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Constitutive modelling and wave propagation through a class of anisotropic elastic metamaterials with local rotation 一类具有局部旋转的各向异性弹性超材料的结构建模和波传播
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-28 DOI: 10.1016/j.wavemoti.2024.103432
{"title":"Constitutive modelling and wave propagation through a class of anisotropic elastic metamaterials with local rotation","authors":"","doi":"10.1016/j.wavemoti.2024.103432","DOIUrl":"10.1016/j.wavemoti.2024.103432","url":null,"abstract":"<div><div>Elastic metamaterials are typically periodic materials possessing unit cells endowed with engineered architecture much smaller than the typical phenomenological length scale. The development of continuum models capable of accurately representing the effects of this aforementioned architecture is extremely challenging, and hence a sparsely developed area. This paper develops a novel 2-D continuum model capable of capturing the dynamic behaviour of a class of anisotropic elastic metamaterials with local rotational elements in the long wavelength limit. A constitutive relation incorporating these local rotational effects is proposed, and ratified using a representative discrete model using linear Hookean springs and identical rigid disks. The new continuum model is used to generate a dispersion relation for harmonic plane waves propagating in an arbitrary direction, which is subsequently compared to the dispersion behaviour of the original discrete model. The general behaviour of this continuum when subjected to 2-D planar harmonic wave propagation in the anisotropic medium is then analysed, with specific attention given to the effect of material anisotropy and wave propagation direction. This work is the first of its kind to create a new continuum model of a class of anisotropic elastic metamaterials with local rotational effects.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On peridynamic acoustics 关于周动声学
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-28 DOI: 10.1016/j.wavemoti.2024.103429
{"title":"On peridynamic acoustics","authors":"","doi":"10.1016/j.wavemoti.2024.103429","DOIUrl":"10.1016/j.wavemoti.2024.103429","url":null,"abstract":"<div><div>We consider a nonlocal (peridynamic) version of the classical forced wave equation. This scalar three-dimensional equation contains a weight function (the “micromodulus”) and a length parameter (the “horizon”) that have to be selected. We investigate various properties (the locality limit as the horizon shrinks, plane waves and group velocity), paying attention to how these properties depend on the choice of the micromodulus. We solve the forced peridynamic equation in the static case (avoiding divergent integrals) and in the time-harmonic case (with a radiation condition, when needed).</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elastic coupled phase theory based on the Cosserat equations: Propagation of coherent waves 基于 Cosserat 方程的弹性耦合相理论：相干波的传播
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-28 DOI: 10.1016/j.wavemoti.2024.103430
{"title":"Elastic coupled phase theory based on the Cosserat equations: Propagation of coherent waves","authors":"","doi":"10.1016/j.wavemoti.2024.103430","DOIUrl":"10.1016/j.wavemoti.2024.103430","url":null,"abstract":"<div><div>We develop a new coupled phase theory (CPT) in order to model the propagation of elastic coherent waves in homogeneous solid media containing randomly distributed spherical elastic inclusions. To this end, the Buyevich’s theory previously developed for fluid media (Buyevich and Shchelchkova, 1978) has been adapted and applied to the Cosserat equations. A key point is to introduce the Independent Scattering Approximation (ISA). We show that the coherent wavenumbers depend explicitly on the external force applied to spheres, the torque characterizing their rotation and the stresslet which is the result of the resistance of the particles to the straining motion. Numerical results are in good agreement with experimental data.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Accurate computation of scattering poles of acoustic obstacles with impedance boundary conditions 带阻抗边界条件的声学障碍物散射极点的精确计算
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-24 DOI: 10.1016/j.wavemoti.2024.103425
{"title":"Accurate computation of scattering poles of acoustic obstacles with impedance boundary conditions","authors":"","doi":"10.1016/j.wavemoti.2024.103425","DOIUrl":"10.1016/j.wavemoti.2024.103425","url":null,"abstract":"<div><div>We propose a computation method for scattering poles of impedance obstacles. Boundary integral equations are used to formulate the problem. It is shown that the scattering poles are the eigenvalues of some integral operator. Then we employ the Nyström method to discretize the integral operator and obtain a nonlinear matrix eigenvalue problem. The eigenvalues are computed using a multistep parallel spectral indicator method. Numerical examples demonstrate the high accuracy of the proposed method and can serve as the benchmarks. Our study provides a practical approach and can be extended to other scattering problems. This paper continues our previous study on the computation method for scattering poles of sound-soft obstacles.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Derivation of weakly interacting lumps for the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation via degeneracy of lump chains 通过块链的退化性推导 (2+1)-dimensional Yu-Toda-Sasa-Fukuyama 公式的弱相互作用块体
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-22 DOI: 10.1016/j.wavemoti.2024.103423
{"title":"Derivation of weakly interacting lumps for the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation via degeneracy of lump chains","authors":"","doi":"10.1016/j.wavemoti.2024.103423","DOIUrl":"10.1016/j.wavemoti.2024.103423","url":null,"abstract":"<div><div>This paper introduces two distinct pathways for degenerating normally interacting lump chains into weakly interacting lump waves for Yu–Toda–Sasa–Fukuyama equation, which will enrich the correlation between lump chains and weakly interacting lump waves. The first pathway involves letting the periods of <span><math><mi>M</mi></math></span> similarly-velocity lump chains approach infinity directly. The second pathway first transforms <span><math><mi>M</mi></math></span> normally interacting lump chains into weakly interacting lump chains with similar dynamic behaviors. Then, by allowing their periods to approach infinity, <span><math><mfrac><mrow><mi>M</mi><mfenced><mrow><mi>M</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> weakly interacting lump waves are produced. Distance between weakly interacting lump chains in this equation is proportional to <span><math><mrow><mo>ln</mo><mo>|</mo><mi>t</mi><mo>|</mo></mrow></math></span>, while between weakly interacting lump waves is proportional to <span><math><mroot><mrow><mo>|</mo><mi>t</mi><mo>|</mo></mrow><mrow><mn>3</mn></mrow></mroot></math></span>. These findings will contribute valuable theoretical insights to the study of wave theory, ocean science and related disciplines.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Compactons in a class of doubly sublinear Gardner equations 一类双次线性加德纳方程中的紧凑子
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-22 DOI: 10.1016/j.wavemoti.2024.103427
{"title":"Compactons in a class of doubly sublinear Gardner equations","authors":"","doi":"10.1016/j.wavemoti.2024.103427","DOIUrl":"10.1016/j.wavemoti.2024.103427","url":null,"abstract":"<div><div>We introduce and study a class of doubly sublinear Gardner equations <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>F</mi><msub><mrow><mrow><mo>(</mo><mi>u</mi><mo>;</mo><mi>n</mi><mo>)</mo></mrow></mrow><mrow><mi>x</mi></mrow></msub><mo>+</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>3</mn><mi>x</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span> where <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>;</mo><mi>n</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>n</mi></mrow></msup><mo>−</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msup></mrow></math></span>, which for <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>n</mi></mrow></math></span> induce solitons and in the doubly sublinear cases wherein <span><math><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>&lt;</mo><mi>n</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>, <em>bi-directional</em> compactons propagating in either direction. Their emergence, evolution, chase and head-on interactions are studied.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Test of the relation between temporal and spatial Q by Knopoff et al. Knopoff 等人对时间和空间 Q 之间关系的测试。
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-22 DOI: 10.1016/j.wavemoti.2024.103424
{"title":"Test of the relation between temporal and spatial Q by Knopoff et al.","authors":"","doi":"10.1016/j.wavemoti.2024.103424","DOIUrl":"10.1016/j.wavemoti.2024.103424","url":null,"abstract":"<div><div>The quality factor is a dimensionless measure of the energy loss per cycle of wave modes in an attenuation medium. Accurate measurement is important in various fields, from seismological studies to detect zones of partial melting to the geophysics of reservoirs to study rock properties such as porosity, fluid properties and saturation and permeability. In seismology, the quality factors measured for normal (standing) modes and propagating waves differ, as well those of equivalent experiments based on resonant rods and ultrasonic pulses performed in the laboratory. These measurements result in temporal and spatial quality factors respectively. A relationship between these two different quality factors and between the corresponding attenuation factors was proposed by Knopoff et al. sixty years ago. The conversion factor is basically the ratio between the phase velocity and the group velocity, while for the attenuation factor is the group velocity. We test these relations, which hold for low-loss solids, for body waves, using a Kelvin–Voigt rheology and a constant <span><math><mi>Q</mi></math></span> model, which provide explicit expressions of the temporal and spatial quality factors and velocities involved in these relations. The proposed theory provides the basis for a complete characterization of temporal and spatial quality factors and velocity dispersion based on arbitrary stress–strain relationships.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The dynamic behaviors between double-hump solitons in birefringent fibers 双折射光纤中双驼峰孤子之间的动态行为
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-22 DOI: 10.1016/j.wavemoti.2024.103426
{"title":"The dynamic behaviors between double-hump solitons in birefringent fibers","authors":"","doi":"10.1016/j.wavemoti.2024.103426","DOIUrl":"10.1016/j.wavemoti.2024.103426","url":null,"abstract":"<div><div>In this paper, we research the fractional coupled Hirota equations with variable coefficients describing the collisions of two waves in deep oceans and the propagation of ultrashort light pulses in birefringent fibers and successfully acquire the double-hump one-soliton, two-solitons and <em>N</em>-solitons solutions via the Hirota bilinear method. At the same time, the Bäcklund transformation and the corresponding soliton solutions are also obtained. Based on the precise forms of the solitons solutions, we gain double-hump solitons images with different shapes including U-shape, V-shape and wave-type by assigning proper functions to the group velocity dispersion and the third-order dispersion and analyze the interaction dynamics of double-hump solitons. It is worth noting that the Hirota bilinear operators involved here are fractional rather than integer, which has never appeared in previous literatures.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localized solutions of the wave equation 波方程的局部解
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-19 DOI: 10.1016/j.wavemoti.2024.103418
{"title":"Localized solutions of the wave equation","authors":"","doi":"10.1016/j.wavemoti.2024.103418","DOIUrl":"10.1016/j.wavemoti.2024.103418","url":null,"abstract":"<div><div>A family of solutions of the wave equation is presented. The simplest waveforms represent sub-cycle pulses; oscillatory pulses with a dominant wavenumber are also discussed. These solutions are sufficiently localized to have finite energy, momentum, and angular momentum when applied to acoustic and electromagnetic pulses. The energy, momentum, and angular momentum of the pulses are simply expressed in terms of the wavenumber weight function.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Longitudinal wave propagation in a practical metamaterial lattice 实用超材料晶格中的纵波传播
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-19 DOI: 10.1016/j.wavemoti.2024.103431
{"title":"Longitudinal wave propagation in a practical metamaterial lattice","authors":"","doi":"10.1016/j.wavemoti.2024.103431","DOIUrl":"10.1016/j.wavemoti.2024.103431","url":null,"abstract":"<div><div>A practical metamaterial lattice is constructed by integrating curved beams, four-link mechanisms, and cantilever beams with lumped masses. It can generate two complete low-frequency bandgaps due to the lateral local resonance, inertia mass, and the main chain. The effective mass density and stiffness are obtained using different effective models, which show negative within the bandgaps. The analysis of the energy distribution and the space wave attenuation reveals that the metamaterial can attenuate the elastic waves in an exponential form within the bandgaps along the lattice. The finite element model is established to show the dynamic behaviour of the elastic wave propagation in the frequency domain and transient domain. Both results show that waves can be efficiently blocked within the bandgaps, while outside the bandgaps, waves can propagate without any attenuation. Finally, the experimental model of practical metamaterial is constructed, and the test piece is excited by a force hammer. Experimental results verify that the practical metamaterial can efficiently suppress the vibration within the bandgap frequency and validate the accuracy of the theoretical prediction.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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