scholarly journals Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210356
Author(s):  
Kuan-Xin Huang ◽  
Guo-Shuang Shui ◽  
Yi-Ze Wang ◽  
Yue-Sheng Wang
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Structural Parameters ◽  
Internal Mass ◽  
Mass Spring Model ◽  
Scattering Of Elastic Waves ◽  
Specific Frequency ◽  
Release Ratio ◽  
Hopf Method ◽  
Mass Spring

Previous investigations on wave scattering and crack propagation in the discrete periodic structure are concentrated on the conditional mass–spring model, in which the internal mass is not included. In this work, elastic wave metamaterials with local resonators are studied to show the scattering of elastic waves by a semi-infinite crack and the arrest behaviour. The influences of internal mass–spring structure are analysed and the discrete Wiener–Hopf method is used to obtain the displacement solution. Numerical calculations are performed to show that the dynamic negative effective mass and band gaps can be observed owing to the local resonance of the internal mass. Therefore, the scattering of an elastic wave with a specific frequency by a semi-infinite crack can be avoided by tuning the structural parameters. Moreover, the energy release ratio which characterizes the splitting resistance is presented and the meta-arrest performance is found. It is expected that this study will increase understanding of how to control the scattering characteristics of elastic waves by a semi-infinite crack in locally resonant metamaterials and also help to improve their fracture resistance.

SCATTERING OF ELASTIC WAVES BY SMALL INHOMOGENEITIES

Geophysics ◽  
1960 ◽  
Vol 25 (3) ◽  
pp. 642-648 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Shear Modulus ◽  
Elastic Wave ◽  
Wave Field ◽  
General Result ◽  
Elastic Waves ◽  
Isotropic Medium ◽  
Scattering Theory ◽  
Rayleigh Scattering ◽  
S Waves ◽  
Scattering Of Elastic Waves

Rayleigh scattering theory is extended to determine the perturbation on an arbitrarily prescribed elastic wave field produced by small inhomogeneities in an otherwise homogeneous, isotropic medium. The general result is applied to the specific problems of the scattering of both plane P- and S-waves. It is found that a change in compressibility acts at a distance as a simple source and a change in density as a dipole, as in the acoustical problem, while a change in shear modulus contributes both simple‐source and quadrapole fields.

Application of the Singularity Expansion Method to Elastic Wave Scattering

1990 ◽  
Vol 43 (10) ◽  
pp. 235-249 ◽  
Author(s):  
Herbert U¨berall ◽  
P. P. Delsanto ◽  
J. D. Alemar ◽  
E. Rosario ◽  
Anton Nagl
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Expansion Method ◽  
Complex Frequency ◽  
Elastic Wave Scattering ◽  
Physical Measurements ◽  
Scattering Of Elastic Waves

The singularity expansion method (SEM), established originally for electromagnetic-wave scattering by Carl Baum (Proc. IEEE 64, 1976, 1598), has later been applied also to acoustic scattering (H U¨berall, G C Gaunaurd, and J D Murphy, J Acoust Soc Am 72, 1982, 1014). In the present paper, we describe further applications of this method of analysis to the scattering of elastic waves from cavities or inclusions in solids. We first analyze the resonances that appear in the elastic-wave scattering amplitude, when plotted vs frequency, for evacuated or fluid-filled cylindrical and spherical cavities or for solid inclusions. These resonances are interpreted as being due to the phase matching, ie, the formation of standing waves, of surface waves that encircle the obstacle. The resonances are then traced to the existence of poles of the scattering amplitude in the fourth quadrant of the complex frequency plane, thus establishing the relation with the SEM. The usefulness of these concepts lies in their applicability for solving the inverse scattering problem, which is the central problem of NDE. Since for the case of inclusions, or of cavities with fluid fillers, the scattering of elastic waves gives rise to very prominent resonances in the scattering amplitude, it will be of advantage to analyze these with the help of the resonance scattering theory or RST (first formulated by L Flax, L R Dragonette, and H U¨berall, J Acoust Soc Am 63, 1978, 723). These resonances are caused by the proximity of the SEM poles to the real frequency axis, on which the frequencies of physical measurements are located. A brief history of the establishment of the RST is included here immediately following the Introduction.

Conversion of Elastic Wave Polarization in Calcium Molybdate Layer

2018 ◽  
Vol 284 ◽  
pp. 95-100
Author(s):  
Yu.N. Belyayev ◽  
E.I. Yashin ◽  
O.Y. Yashina
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Wave Polarization ◽  
Anisotropic Layer ◽  
Calcium Molybdate ◽  
Algebraic Problem ◽  
Scattering Of Elastic Waves ◽  
Conversion Coefficients ◽  
Beam Diffraction ◽  
Incident Wave Energy

Scattering of elastic waves in calcium molybdate films is considered. The transformation of elastic waves as a result of six-beam diffraction in an anisotropic layer is analyzed. This analysis is based on the transfer matrix method. The distribution of incident wave energy between six scattered waves is characterized by conversion coefficients. The method for conversion coefficients calculations is presented. It does not require solving algebraic problem on eigenvalues for waves in an anisotropic layer. Features of dependencies of conversion coefficients of CaMoO4 layers on angles of incidence, frequency and the thickness of the layer are demonstrated.

One-Dimensional Analysis on the Dynamic Response of Cellular Chains to Pulse Loading

2006 ◽  
Vol 220 (5) ◽  
pp. 679-689 ◽  
Author(s):  
Z. Y. Gao ◽  
T. X. Yu
Keyword(s):  
Dynamic Response ◽  
Elastic Wave ◽  
Deformation Characteristic ◽  
Cell Number ◽  
Pulse Loading ◽  
Plastic Collapse ◽  
Spring Model ◽  
One Dimensional ◽  
Mass Spring Model ◽  
Mass Spring

On the basis of our previous studies of a typical type II structure (i.e. a pair of prebent plates), a simplified one-dimensional mass-spring model is proposed to describe the uniaxial load-deformation characteristic of cellular materials and structures. When compared with the previous mass-spring model proposed by Shim et al., the present model employs fewer parameters (only two) to describe elastic-plastic behaviour, and the structural hardening/softening is represented by only one of the parameters. The model is then used to study the dynamic response of a cellular chain to a pulse loading of specified force intensity and duration. By adjusting the value of a single parameter adopted in the model, each cell of the cellular chain is identically assigned to possess either an elastic-hardening or an elastic-softening-consolidation property. The effects of material elasticity, cell compliance characteristic, cell number, and pulse intensity and duration are all examined by this model and discussed in detail. A special attention is paid to the initiation and propagation of the plastic collapse of the cells in the cellular chain so as to identify the governing parameters. Apart from the elastic wave speed, two other characteristic velocities, i.e. the particle velocity induced by the elastic wave and the plastic collapse propagation velocity, are defined and analytically evaluated. It is found that these three characteristic velocities completely govern the elastic and plastic dynamic behaviour of the cellular chains.

scholarly journals Numerical Modelling and Optimization of Two-Dimensional Phononic Band Gaps in Elastic Metamaterials with Square Inclusions

2021 ◽  
Vol 11 (7) ◽  
pp. 3124
Author(s):  
Alya Alhammadi ◽  
Jin-You Lu ◽  
Mahra Almheiri ◽  
Fatima Alzaabi ◽  
Zineb Matouk ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Tungsten Carbide ◽  
Composite Structure ◽  
Elastic Waves ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Filling Fraction ◽  
Carbide Composite ◽  
Elastic Metamaterials ◽  
Tungsten Carbide Composite

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.

scholarly journals Review on the 3-D simulation for weft knitted fabric

2021 ◽  
Vol 16 ◽  
pp. 155892502110125
Author(s):  
Sha Sha ◽  
Anqi Geng ◽  
Yuqin Gao ◽  
Bin Li ◽  
Xuewei Jiang ◽  
...  
Keyword(s):  
Physical Models ◽  
Spring Model ◽  
Finite Element Analyses ◽  
Knitted Fabrics ◽  
Piecewise Function ◽  
Fabric Structure ◽  
Weft Knitted Fabric ◽  
Mass Spring Model ◽  
Virtual Display ◽  
Mass Spring

There are different kinds of geometrical models and physical models used to simulate weft knitted fabrics nowadays, such as loop models based on Pierce, piecewise function, spline curve, mass-spring model, and finite element analyses (FEA). Weft knitting simulation technology, including modeling and yarn reality, has been widely adopted in fabric structure designing for the manufacturer. The technology has great potentials in both industries and dynamic virtual display. The present article is aimed to review the current development of 3-D simulation technique for weft knitted fabrics.

scholarly journals Computational Approach to Seasonal Changes of Living Leaves

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ying Tang ◽  
Dong-Yan Wu ◽  
Jing Fan
Keyword(s):  
Seasonal Changes ◽  
Markov Chain Model ◽  
Geometric Model ◽  
Environmental Parameters ◽  
Computational Approach ◽  
Chain Model ◽  
Color Changes ◽  
Mass Spring Model ◽  
Scanned Image ◽  
Mass Spring

This paper proposes a computational approach to seasonal changes of living leaves by combining the geometric deformations and textural color changes. The geometric model of a leaf is generated by triangulating the scanned image of a leaf using an optimized mesh. The triangular mesh of the leaf is deformed by the improved mass-spring model, while the deformation is controlled by setting different mass values for the vertices on the leaf model. In order to adaptively control the deformation of different regions in the leaf, the mass values of vertices are set to be in proportion to the pixels' intensities of the corresponding user-specified grayscale mask map. The geometric deformations as well as the textural color changes of a leaf are used to simulate the seasonal changing process of leaves based on Markov chain model with different environmental parameters including temperature, humidness, and time. Experimental results show that the method successfully simulates the seasonal changes of leaves.

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