This work demonstrated to attain a multiband absorption in the terahertz region with high degree simplification and tunable absorption characteristics. The design model composed of an H-type resonator placed above on a middle layer (dielectric medium) and a metallic layer at the bottom. The single sized resonator strongly interacts with incident electromagnetic wave resulting four near perfect absorption peaks located at 0.625 THz, 1.85 THz, 2.075 THz, and 2.5 THz. Moreover, the suggested design was also investigated for active modulation features by inserting vanadium dioxide (VO2) material into the design metamaterial structure due to which the quad-band absorption profile exhibits a switchable function by variation in the state phase of VO2 from insulator to metallic phase. Therefore, the design structure could have wide range of potential THz technology related field applications.
{"title":"High degree simplification and tunable absorption features of terahertz metamaterial absorber","authors":"Shahzad Anwar , Ghafar Ali , Maaz Khan , Forough Bozorgzadeh","doi":"10.1016/j.wavemoti.2024.103450","DOIUrl":"10.1016/j.wavemoti.2024.103450","url":null,"abstract":"<div><div>This work demonstrated to attain a multiband absorption in the terahertz region with high degree simplification and tunable absorption characteristics. The design model composed of an H-type resonator placed above on a middle layer (dielectric medium) and a metallic layer at the bottom. The single sized resonator strongly interacts with incident electromagnetic wave resulting four near perfect absorption peaks located at 0.625 THz, 1.85 THz, 2.075 THz, and 2.5 THz. Moreover, the suggested design was also investigated for active modulation features by inserting vanadium dioxide (VO2) material into the design metamaterial structure due to which the quad-band absorption profile exhibits a switchable function by variation in the state phase of VO2 from insulator to metallic phase. Therefore, the design structure could have wide range of potential THz technology related field applications.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103450"},"PeriodicalIF":2.1,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747188","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}
Pub Date : 2024-11-16DOI: 10.1016/j.wavemoti.2024.103444
Ben Wilks , Fabien Montiel , Luke G. Bennetts , Sarah Wakes
Eigenmodes are studied for a fluid-filled rectangular tank containing one or more vertical barriers, and on which either Dirichlet or Neumann boundary conditions are prescribed on the lateral walls. In the case where the tank contains a single barrier, the geometry of the tank is equivalent to the unit cell of the cognate periodic array, and its eigenmodes are equivalent to standing Bloch waves. As the submergence depth of the barrier increases, it is shown that the passbands (i.e. frequency intervals in which the periodic array supports Bloch waves) become thinner, and that this effect becomes stronger at higher frequencies. The eigenmodes of a uniform array of vertical barriers in a rectangular tank are also considered. They are found to be a superposition of left- and right-propagating Bloch waves, which couple together at the lateral walls of the tank. A homotopy procedure is used to relate the eigenmodes to the quasimodes of the same uniform array in a fluid of infinite horizontal extent, and the quasimodes are shown to govern the response of the array to incident waves. Qualitative features of the mode shapes are typically preserved by the homotopy, which suggests that the resonant responses of the array in an infinite fluid can be understood in terms of modes of the array in a finite tank.
{"title":"Water wave interactions with surface-piercing vertical barriers in a rectangular tank: Connections with Bloch waves and quasimodes","authors":"Ben Wilks , Fabien Montiel , Luke G. Bennetts , Sarah Wakes","doi":"10.1016/j.wavemoti.2024.103444","DOIUrl":"10.1016/j.wavemoti.2024.103444","url":null,"abstract":"<div><div>Eigenmodes are studied for a fluid-filled rectangular tank containing one or more vertical barriers, and on which either Dirichlet or Neumann boundary conditions are prescribed on the lateral walls. In the case where the tank contains a single barrier, the geometry of the tank is equivalent to the unit cell of the cognate periodic array, and its eigenmodes are equivalent to standing Bloch waves. As the submergence depth of the barrier increases, it is shown that the passbands (i.e. frequency intervals in which the periodic array supports Bloch waves) become thinner, and that this effect becomes stronger at higher frequencies. The eigenmodes of a uniform array of vertical barriers in a rectangular tank are also considered. They are found to be a superposition of left- and right-propagating Bloch waves, which couple together at the lateral walls of the tank. A homotopy procedure is used to relate the eigenmodes to the quasimodes of the same uniform array in a fluid of infinite horizontal extent, and the quasimodes are shown to govern the response of the array to incident waves. Qualitative features of the mode shapes are typically preserved by the homotopy, which suggests that the resonant responses of the array in an infinite fluid can be understood in terms of modes of the array in a finite tank.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103444"},"PeriodicalIF":2.1,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698664","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}
Pub Date : 2024-11-15DOI: 10.1016/j.wavemoti.2024.103452
Ali R. Hadjesfandiari , Gary F. Dargush
Consistent couple stress theory (C-CST) provides the framework for the present investigation of size-dependent effects in the torsional oscillation of elastic circular wires. By using this form of couple stress theory, we are able to develop the first self-consistent size-dependent mechanics solution for this fundamental continuum dynamics problem that satisfies all boundary conditions without approximation. In addition, we derive the dispersion relations and characteristics for torsional waves in C-CST and the natural torsional modes for a finite length wire with fixed ends. Appendices provide a study of the general character of the C-CST eigensolutions and examine the torsional oscillation problem under classical and Mindlin-Tiersten-Koiter couple stress elastodynamics.
{"title":"Size-dependent torsional oscillation of an elastic wire with circular cross-section","authors":"Ali R. Hadjesfandiari , Gary F. Dargush","doi":"10.1016/j.wavemoti.2024.103452","DOIUrl":"10.1016/j.wavemoti.2024.103452","url":null,"abstract":"<div><div>Consistent couple stress theory (C-CST) provides the framework for the present investigation of size-dependent effects in the torsional oscillation of elastic circular wires. By using this form of couple stress theory, we are able to develop the first self-consistent size-dependent mechanics solution for this fundamental continuum dynamics problem that satisfies all boundary conditions without approximation. In addition, we derive the dispersion relations and characteristics for torsional waves in C-CST and the natural torsional modes for a finite length wire with fixed ends. Appendices provide a study of the general character of the C-CST eigensolutions and examine the torsional oscillation problem under classical and Mindlin-Tiersten-Koiter couple stress elastodynamics.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103452"},"PeriodicalIF":2.1,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747044","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}
Pub Date : 2024-11-09DOI: 10.1016/j.wavemoti.2024.103443
Kuldeep Singh , Ioannis Kourakis
The Korteweg–de Vries (KdV) equation can be derived from a plasma-fluid model via a reductive perturbation technique. The associated methodology is summarized, from first principles, focusing on the underlying physical assumptions involved in the plasma-theoretical framework. A beam permeated electron-ion plasma is assumed, although the main findings of this study may be extended to more complicated plasma configurations. Rather counter-intuitively, it is shown that either of the (two) real coefficients appearing in the KdV equation (actually, both depending parametrically on the plasma configuration and on the beam characteristics) may take either positive or negative values, a possibility overlooked in the past. Different possibilities are investigated, from first principles, regarding the sign of the nonlinearity coefficient (that is determined by the electron background statistics, in combination with the beam velocity) and the sign of the dispersion coefficient (that is solely determined by the beam velocity and is always positive in its absence). The possibility of polarity reversal is investigated from first principles, in relation with both the electrostatic potential (pulse) profile and its associated electric field (bipolar pulse) in the electrostatic approximation. Different types of excitations are shown to exist and the role of the (sign of the) various coefficients in the pulse-shaped solution’s propagation characteristics is discussed.
Korteweg-de Vries（KdV）方程可以通过还原扰动技术从等离子体流体模型中推导出来。本文从第一原理出发，总结了相关方法，重点介绍了等离子体理论框架所涉及的基本物理假设。虽然本研究的主要发现可以扩展到更复杂的等离子体配置，但我们还是假设了一种束渗透电子-离子等离子体。与直觉相反的是，研究表明 KdV 方程中出现的（两个）实系数（实际上，这两个系数都取决于等离子体构型和束流特性的参数）既可以取正值，也可以取负值，而这种可能性过去一直被忽视。我们从第一原理出发，研究了非线性系数 A 的符号（由电子背景统计和光束速度共同决定）和色散系数 B 的符号（仅由光束速度决定，在没有光束速度的情况下始终为正）的不同可能性。根据静电近似的静电势（脉冲）剖面及其相关电场（双极脉冲）E=-∇j，从第一原理研究了极性反转的可能性。结果表明存在不同类型的激励，并讨论了各种系数（符号）在脉冲形溶液传播特性中的作用。
{"title":"Generalized analytical solutions of a Korteweg–de Vries (KdV) equation with arbitrary real coefficients: Association with the plasma-fluid framework and physical interpretation","authors":"Kuldeep Singh , Ioannis Kourakis","doi":"10.1016/j.wavemoti.2024.103443","DOIUrl":"10.1016/j.wavemoti.2024.103443","url":null,"abstract":"<div><div>The Korteweg–de Vries (KdV) equation can be derived from a plasma-fluid model via a reductive perturbation technique. The associated methodology is summarized, from first principles, focusing on the underlying physical assumptions involved in the plasma-theoretical framework. A beam permeated electron-ion plasma is assumed, although the main findings of this study may be extended to more complicated plasma configurations. Rather counter-intuitively, it is shown that either of the (two) real coefficients appearing in the KdV equation (actually, both depending parametrically on the plasma configuration and on the beam characteristics) may take either positive or negative values, a possibility overlooked in the past. Different possibilities are investigated, from first principles, regarding the sign of the nonlinearity coefficient <span><math><mi>A</mi></math></span> (that is determined by the electron background statistics, in combination with the beam velocity) and the sign of the dispersion coefficient <span><math><mi>B</mi></math></span> (that is solely determined by the beam velocity and is always positive in its absence). The possibility of polarity reversal is investigated from first principles, in relation with both the electrostatic potential (pulse) profile and its associated electric field (bipolar pulse) <span><math><mrow><mi>E</mi><mo>=</mo><mo>−</mo><mo>∇</mo><mi>ϕ</mi></mrow></math></span> in the electrostatic approximation. Different types of excitations are shown to exist and the role of the (sign of the) various coefficients in the pulse-shaped solution’s propagation characteristics is discussed.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103443"},"PeriodicalIF":2.1,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650918","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}
A hydroelastic model has been introduced to study the impact of free surface tension on the propagation of oblique incident waves over small distortions on a thin, flexible floor of a fluid region. There are two varieties of time-harmonic propagating waves (free-surface and flexural modes) that exist in the region in the case of any specific frequency. One variety of proliferating waves having smaller wavenumber spreads on the top surface, while another spreads along the thin, flexible base. Using perturbation expansion involving a small parameter , the primary boundary value problem (bvp) is converted to a new bvp for the first-order approximation of the potential function. Subsequently, employing the Fourier transform approach, the first-order approximation of reflected and transmitted energy are acquired in the case of both modes of waves. Two specific examples of irregular floor are taken up to validate the theoretical outcomes flourished in this study. The influence of free-surface tension and flexible floor on the oblique wave propagation over uneven floor are analyzed and depicted graphically for certain sets of parametric values involved in the problem. The presence of free-surface tension on the upper boundary of the fluid introduces a third-order linearized boundary condition into the formulation of the wave-structure interaction problem, unlike the usual homogeneous first-order condition applicable for a free-surface. When a series of obliquely incident waves corresponding to free-surface and flexural modes spread over an irregular flexible floor of the fluid, the free-surface tension acts as a resistive force to the surface gravity waves. It can be inferred from this that the influence of surface tension at the free-surface of the fluid should not always be overlooked while dealing with the linear wave-structure interaction problem. Further, numerical estimation of reflected and transmitted energy for both varieties of time-harmonic waves are presented to confirm the analytical forms of energy relations almost accurately.
{"title":"Oblique wave propagation over uneven flexible base in a fluid having free-surface tension","authors":"Balaram Sahu , Smrutiranjan Mohapatra , Manas Ranjan Sarangi","doi":"10.1016/j.wavemoti.2024.103433","DOIUrl":"10.1016/j.wavemoti.2024.103433","url":null,"abstract":"<div><div>A hydroelastic model has been introduced to study the impact of free surface tension on the propagation of oblique incident waves over small distortions on a thin, flexible floor of a fluid region. There are two varieties of time-harmonic propagating waves (free-surface and flexural modes) that exist in the region in the case of any specific frequency. One variety of proliferating waves having smaller wavenumber spreads on the top surface, while another spreads along the thin, flexible base. Using perturbation expansion involving a small parameter <span><math><mi>ϵ</mi></math></span>, the primary boundary value problem (<span>bvp</span>) is converted to a new <span>bvp</span> for the first-order approximation of the potential function. Subsequently, employing the Fourier transform approach, the first-order approximation of reflected and transmitted energy are acquired in the case of both modes of waves. Two specific examples of irregular floor are taken up to validate the theoretical outcomes flourished in this study. The influence of free-surface tension and flexible floor on the oblique wave propagation over uneven floor are analyzed and depicted graphically for certain sets of parametric values involved in the problem. The presence of free-surface tension on the upper boundary of the fluid introduces a third-order linearized boundary condition into the formulation of the wave-structure interaction problem, unlike the usual homogeneous first-order condition applicable for a free-surface. When a series of obliquely incident waves corresponding to free-surface and flexural modes spread over an irregular flexible floor of the fluid, the free-surface tension acts as a resistive force to the surface gravity waves. It can be inferred from this that the influence of surface tension at the free-surface of the fluid should not always be overlooked while dealing with the linear wave-structure interaction problem. Further, numerical estimation of reflected and transmitted energy for both varieties of time-harmonic waves are presented to confirm the analytical forms of energy relations almost accurately.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103433"},"PeriodicalIF":2.1,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650916","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}
Pub Date : 2024-11-01DOI: 10.1016/j.wavemoti.2024.103434
Shawn Samuel Carl McAdam, Samuel Opoku Agyemang, Alexei Cheviakov
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves propagating on an interface between materials with different mechanical properties. The model is valid for a broad class of hyper-viscoelastic materials. For the Murnaghan constitutive model, shear wave equations contain cubic and quintic differential polynomial terms, including viscoelasticity contributions in terms of dispersion terms that include mixed derivatives of the material displacement. Full (2+1)-dimensional numerical simulations of waves propagating in the bulk of a two-layered solid are undertaken and analysed with respect to the source position and mechanical properties of the layers. Interfacial nonlinear Love waves and free upper surface shear waves are tracked; it is demonstrated that in the fully nonlinear case, the variable wave speed of interface and surface waves generally satisfies the linear Love wave existence condition , while tending to the larger material wave speed or for large times.
{"title":"Nonlinear incompressible shear wave models in hyperelasticity and viscoelasticity frameworks, with applications to Love waves","authors":"Shawn Samuel Carl McAdam, Samuel Opoku Agyemang, Alexei Cheviakov","doi":"10.1016/j.wavemoti.2024.103434","DOIUrl":"10.1016/j.wavemoti.2024.103434","url":null,"abstract":"<div><div>General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves propagating on an interface between materials with different mechanical properties. The model is valid for a broad class of hyper-viscoelastic materials. For the Murnaghan constitutive model, shear wave equations contain cubic and quintic differential polynomial terms, including viscoelasticity contributions in terms of dispersion terms that include mixed derivatives <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi><mi>t</mi></mrow></msub></math></span> of the material displacement. Full (2+1)-dimensional numerical simulations of waves propagating in the bulk of a two-layered solid are undertaken and analysed with respect to the source position and mechanical properties of the layers. Interfacial nonlinear Love waves and free upper surface shear waves are tracked; it is demonstrated that in the fully nonlinear case, the variable wave speed of interface and surface waves generally satisfies the linear Love wave existence condition <span><math><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo><</mo><mfenced><mrow><mi>v</mi></mrow></mfenced><mo><</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, while tending to the larger material wave speed <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> for large times.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103434"},"PeriodicalIF":2.1,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650910","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}
Pub Date : 2024-10-31DOI: 10.1016/j.wavemoti.2024.103442
Wei-Ping Zhong , Milivoj Belić , Zhengping Yang
The Snyder-Mitchell model of accessible solitons is a simple model that reduces the dynamics of solitons in highly nonlocal nonlinear media to a linear dynamical system with harmonic potential. Utilizing this model in a system with a nonlinearity coefficient and an external potential generated in highly nonlocal media, we explore its solution by the methods of variable separation and self-similar transformation. We discover a special solution of the model that includes Scorer functions, for which reason we call it the Scorer beam. The transmission dynamics of the Scorer beam in strongly nonlocal nonlinear media is analytically and numerically investigated. Under the specific condition of applying an exponential truncation factor, the evolution of the Scorer beam is more stable and converges faster. We also find that the Scorer beam exhibits self-bending and self-healing characteristics. Our results provide theoretical and numerical guidance for generating Scorer beams that might prove useful for future experimental exploration.
{"title":"Scorer beams in highly nonlocal media with a nonlinearity coefficient and an external potential","authors":"Wei-Ping Zhong , Milivoj Belić , Zhengping Yang","doi":"10.1016/j.wavemoti.2024.103442","DOIUrl":"10.1016/j.wavemoti.2024.103442","url":null,"abstract":"<div><div>The Snyder-Mitchell model of accessible solitons is a simple model that reduces the dynamics of solitons in highly nonlocal nonlinear media to a linear dynamical system with harmonic potential. Utilizing this model in a system with a nonlinearity coefficient and an external potential generated in highly nonlocal media, we explore its solution by the methods of variable separation and self-similar transformation. We discover a special solution of the model that includes Scorer functions, for which reason we call it the Scorer beam. The transmission dynamics of the Scorer beam in strongly nonlocal nonlinear media is analytically and numerically investigated. Under the specific condition of applying an exponential truncation factor, the evolution of the Scorer beam is more stable and converges faster. We also find that the Scorer beam exhibits self-bending and self-healing characteristics. Our results provide theoretical and numerical guidance for generating Scorer beams that might prove useful for future experimental exploration.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103442"},"PeriodicalIF":2.1,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650917","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}
Pub Date : 2024-10-28DOI: 10.1016/j.wavemoti.2024.103432
Antonio Schiavone , Xiaodong Wang
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.
{"title":"Constitutive modelling and wave propagation through a class of anisotropic elastic metamaterials with local rotation","authors":"Antonio Schiavone , Xiaodong Wang","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":"132 ","pages":"Article 103432"},"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}
Pub Date : 2024-10-28DOI: 10.1016/j.wavemoti.2024.103429
P.A. Martin
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).
{"title":"On peridynamic acoustics","authors":"P.A. Martin","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":"132 ","pages":"Article 103429"},"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}
Pub Date : 2024-10-28DOI: 10.1016/j.wavemoti.2024.103430
Alverède Simon, Tony Valier-Brasier, Jean-Marc Conoir
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.
{"title":"Elastic coupled phase theory based on the Cosserat equations: Propagation of coherent waves","authors":"Alverède Simon, Tony Valier-Brasier, Jean-Marc Conoir","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":"132 ","pages":"Article 103430"},"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}
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