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.

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.

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.

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.

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.

ACOUSTIC BAND GAP FORMATION IN TWO-DIMENSIONAL LOCALLY RESONANT SONIC CRYSTALS COMPRISED OF HELMHOLTZ RESONATORS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4234-4243 ◽  
Author(s):  
L. CHALMERS ◽  
D. P. ELFORD ◽  
F. V. KUSMARTSEV ◽  
G. M. SWALLOWE
Keyword(s):  
Band Gap ◽  
Experimental Testing ◽  
Wide Band ◽  
Band Gaps ◽  
Gap Formation ◽  
Helmholtz Resonators ◽  
Multiple Resonance ◽  
Resonance Band ◽  
Sonic Crystal ◽  
Sonic Crystals

We present a new type of sonic crystal technology offering a novel method of achieving broad acoustic band gaps. The proposed design of a locally resonating sonic crystal (LRSC) is constructed from "C"-shaped Helmholtz resonators as opposed to traditional solid scattering units. This unique construction enables a two band gap system to be generated in which the first — a Bragg type band gap, arises due to the periodic nature of the crystal, whilst the second gap results from resonance of the air column within the resonators. The position of this secondary band gap is found to be dependent upon the dimensions of the resonating cavity. The band gap formation is investigated theoretically using finite element methods, and confirmed through experimental testing. It is noted that the resonance band gaps detected cover a much broader frequency range (in the order of kHz) than has been achieved to date. In addition the possibility of overlapping such a wide band gap with the characteristic Bragg gap generated by the structure itself could yield gaps of even greater range. A design of sonic crystal is proposed, that comprises of several resonators with differing cavity sizes. Such a structure generates multiple resonance gaps corresponding to the various resonator sizes, which may be overlapped to form yet larger band gaps. This multiple resonance gap system can occur in two configurations. Firstly a simple mixed array can be created by alternating resonator sizes in the array and secondly using a system coined the Matryoshka (Russian doll) array in which the resonators are distributed inside one another. The proposed designs of LRSC's offer a real potential for acoustic shielding using sonic crystals, as both the size and position of the band gaps generated can be controlled. This is an application which has been suggested and investigated for several years with little progress. Furthermore the frequency region attenuated by resonance is unrelated to the crystals lattice constant, providing yet more flexibility in the design of such devices.

The effects of composite primitive cells on band gap property of locally resonant phononic crystal

2021 ◽  
pp. 2150334
Author(s):  
Lijian Lei ◽  
Linchang Miao ◽  
Chao Li ◽  
Xiaodong Liang ◽  
Junjie Wang
Keyword(s):  
Band Gap ◽  
Formation Mechanism ◽  
Phononic Crystal ◽  
Engineering Application ◽  
Low Frequency ◽  
Structure Design ◽  
Band Gaps ◽  
Gap Formation ◽  
Cell Spacing ◽  
Low Frequency Vibration

Locally resonant phononic crystal (LRPC) has the extraordinary property to prohibit the wave propagation in specific low-frequency ranges, however it exists limitation in engineering application due to narrow band gap width. Extensive achievements have been obtained on the locally resonant band gap (LRBG) tunability, whereas existing investigations mainly concern the independent primitive cells structure, which have the limitation in obtaining low-frequency and broadband simultaneously. In this paper, the composited locally resonant phononic crystals (CLRPC) are proposed and the effects of primitive cells contact state on the LRBG properties are investigated. The dispersion curves are applied to obtain the LRBG, and the corresponding modal features are analyzed to explain the band gap formation mechanism. The band structure indicates the design of composite primitive cells is able to increase the band gap number and obtain lower band gap, which is verified by the frequency response function (FRF). For the band gap formation mechanism, the asymmetric vibration due to primitive cells contact leads to diverse and strong coupling response, which generates more band gaps and reduces the band gap starting frequency, therefore the band gaps can be tuned by designing carefully the geometry structure of CLRPC. Further researches on band gap optimization demonstrate that the smaller cell spacing, smaller lattice constant and larger damping of coating layer should be satisfied to obtain broader LRBG and considerable attenuation synchronously. This investigation can provide references for the locally resonant isolation structure design in the low-frequency vibration control field.

A novel modal calculation method of 1-D phononic crystal band gap

2015 ◽  
Vol 11 (1) ◽  
pp. 16-22
Author(s):  
Lei Li ◽  
Qing Liu
Keyword(s):  
Band Gap ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Mode Shapes ◽  
Response Analysis ◽  
Content Type ◽  
Existence Conditions ◽  
Harmonic Response Analysis ◽  
Modal Method

Purpose – The purpose of this paper is to propose a modal method to calculate the band gaps of one-dimensional (1D) phononic crystals. Design/methodology/approach – The phononic crystals have modes with exponential form envelope in the band gaps, however, outside the band gaps the modes are of amplitude modulation periodic form. Thus the start and end frequencies of band gaps can be determined from the existence conditions of periodic modes. So, the band gaps calculation of 1D phononic crystal is transformed into the existence discussion of periodic solution of mode shapes equation. The results are verified by finite element harmonic response analysis. Findings – At the start and end frequencies of the band gap, the mode equation have solution with period of lattice constant. Originality/value – Compared with the traditional theoretical methods, the proposed modal method has a clearer principle and easier calculation.

scholarly journals Band Gap Formation and Tunability in Stretchable Serpentine Interconnects

2017 ◽  
Vol 84 (9) ◽  
Author(s):  
Pu Zhang ◽  
William J. Parnell
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Band Gap ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Electronic Systems ◽  
Gap Formation ◽  
Highly Stretchable ◽  
Metallic Interconnects ◽  
Phononic Band Gaps

Serpentine interconnects are highly stretchable and frequently used in flexible electronic systems. In this work, we show that the undulating geometry of the serpentine interconnects will generate phononic band gaps to manipulate elastic wave propagation. The interesting effect of “bands-sticking-together” is observed. We further illustrate that the band structures of the serpentine interconnects can be tuned by applying prestretch deformation. The discovery offers a way to design stretchable and tunable phononic crystals by using metallic interconnects instead of the conventional design with soft rubbers and unfavorable damping.

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