resonant acoustic band gap materials have steered a new sensing technology era. This study is presented to investigate of the one-dimensional (1D) phononic crystals (PnCs), involving periodic, as well as quasi-periodic 1D layered PnCs represented as a highly sensitive biosensor to detect and monitor the quality of milk. In this regard, the numerical findings show that the examined periodic PnCs structure outperformed the quasi-periodic structure. In particular, it provides a wider phononic band gap and greater sensitivity as well. In addition, the quasi-periodic design (especially Fibonacci sequence S4) introduces multiple resonance peaks via transmission spectra, which may lead to some conflicts during the detection process. The findings reveal that the frequency of the resonant peak can effectively change with varied milk solution concentrations and temperatures. The optimized sensor is capable of differentiating between concentrations ranging between 0 and 50 % with a 10 % step, and it can also differentiate between temperatures, which range between 5 °C and 50 °C. This makes it ideal for precise detection of other liquids and solutions. The sensor performs efficiently for all milk solution concentrations. Here, the findings demonstrated that the examined defective PnC structure exhibited the most favorable sensitivity of the value of 94.34 MHz, so it showed the highest sensitivity when varying milk concentrations. In addition, the configurated sensor provided high QF and FOM values of 3,853.645161 and 157.42, respectively. On the other hand, the sensor performs very well for all temperatures of the milk solution. As such, the S 4 quasi-periodic structure is characterized as the optimal sensor structure when varying temperatures, introducing a sensitivity of 4.78 MHz/°C, QF of 4,278.521, and FOM of 7.48 °C−1.

Periodic and quasi-periodic one-dimensional phononic crystal biosensor: a comprehensive study for optimum sensor design.

The resonant acoustic band gap materials have introduced an innovative generation of sensing technology. Based on the local resonant transmitted peaks, this study aims to comprehensively investigate the use of periodic and quasi-periodic one-dimension (1D) layered phononic crystals (PnCs) as a highly sensitive biosensor for the detection and monitoring of sodium iodide (NaI) solution. Meanwhile, a defect layer is introduced defect layer inside the phononic crystal designs to be filled with NaI solution. The proposed biosensor is developed based on the periodic PnCs structure and quasi-periodic PnCs structure. The numerical findings demonstrated that the quasi-periodic PnCs structure provided a wide phononic band gap and a large sensitivity compared to the periodic one. Moreover, many resonance peaks through the transmission spectra are introduced for the quasi-periodic design. The results also show that the resonant peak frequency changes effectively with varying NaI solution concentrations in the third sequence of the quasi-periodic PnCs structure. The sensor can differentiate between concentrations ranging from 0 to 35% with a 5% step, which is extremely satisfying for precise detection and can contribute to a variety of issues in medical applications. Additionally, the sensor provided excellent performance for all the concentrations of the NaI solution. For instance, the sensor has a sensitivity of 959 MHz, a quality factor of 6947, a very low damping factor of 7.19 × 10-5, and a figure of merit of 323.529.

Nature-inspired designs for disordered acoustic bandgap materials.

We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumor invasion. Here we use this bio-inspired structure as a design template to construct mechanical metamaterials and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable acoustic bandgaps. Unlike acoustic crystals with periodic structures, the bandgaps here are directionally isotropic and robust to defects due to their complete lack of positional order. Possible ways to manipulate bandgaps are explored with a combination of the tissue-level elastic modulus and local stiffness heterogeneity of cells. To further demonstrate the existence of bandgaps, we dynamically perturb the system with an external sinusoidal wave in the perpendicular and horizontal directions. The transmission coefficients are calculated and show valleys that coincide with the location of bandgaps. Experimentally this design should lead to the engineering of self-assembled rigid acoustic structures with full bandgaps that can be controlled via mechanical tuning and promote applications in a broad area from vibration isolations to mechanical waveguides.

Fano resonance based defected 1D phononic crystal for highly sensitive gas sensing applications

The defected acoustic band gap materials are promising a new generation of sensing technology based on layered cavities. We introduced a novel 1D defected phononic crystal (1D-DPC) as a high-sensitive gas sensor based on the Fano resonance transmitted window. Our designed (Lead–Epoxy) 1D-DPC multilayer has filled with a defect layer with different gases at different temperatures. In this study, Fano resonance—based acoustic band gap engineering has used to detect several gases such as O2, CO2, NH3, and CH4. For the first time, Fano resonance peaks appeared in the proposed gas sensor structures which attributed to high sensitivity, Q-factor, and figure-of-merit values for all gases. Also, the relation between the Fano resonance frequency and acoustic properties of gases at different temperatures has been studied in detail. The effect of the damping rate on the sensitivity of the gas sensor shows a linear behavior for CO2, O2, and NH3. Further, we introduced the effect of temperature on the damping rate of the incident waves inside the 1D-DPC gas sensor. The highest sensitivity and figure of merit were obtained for O2 of 292 MHz/(kg/m3) and 647 m3/Kg, respectively. While the highest figure-of-merit value of 60 °C−1 at 30 °C was attributed to O2. The transfer matrix method is used for calculating the transmission coefficient of the incident acoustic wave. We believe that the proposed sensor can be experimentally implemented.

Validation of low frequency noise attenuation using locally resonant patches.

Since conventional silencers in acoustic ducts have problems of size limitations at low frequencies and being prone to high backpressure, locally resonant aluminum patches are introduced in acoustic duct walls aiming at creating frequency stop bands in the low frequency region (below 1 KHz). With these flush mounted patches, promising noise reductions, with no such drawbacks, can be obtained, building on local resonance phenomenon implemented in acoustic metamaterials techniques. The objective of the current paper is to experimentally validate the performance of an array of flexible side-wall-mounted patches inside ducts. The experimental results are compared with Analytical Green's function method as well as Numerical Finite Element Method and a close agreement was found. The results show that the presence of the patches singly or periodically can play a prominent role in designing any acoustic bandgap materials. The effect of the arrays of patches on the effective dynamic density and bulk modulus has also been investigated.

Harnessing fluid-structure interactions to design self-regulating acoustic metamaterials

The design of phononic crystals and acoustic metamaterials with tunable and adaptive wave properties remains one of the outstanding challenges for the development of next generation acoustic devices. We report on the numerical and experimental demonstration of a locally resonant acoustic metamaterial with dispersion characteristics, which autonomously adapt in response to changes of an incident aerodynamic flow. The metamaterial consists of a slender beam featuring a periodic array or airfoil-shaped masses supported by a linear and torsional springs. The resonance characteristics of the airfoils lead to strong attenuation at frequencies defined by the properties of the airfoils and the speed on the incident fluid. The proposed concept expands the ability of existing acoustic bandgap materials to autonomously adapt their dispersion properties through fluid-structure interactions, and has the potential to dramatically impact a variety of applications, such as robotics, civil infrastructures, and defense systems.

Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids.

Recently, disordered photonic media and random textured surfaces have attracted increasing attention as strong light diffusers with broadband and wide-angle properties. We report the experimental realization of an isotropic complete photonic band gap (PBG) in a 2D disordered dielectric structure. This structure is designed by a constrained optimization method, which combines advantages of both isotropy due to disorder and controlled scattering properties due to low-density fluctuations (hyperuniformity) and uniform local topology. Our experiments use a modular design composed of Al2O3 walls and cylinders arranged in a hyperuniform disordered network. We observe a complete PBG in the microwave region, in good agreement with theoretical simulations, and show that the intrinsic isotropy of this unique class of PBG materials enables remarkable design freedom, including the realization of waveguides with arbitrary bending angles impossible in photonic crystals. This experimental verification of a complete PBG and realization of functional defects in this unique class of materials demonstrate their potential as building blocks for precise manipulation of photons in planar optical microcircuits and has implications for disordered acoustic and electronic band gap materials.

Acoustic impulse response method as a source of undergraduate research projects and advanced laboratory experiments

A straightforward and inexpensive implementation of acoustic impulse response measurement is described utilizing the signal processing technique of coherent averaging. The technique is capable of high signal-to-noise measurements with personal computer data acquisition equipment, an amplifier/speaker, and a high quality microphone. When coupled with simple waveguide test systems fabricated from commercial PVC plumbing pipe, impulse response measurement has proven to be ideal for undergraduate research projects-often of publishable quality-or for advanced laboratory experiments. The technique provides important learning objectives for science or engineering students in areas such as interfacing and computer control of experiments; analog-to-digital conversion and sampling; time and frequency analysis using Fourier transforms; signal processing; and insight into a variety of current research areas such as acoustic bandgap materials, acoustic metamaterials, and fast and slow wave manipulation.

1D and 2D phononic crystal sensors

Acoustic band gap materials, so-called phononic crystals, provide a new sensor platform for determination of material properties in small cavities. The sensor employs specific transmission windows within the band gap to determine properties of a component that builds the phononic crystal. The frequency where transmission takes place is correlated to material properties and permits the determination of several parameters of practical interest like concentration of an analyte. The capability of the concept will be demonstrated with a one-dimensional arrangement of solid plates and liquid filled cavities and a two-dimensional periodic arrangement of liquid filled holes in a solid matrix.

Frequency modulation of waveguides in acoustic band-gap materials consisting of solid cylinders in viscous liquid

We investigated waveguides in acoustic band-gap materials consisting of steel cylinders in a liquid with viscous damping. Numerical results show that when the viscous penetration depth is comparable to the structural length scale, linear defect states fall in complete acoustic band gaps forming waveguides. It is also found that the magnitude of the viscosity in the liquid has an influence on the frequency of waveguides, that large viscous damping can make the defect modes ascend. An expected frequency of waveguides can be obtained by modulating the viscous damping parameter θ.

Phononic crystals for liquid sensor applications

Acoustic band gap materials, so-called phononic crystals, are introduced as a new platform for sensing material properties in small cavities. The sensor employs specific transmission windows within the band gap to determine properties of one component that builds the phononic crystal. The dependence of the frequency where transmission takes place is correlated to material properties, specifically to the sound velocity of a liquid. This value is related to several parameters of practical interest like the concentration of one component in a mixture or conversion rate in a microreactor. The capability of the concept will be demonstrated with a one-dimensional arrangement of solid plates and liquid-filled cavities and a two-dimensional periodic arrangement of liquid-filled holes in a solid matrix. The properties of 1D phononic crystals will be analysed in terms of the effective acoustic impedance and the resulting transmission behaviour and experimentally verified. The transmission properties of the 2D phononic crystal will be modelled with the layer multiple-scattering theory. Similar features which can be employed for sensing purposes will be discussed.

Point defect states in 2D acoustic band gap materials consisting of solid cylinders in viscous liquid

We investigated point defect states in two-dimensional acoustic band gap materials consisting of steel cylinders in liquid with viscous damping. Numerical results show that when the viscous penetration depth is comparable to the structural length scale, point defect states fall in large complete acoustic band gaps. It is also found that the magnitude of the viscosity in the liquid has an influence on the gap and defect state properties at the same time and that large viscous damping can enlarge the band gap but assemble the defect states. An expected gap frequency and a defect state frequency can be obtained by choosing a proper viscous damping parameter θ.

Rubber/air acoustic band gap materials: Elastic and viscoelastic effects

Two‐dimensional elastic and viscoelastic phononic crystals structures are investigated theoretically and experimentally. These are two‐dimensional arrays of cylinders of air inclusions in a solid silicone rubber matrix as well as arrays of silicone rubber cylinders in an air matrix. In this study, viscoelasticity is modeled with a compressible general linear viscoelastic fluid model. Numerical calculations of transmission spectra and band structures are conducted by extending the finite difference time domain (FDTD) method to account for linear viscoelastic materials which exhibit time‐dependent moduli. These systems demonstrate very wide band gaps in their transmission spectra that extend to frequencies in the audible range of the spectrum. Experimental and calculated transmission spectra for a rubber matrix/air inclusions phononic crystal show that the system behaves as a fluid/fluid composite with respect to the longitudinal polarization of acoustic waves due to the large contrast between the transverse and longitudinal speeds of sound. We also demonstrate that viscoelasticity can attenuate transmission over very wide ranges of frequency leaving only passing bands at very low frequency. These phononic crystals demonstrate the practical design of elastic or viscoelastic solid rubber/air acoustic band gap sound barrier with small dimensions.

Acoustic wave propagation in one-dimensional phononic crystals containing Helmholtz resonators

One-dimensional acoustic waveguide containing subwavelength-sized Helmholtz resonators is known to exhibit novel physical phenomena. However, no systematic theoretical study on this system has been carried out so far except on a few limited cases. We present a thorough theoretical calculation on the acoustic wave propagation in phononic crystals containing Helmholtz resonators without any geometrical size restrictions. The band structures, transmission spectra, and defect states are studied for diverse geometries using the interface response theory. It is shown that the acoustic band structure of the model is fundamentally different from the conventional acoustic–elastic cases and richer due to the coexistence of the resonant and the Bragg gaps. It is also shown that the presence of a defect resonator in the system can give rise to a localized mode inside the resonance gaps. The results clearly show that the presence of the Helmholtz resonators singly or periodically can play a prominent role in designing any acoustic band gap materials.

Tunable filtering and demultiplexing in phononic crystals with hollow cylinders.

Acoustic band gap (ABG) materials constituted of steel hollow cylinders immersed in water can exhibit a tunable narrow pass band (NPB) located inside their gap. We theoretically investigate, using the finite difference time domain (FDTD) method, the properties of waveguides composed of a row of hollow cylinders in a two-dimensional (2D) phononic crystal made of filled steel cylinders. These waveguides exhibit NPB's at frequencies slightly higher than their infinite periodic ABG counterpart. The frequency of the waveguide's NPB can be selected by adjusting the inner radius of the hollow cylinders or by changing the nature of the fluid that fills them. We show that a waveguide constituted of a row of hollow cylinders with different inner radii can transport waves at two different frequencies. By selectively filling the cylinders with water or mercury we have created an active device that permits the transmission of waves at one, both, or neither of these frequencies. Finally, we examine the multiplexing and demultiplexing capabilities of Y shaped waveguides constituted of hollow cylinders.

Defect states in 2D acoustic band-gap materials with bend-shaped linear defects

Using the supercell plane wave method, we investigated defect modes created by introducing a bend-shaped linear defect in a two-dimensional acoustic band-gap material consisting of water cylinders in mercury background. The bend-shaped linear defect is made up of the water cylinders with different size, and the size of the defect cylinders is shown to strongly influence the defect modes existing in the frequency regime of the gap. By analyzing the pressure field of defect modes, we found the waves are localized in the bend-shaped linear defect. It provides us a foundation in theory to design a bent waveguide in engineering application.

Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency

We study theoretically the propagation of elastic waves in two-dimensional composite media composed of a square array of hollow steel cylinders embedded in water using the finite-difference time-domain method. These composite media constitute a class of acoustic band gap materials with narrow pass bands in their transmission stop bands. The frequency at which the pass band occurs is tunable by controlling the inner radius of the tubular steel inclusions. The effect of the tube inner radius on the transmission spectrum is semiquantitatively separable from the effect of the composite periodicity. A linear defect formed of a row of hollow cylinders in an array of filled cylinders produces an elastic waveguide that transmits at the narrow pass band frequency. We show that two of these tunable waveguides with different inner radii can be employed to filter and separate two specific frequencies from a broad band input signal.

Acoustic band-gap engineering using finite-size layered structures of multiple periodicity

The transmission coefficient of a layered structure made of glass and water was calculated using transfer matrix method and also measured as a function of frequency. It was found that acoustic band gaps can be created using only 3–4 cells of a two-phase layered structure. By introducing two or more periods into the layered structure, very sharp passbands and very broad stopbands can be engineered for acoustic waves. Such acoustic band-gap materials could be used for making high-quality acoustic filters, acoustic mirrors and vibration insulation devices in selective frequency range.

An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials: I. Scalar Case

The paper describes an efficient finite element method for computing spectra of photonic and acoustic band-gap materials. In the photonic case only the scalar models are treated. The full vector model will be considered in the next publication.