Band Gap Formation in Composite Models With Quasi-Random Fiber Arrangements

2005 ◽  
Author(s):  
Shashidhar Patil ◽  
Liang-Wu Cai
Keyword(s):  
Band Gap ◽  
Large Scale ◽  
Composite Plates ◽  
Two Dimensions ◽  
Band Gaps ◽  
Gap Formation ◽  
Statistical Parameters ◽  
Composite Models ◽  
Gap Characteristics ◽  
Primary Band

Large-scale deterministic simulations are performed in order to observe the band gap formation in composite models having quasi-random fiber arrangements. Composite plates are modeled in two-dimensions with various unidirectional fiber arrangements. The quasi-random fiber arrangements can be qualified as essentially regular with slight randomness. Simulation results are compared with the corresponding case of ideally regular fiber arrangement. The most interesting observation is that the slight randomness in the fiber arrangements enhances the band gap phenomenon by introducing a few secondary band gaps adjacent to the primary band gap. An attempt is made to relate the band gap characteristics to the statistical parameters of fiber arrangements.

Effects of Randomness on Band Gap Formation in Models of Fiber-Reinforced Composite Panels Having Quasirandom Fiber Arrangements

2007 ◽  
Vol 129 (5) ◽  
pp. 663-671 ◽  
Author(s):  
Liang-Wu Cai ◽  
Shashidhar Patil
Keyword(s):  
Band Gap ◽  
Large Scale ◽  
Dimensional Space ◽  
Base Line ◽  
Composite Panels ◽  
Fiber Reinforced ◽  
Gap Formation ◽  
Statistical Parameters ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Large-scale deterministic simulations are performed in order to observe the band gap formation in composite models having quasirandom fiber arrangements. Unidirectional fiber-reinforced composite panels are modeled in two-dimensional space with quasirandom fiber arrangements that can be qualified as “essentially regular with slight randomness.” Different quasirandom fiber arrangements are computationally generated using the same control parameters. Statistical parameters are used to quantitatively describe the fiber arrangements. Subsequently, a series of arrangements is generated from each base line arrangement by scaling up the coordinates of fiber centers, while the fiber diameter remains unchanged in order to study the effects of fiber spacing. Simulation results are compared with the corresponding case of ideally regular fiber arrangement. The most interesting observation is that the slight randomness in the fiber arrangements enhances the band gap phenomenon by introducing a few secondary band gaps adjacent to the primary band gap.

scholarly journals Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1656 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Forced Response ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Response Analysis ◽  
Flexural Waves ◽  
Single Wave

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

scholarly journals ACOUSTIC BAND GAP FORMATION IN METAMATERIALS

2010 ◽  
Vol 24 (25n26) ◽  
pp. 4935-4945 ◽  
Author(s):  
D. P. ELFORD ◽  
L. CHALMERS ◽  
F. KUSMARTSEV ◽  
G. M. SWALLOWE
Keyword(s):  
Band Gap ◽  
Lattice Constant ◽  
Low Frequency ◽  
Band Gaps ◽  
Gap Formation ◽  
Individual Band ◽  
Resonance Band ◽  
Frequency Regime ◽  
Sonic Crystal ◽  
The Individual

We present several new classes of metamaterials and/or locally resonant sonic crystal that are comprised of complex resonators. The proposed systems consist of multiple resonating inclusion that correspond to different excitation frequencies. This causes the formation of multiple overlapped resonance band gaps. We demonstrate theoretically and experimentally that the individual band gaps achieved, span a far greater range (≈ 2kHz) than previously reported cases. The position and width of the band gap is independent of the crystal's lattice constant and forms in the low frequency regime significantly below the conventional Bragg band gap. The broad envelope of individual resonance band gaps is attractive for sound proofing applications and furthermore the devices can be tailored to attenuate lower or higher frequency ranges, i.e., from seismic to ultrasonic.

The Band Gap Formation in Rotors with Longitudinal Periodicity and Quasi-Periodicity

2021 ◽  
Author(s):  
Patrick Bueno Lamas ◽  
Rodrigo Nicoletti
Keyword(s):  
Band Gap ◽  
Frequency Spectrum ◽  
Analytical Modeling ◽  
Vibration Response ◽  
Band Gaps ◽  
Mode Shapes ◽  
Local Mode ◽  
Rotating Machines ◽  
Gap Formation

Abstract Modal spacing (band gaps) in the frequency spectrum of rotating machines can be imposed by geometric periodicity. By designing the rotor with a geometry that repeats periodically, we can impose to the vibration response of the rotor a modal "gap" considerably large, where no resonances appear. In this work, we consider that the rotating elements of the machine (e.g. the stages or the impellers) are the periodic elements of the rotor. In this disk-like configuration of the rotor, the system can present band gaps due to two different reasons: due to matching between the number of disks and the eigenmode wavenumber (usually in slender rotors); due to the presence of local-mode shapes (usually in large rotors). Analytical modeling of the system is presented, whose approximated solution can be used to predict the start and stop frequencies of the band gaps. It is also shown the limitations in band gap formation when the rotor is not perfectly periodic (quasi-periodic geometry). In this case, disk positioning plays an important role in the band gap formation.

scholarly journals Band gap formation and Anderson localization in disordered photonic materials with structural correlations

2017 ◽  
Vol 114 (36) ◽  
pp. 9570-9574 ◽  
Author(s):  
Luis S. Froufe-Pérez ◽  
Michael Engel ◽  
Juan José Sáenz ◽  
Frank Scheffold
Keyword(s):  
Band Gap ◽  
Multiple Scattering ◽  
Anderson Localization ◽  
Dielectric Material ◽  
Dielectric Materials ◽  
Band Gaps ◽  
Gap Formation ◽  
Weakly Coupled ◽  
Unified View ◽  
Wavelength Radiation

Disordered dielectric materials with structural correlations show unconventional optical behavior: They can be transparent to long-wavelength radiation, while at the same time have isotropic band gaps in another frequency range. This phenomenon raises fundamental questions concerning photon transport through disordered media. While optical transparency in these materials is robust against recurrent multiple scattering, little is known about other transport regimes like diffusive multiple scattering or Anderson localization. Here, we investigate band gaps, and we report Anderson localization in 2D disordered dielectric structures using numerical simulations of the density of states and optical transport statistics. The disordered structures are designed with different levels of positional correlation encoded by the degree of stealthiness χ. To establish a unified view, we propose a correlation-frequency (χ–ν) transport phase diagram. Our results show that, depending only on χ, a dielectric material can transition from localization behavior to a band gap crossing an intermediate regime dominated by tunneling between weakly coupled states.

Design of Band Gap Formation in Periodic Rotors via Optimization

2021 ◽  
Author(s):  
Patrick B. Lamas ◽  
Rodrigo Nicoletti
Keyword(s):  
Frequency Response ◽  
Band Gap ◽  
Optimization Procedure ◽  
Band Gaps ◽  
Rotational Inertia ◽  
Gap Formation ◽  
Central Frequency ◽  
Periodic Condition

Abstract Rotors are usually composed of rotating elements (e.g. disks, impellers, blade stages) which add mass and rotational inertia to the system. When this additional inertia of the rotating elements is evenly distributed along the rotor, inertia periodicity appears and the system presents considerably large band gaps in its frequency response, where no resonances appear. The present work shows that we can change the central frequency of these band gaps, without significantly affecting its bandwidth, by changing the distribution of the inertia along the rotor to a quasi-periodic condition. Such designing of the rotor, and consequently of the band gap, is achieved by an optimization procedure.

Coupled Band Gaps in the Piezoelectric Composite Plate With Interconnected Electric Impedance

2018 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Single Wave ◽  
Electric Parameters ◽  
Sub Wavelength

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electrical and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electrical wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to create sub-wavelength band gaps.

Flexural vibration band gaps in periodic Timoshenko beams with oscillators in series resting on flexible supports

2020 ◽  
Vol 23 (14) ◽  
pp. 3117-3127
Author(s):  
Lan Ding ◽  
Zhi Ye ◽  
Qiao-Yun Wu
Keyword(s):  
Band Gap ◽  
Transfer Matrix ◽  
Propagation Constant ◽  
Dynamic Stiffness ◽  
Band Gaps ◽  
Vibration Band ◽  
Timoshenko Beams ◽  
Gap Formation ◽  
Flexible Supports ◽  
In Series

The propagation properties of waves in Timoshenko beams resting on flexible supports and with periodically attached harmonic locally resonant oscillators are studied by the transfer matrix methodology. Through calculating the differential equations of the beam for the flexible vibration and the dynamic equations of the oscillators in series, the matrix of dynamic stiffness and the resulting transfer matrix are derived. Accordingly, the band gap in infinite system characterized by the propagation constant can be verified by comparing to the curve of transmission property, determined with the finite element method for the finite system. The mechanism of each band gap formation is further explored. Numerical results show that different from the single degree-of-freedom mass-spring model, one more locally resonant band gap is generated in the system of two oscillators in series. The introduction of flexible supports, allowing for variable internal coupling between the adjacent cells, produces an extra band gap with a minimum frequency of zero. It is also found that the starting frequencies of the locally resonant gaps are related to the spring stiffness and mass of the oscillator. Therefore, the positions and widths of the band gaps can be tuned by properly adjusting the four parameters of the oscillators and also the stiffness of the flexible supports.

Vibration response and band gap characteristics of functionally graded frame structure

2020 ◽  
pp. 107754632097481
Author(s):  
Qifa Lu ◽  
Chunchuan Liu ◽  
Wei Yuan ◽  
Wei Wei ◽  
Fengming Li
Keyword(s):  
Band Gap ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Vibration Response ◽  
Band Gaps ◽  
Frame Structure ◽  
Frame Structures ◽  
Graded Material ◽  
Gap Characteristics ◽  
Material Frame

Vibration response and band gap characteristics of the functionally graded frame structures are investigated based on the first-order shear deformation theory. The material properties of functionally graded material rods vary continuously in thickness direction according to a power law. Spectral stiffness matrix of the periodic functionally graded material frame structure in the global coordinate system is derived in detail. Consequently, the vibration band gap properties of the functionally graded material frame structure can be calculated and analyzed by using the spectral element method. The calculation accuracy for dynamic responses of the functionally graded material frame structure is validated by the finite element method. The results demonstrate that the wider band gaps in the low and medium frequency ranges can be achieved for the functionally graded frame structures comparing with the homogeneous ones. Moreover, the frequency windows and ranges for the band gaps of the functionally graded material frame structure can be effectively adjusted through designing the gradient indexes for the functionally graded material rods, which provide a novel idea for vibration suppression of frame structures.

scholarly journals Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Anna Miglio ◽  
Véronique Brousseau-Couture ◽  
Emile Godbout ◽  
Gabriel Antonius ◽  
Yang-Hao Chan ◽  
...  
Keyword(s):  
Band Gap ◽  
First Principles ◽  
Large Scale ◽  
Zero Point ◽  
Band Gaps ◽  
Electronic Band ◽  
Electron Phonon Interaction ◽  
Point Motion ◽  
Optical Properties Of Materials ◽  
Global Agreement

Abstract Electronic and optical properties of materials are affected by atomic motion through the electron–phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account. They even dominate zero-point renormalization for many materials, as shown by a generalized Fröhlich model that includes multiple phonon branches, anisotropic and degenerate electronic extrema, whose range of validity is established by comparison with first-principles results.

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