Locally resonant phononic crystals band-gap analysis on a two dimensional phononic crystal with a square and a triangular lattice

Sellami, Khouloud; Ketata, Hajer; Ghozlen, Mohamed Hédi Ben

doi:10.1007/s11082-019-2028-0

Cited by 14 publications

(5 citation statements)

References 19 publications

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“…Then, the applied stress and wave displacement continuity are expected at the border between every two adjacent layers. Therefore, the stress introduced due to the propagating acoustic waves through the desired design can be defined as [52][53][54]:…”

Section: Theoretical Methodologymentioning

confidence: 99%

Enhanced Sensitivity of Binary/Ternary Locally Resonant Porous Phononic Crystal Sensors for Sulfuric Acid Detection: A New Class of Fluidic-Based Biosensors

et al. 2023

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This research presented a comprehensive study of a one-dimensional (1D) porous silicon phononic crystal design as a novel fluidic sensor. The proposed sensor is designed to detect sulfuric acid (H2SO4) within a narrow concentration range of 0–15%. Sulfuric acid is a mineral acid extensively utilized in various physical, chemical, and industrial applications. Undoubtedly, its concentration, particularly at lower levels, plays a pivotal role in these applications. Hence, there is an urgent demand for a highly accurate and sensitive tool to monitor even the slightest changes in its concentration, which is crucial for researchers. Herein, we presented a novel study on the optimization of the phononic crystal (PnC) sensor. The optimization process involves a comparative strategy between binary and ternary PnCs, utilizing a multilayer stack comprising 1D porous silicon (PSi) layers. Additionally, a second comparison is conducted between conventional Bragg and local resonant PnCs to demonstrate the design with the highest sensitivity. Moreover, we determine the optimum values for the materials’ thickness and number of periods. The results revealed that the ternary local resonant PnC design with the configuration of {silicone rubber/[PSi1/PSi2/PSi3]N/silicone rubber} is the optimal sensor design. The sensor provided a super sensitivity of 2.30 × 107 Hz for a concentration change of just 2%. This exceptional sensitivity is attributed to the presence of local resonant modes within the band gap of PnCs. The temperature effects on the local resonant modes and sensor performance have also been considered. Furthermore, additional sensor performance parameters such as quality factor, figure of merit, detection limit, and damping rate have been calculated to demonstrate the effectiveness of the proposed liquid sensor. The transfer matrix method was utilized to compute the transmission spectra of the PnC, and Hashin’s expression was employed to manipulate the porous silicon media filled with sulfuric acid at various concentrations. Lastly, the proposed sensor can serve as an efficient tool for detecting acidic rain, contaminating freshwater, and assessing food and liquid quality, as well as monitoring other pharmaceutical products.

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Section: Theoretical Methodologymentioning

confidence: 99%

Enhanced Sensitivity of Binary/Ternary Locally Resonant Porous Phononic Crystal Sensors for Sulfuric Acid Detection: A New Class of Fluidic-Based Biosensors

et al. 2023

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“…The solution for the Minldin's piezoelectric plate can be obtained by setting ψ y = ψ z = 0, ψ x = ψ 0 e iω1t , Φ ′ = φ 0 e iω1t for xy -plane, (26a) ψ y = ψ x = 0, ψ z = ψ 0 e iω2t , Φ ′ = φ 0 e iω2t for zy -plane. (26b) Substituting equation (26) into equation (13), and using equation (15), the circular frequency ω 2 r on the xy-plane and zyplane of the piezoelectric plate cross-section can be obtained…”

Section: Determine the Shear Correction Factor κ 2 Rmentioning

confidence: 99%

“…The timedomain wavefield images obtained from the experiment were used to evaluate the dispersion relations of the bending waves and compared with numerical predictions. Most research on phononic crystals focuses on elastic waves based on threedimensional governing equations [15,16]. The typically considered structures are thin plates, and often the classical plate theory is discussed [12,13,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Research on bending vibration characteristics of phononic crystal plates based on Mindlin’s piezoelectric plate theory

Wang,

Zhou,

Dong

et al. 2023

Smart Mater. Struct.

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Based on Mindlin's theory and the Plane Wave Expansion Method, the formulas are proposed for the governing equations and dispersion relations of bending waves in piezoelectric phononic crystal plates. The shear correction factors can be obtained through transcendental equations based on forced vibrations of the plate. The plates are made of inclusions of different shapes and lattice types, finding that the inclusion shape dramatically affects the mid-to-high frequency band gaps. Piezoelectric materials exhibit distinct eigenfrequencies at the high-symmetry point Γ at low frequencies. Thickness affects the band gap width differently than in two-dimensional models, and cuts influence band gap width significantly.

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“…For a long time, the research of phononic crystals has mostly focused on the bandgap forward problems, where theoretical derivation and numerical simulation are carried out by known material and structural parameters to obtain bandgap laws affecting the elastic wave propagation. At present, there are more mature studies having been conducted on different structural forms of phononic crystals such as rods [3][4][5], beams [6][7][8], and plates [9][10][11], etc Lu et al [12] proposed a broadband hybrid mechanism gradient elastic metamaterial rod, which broaden the attenuation bandgap range by increasing the gradient variation filling rate and local resonators. Liu et al [13] continuously regulated the lattice constants of the local resonant phononic crystal beam and the structural parameters of the resonators so as to tune the bandgap.…”

Section: Introductionmentioning

confidence: 99%

Research on the design of phononic crystal shaft bandgaps based on lumped mass method

et al. 2023

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Phononic crystals tend to mature in the research of forward problems due to their unique bandgap characteristics, but it is difficult to realize reasonable parameter design at specific bandgap frequencies in practical engineering applications. Thus, based on the lumped mass method, a research method for the inverse problem of phononic crystal shaft bandgaps is proposed in this paper. On the basis of the discretization model, the relationship between polynomials and the characteristic of bandgaps is discussed through derivation of the dispersive polynomial, and the feasible regions of the corresponding parameters are solved according to the bandgap existence criterion established by the characteristic rules for analytical verification. The results show that the bandgap existence criterion for frequency points and frequency bands can accurately and effectively invert the relevant parameters that meet the requirements, and the method is of great practical significance for promoting the development of phononic crystal shaft parameter design under the target bandgap in engineering applications.

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Locally resonant phononic crystals band-gap analysis on a two dimensional phononic crystal with a square and a triangular lattice

Cited by 14 publications

References 19 publications

Enhanced Sensitivity of Binary/Ternary Locally Resonant Porous Phononic Crystal Sensors for Sulfuric Acid Detection: A New Class of Fluidic-Based Biosensors

Enhanced Sensitivity of Binary/Ternary Locally Resonant Porous Phononic Crystal Sensors for Sulfuric Acid Detection: A New Class of Fluidic-Based Biosensors

Research on bending vibration characteristics of phononic crystal plates based on Mindlin’s piezoelectric plate theory

Research on the design of phononic crystal shaft bandgaps based on lumped mass method

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