Structural Intensity Analysis of Periodic Elastic Structures With Frequency Stop Bands

2016 ◽  
Author(s):  
M. Nouh
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Periodic Structures ◽  
External Disturbance ◽  
Stop Band ◽  
Bloch Wave ◽  
Periodic Medium ◽  
Elastic Structures ◽  
Structural Intensity ◽  
Wide Range

Periodic elastic structures consisting of self-repeating geometric or material arrangements exhibit unique wave propagation characteristics culminating in frequency stop bands, i.e. ranges of frequency where elastic waves can propagate the periodic medium. Such features make periodic structures appealing for a wide range of vibration suppression and noise control applications. Stop bands in periodic media are achieved via Bragg scattering of elastic which is attributed to impedance mismatches between the different constituents of the self-repeating cells. Stop band frequencies can be numerically predicted using mathematical models which generally utilize the Bloch wave theorem and a transfer matrix method to track the spatial and temporal parameters of the propagating waves from one cell to the next. Such analysis generates what is referred to as the band structure (or the dispersion curves) of the periodic medium which can be used to predict the location of the pass and stop bands. Although capable, these models become significantly more involved when analyzing structures with dissipative constituents and/or material damping and need further adjustments to account for complex elastic moduli and frequency dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power and energy transmission paths. It is shown that the steady-state spatial propagation of vibrational power caused by an external disturbance accurately reflects the wave propagation pattern in the periodic medium, and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The developed framework is mathematically applied to a one-dimensional periodic rod to validate the proposed method.

An Investigation of Vibrational Power Flow in One-Dimensional Dissipative Phononic Structures

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
H. Al Ba'ba'a ◽  
M. Nouh
Keyword(s):  
Wave Propagation ◽  
Power Flow ◽  
Vibration Suppression ◽  
Wave Attenuation ◽  
External Disturbance ◽  
Stop Band ◽  
Bragg Scattering ◽  
Spatial Propagation ◽  
The Individual ◽  
Vibrational Power Flow

Owing to their ability to block propagating waves at certain frequencies, phononic materials of self-repeating cells are widely appealing for acoustic mitigation and vibration suppression applications. The stop band behavior achieved via Bragg scattering in phononic media is most commonly evaluated using wave propagation models which predict gaps in the dispersion relations of the individual unit cells for a given frequency range. These models are in many ways limited when analyzing phononic structures with dissipative constituents and need further adjustments to account for viscous damping given by complex elastic moduli and frequency-dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power flow in finite phononic structures. It is shown that the steady-state spatial propagation of vibrational power flow initiated by an external disturbance reflects the wave propagation pattern in the phononic medium and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The treatment is shown to be very effective for phononic structures with viscoelastic components and provides a clear distinction between Bragg scattering effects and wave attenuation due to material damping. Since the approach is integrated with finite element methods, the presented analysis can be extended to two-dimensional lattices with complex geometries and multiple material constituents.

A Physical Interpretation for Broken Reciprocity in Spatiotemporal Modulated Periodic Rods

2017 ◽  
Author(s):  
Jacopo Marconi ◽  
Gabriele Cazzulani ◽  
Massimo Ruzzene ◽  
Francesco Braghin
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Periodic Structures ◽  
Previous Analysis ◽  
Travelling Waves ◽  
Periodic Systems ◽  
Mathematical Methods ◽  
Elastic Structures ◽  
The Mean ◽  
And Control

Periodic systems have long been known for their peculiar characteristics in wave propagation and have been studied in many fields over the last century, going from electro-magnetics and optics to elastic structures, which drew an increasing interest in structural and mechanical engineering for vibration suppression and control spanning over broadband frequency ranges. Recently, on the stream of other studies conducted in different fields, spatiotemporal modulated elastic structures have been studied, showing promising results for wave control in that one-way propagation in the so called directional-bands can be achieved, constituting what may be called a mechanical diode. Despite of the fact that mathematical methods for the analysis of such structures have already been developed, often physics behind them is difficult to grasp. In this work, a simplified interpretation of the undergoing phenomena is thus given relating wave propagation in the mean to its physical characteristics as well as to modulation parameters. Exploiting Doppler effect and passive equivalent structures, it is shown that the broken reciprocity is due to the fact that opposite travelling waves effectively see two different periodic structures. To this aim the rod case is analysed for low modulation speeds and low modulation amplitudes; finally, in the light of the previous analysis, an explanation for First Brillouin Zone’s asymmetry is given.

Wave Propagation in Periodic Piezoelectric Elastic Waveguides

2012 ◽  
Author(s):  
D. G. Piliposyan ◽  
K. B. Ghazaryan ◽  
G. T. Piliposian ◽  
A. S. Avetisyan
Keyword(s):  
Wave Propagation ◽  
Stop Band ◽  
Transmission Conditions ◽  
Band Gaps ◽  
Full System ◽  
One Dimensional ◽  
Dynamic Setting ◽  
Floquet Waves ◽  
Wide Range ◽  
Shear Horizontal

The prorogation of electro-magneto-elastic coupled shear-horizontal waves in one dimensional infinite periodic piezoelectric waveguides is considered within a full system of the Maxwell’s equations. Such setting of the problem allows to investigate the Bloch-Floquet waves in a wide range of frequencies. Two different conditions along the guide walls and three kinds of transmission conditions at the interfaces between the laminae of waveguides have been studied. Stop band structures have been identified for Bloch-Floquet waves both at acoustic and optical frequencies. The results demonstrate the significant effect of piezoelectricity on the widths of band gaps at acoustic frequencies and confirm that it does not affect the band structure at optical frequencies. The results show that under electrically shorted transmission conditions Bloch-Floquet waves exist only at acoustic frequencies. For electrically open interfaces the dynamic setting provides solutions only for photonic crystals. In this case the piezoelectricity has no effect on band gaps.

Wave Propagation in One-Dimensional Structure of Periodic Inelasticity Composites

2011 ◽  
Author(s):  
Helio Aparecido Navarro ◽  
Meire Pereira de Souza Braun
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Stop Band ◽  
Dimensional Structure ◽  
Material Models ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Structural Problems ◽  
Plastic Damage ◽  
Non Linear

This study involves the analysis of elastic-plastic-damage dynamics of one-dimensional structures comprising of periodic materials. These structures are composed by multilayer unit cells with different materials. The dynamical characteristics of the composite material present distinct frequency ranges where wave propagation is blocked. The steady-state forced analyses are conducted on a structure constructed from a periodic inelasticity material. The material models have a linear dependence for elasticity problems and non-linear for elastoplasticity-damage problems. This paper discusses the pass and stop-band dispersive behavior of material models on temporal and spatial domains. For this purpose, some structural problems are composed of periodic and damping materials for analysis of vibration suppression have been simulated. This work brings a formulation of Galerkin method for one-dimensional elastic-plastic-damage problems. A time-stepping algorithm for non-linear dynamics is also presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spatial discretization the standard finite element method is used. The procedure proposed in this work can be extended to multidimensional problems, analysis of strain localization, and for others material models.

Elastic Wave Propagation in a Bio-Inspired Phononic Crystal

2020 ◽  
Vol 1012 ◽  
pp. 9-13
Author(s):  
H.V. Cantanhêde ◽  
E.J.P. Miranda Jr. ◽  
J.M.C. dos Santos
Keyword(s):  
Wave Propagation ◽  
Band Structure ◽  
Vibrational Energy ◽  
Periodic Structures ◽  
Chemical Elements ◽  
Phononic Crystal ◽  
Stop Band ◽  
Elastic Vibration ◽  
Band Gaps ◽  
Sound Waves

The wave propagation in a two-dimensional bio-inspired phononic crystal (PC) is analysed. When composite materials and structures consist of two or more different materials periodically, there will be stop band characteristic, in which there are no mechanical propagating waves. These periodic structures are known as PCs. PCs have shown an excellent potential in many disciplines of science and technology in the last decade. They have generated lots of interests due to their ability to manipulate mechanical waves like sound waves and thermal properties which are not available in nature. The physical properties of PCs are not essentially determined by chemical elements and bonds in the materials, but rather on the internal specific structures. Structures of this type have the ability to inhibit the propagation of vibrational energy over certain ranges of frequencies forming band gaps. The main purpose of this study is to investigate the band structure and especially the location and width of band gaps. For this analysis, it is used the finite element method (FEM) and plane wave expansion (PWE). The results are shown in the form of band structure and wave modes. Band structures calculated by FEM and PWE present good agreement. We suggest that the bio-inspired PC considered should be feasible for elastic vibration control.

scholarly journals Novel Bloch wave excitation platform based on few-layer photonic crystal deposited on D-shaped optical fiber

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Esteban Gonzalez-Valencia ◽  
Ignacio Del Villar ◽  
Pedro Torres
Keyword(s):  
Optical Fibers ◽  
High Performance ◽  
Light Propagation ◽  
Fiber Optic ◽  
Layer Structure ◽  
Optical Network ◽  
Building Blocks ◽  
Bloch Wave ◽  
Nanophotonic Devices ◽  
Wide Range

AbstractWith the goal of ultimate control over the light propagation, photonic crystals currently represent the primary building blocks for novel nanophotonic devices. Bloch surface waves (BSWs) in periodic dielectric multilayer structures with a surface defect is a well-known phenomenon, which implies new opportunities for controlling the light propagation and has many applications in the physical and biological science. However, most of the reported structures based on BSWs require depositing a large number of alternating layers or exploiting a large refractive index (RI) contrast between the materials constituting the multilayer structure, thereby increasing the complexity and costs of manufacturing. The combination of fiber–optic-based platforms with nanotechnology is opening the opportunity for the development of high-performance photonic devices that enhance the light-matter interaction in a strong way compared to other optical platforms. Here, we report a BSW-supporting platform that uses geometrically modified commercial optical fibers such as D-shaped optical fibers, where a few-layer structure is deposited on its flat surface using metal oxides with a moderate difference in RI. In this novel fiber optic platform, BSWs are excited through the evanescent field of the core-guided fundamental mode, which indicates that the structure proposed here can be used as a sensing probe, along with other intrinsic properties of fiber optic sensors, as lightness, multiplexing capacity and easiness of integration in an optical network. As a demonstration, fiber optic BSW excitation is shown to be suitable for measuring RI variations. The designed structure is easy to manufacture and could be adapted to a wide range of applications in the fields of telecommunications, environment, health, and material characterization.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

2007 ◽  
Vol 129 (5) ◽  
pp. 559-566 ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Vibration Suppression ◽  
Periodic Structures ◽  
Electric Circuit ◽  
Forced Response ◽  
Bladed Disks ◽  
Vibration Localization ◽  
Network Concept ◽  
Engine Order ◽  
The Individual ◽  
Local Circuits

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

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