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Back matter 背景材料
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-08-01
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引用次数: 0
Front matter 前页
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-08-01
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引用次数: 0
Spectral study of the Laplace–Beltrami operator arising in the problem of acoustic wave scattering by a quarter-plane 声波经四分之一平面散射问题中拉普拉斯-贝尔特拉米算子的频谱研究
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-08-01 DOI: 10.1093/qjmam/hbw008
R. C. Assier;C. Poon;N. Peake
{"title":"Spectral study of the Laplace–Beltrami operator arising in the problem of acoustic wave scattering by a quarter-plane","authors":"R. C. Assier;C. Poon;N. Peake","doi":"10.1093/qjmam/hbw008","DOIUrl":"https://doi.org/10.1093/qjmam/hbw008","url":null,"abstract":"The Laplace-Beltrami operator (LBO) on a sphere with a cut arises when considering the problem of wave scattering by a quarter-plane. Recent methods developed for sound-soft (Dirichlet) and sound-hard (Neumann) quarter-planes rely on an a priori knowledge of the spectrum of the LBO. In this article we consider this spectral problem for more general boundary conditions, including Dirichlet, Neumann, real and complex impedance, where the value of the impedance varies like \u0000<tex>${alpha / r, r}$</tex>\u0000 being the distance from the vertex of the quarter-plane and \u0000<tex>$alpha$</tex>\u0000 being constant, and any combination of these. We analyse the corresponding eigenvalues of the LBO, both theoretically and numerically. We show in particular that when the operator stops being self-adjoint, its eigenvalues are complex and are contained within a sector of the complex plane, for which we provide analytical bounds. Moreover, for impedance of small enough modulus \u0000<tex>${|alpha|}$</tex>\u0000, the complex eigenvalues approach the real eigenvalues of the Neumann case.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"69 3","pages":"281-317"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49954118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Influence of surface effect of the edge of a half-plane on the stress concentration around a nearby nanosized hole of arbitrary shape 半平面边缘表面效应对任意形状纳米孔附近应力集中的影响
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-08-01 DOI: 10.1093/qjmam/hbw005
Ming Dai;Peter Schiavone;Cun-Fa Gao
{"title":"Influence of surface effect of the edge of a half-plane on the stress concentration around a nearby nanosized hole of arbitrary shape","authors":"Ming Dai;Peter Schiavone;Cun-Fa Gao","doi":"10.1093/qjmam/hbw005","DOIUrl":"https://doi.org/10.1093/qjmam/hbw005","url":null,"abstract":"In the problem of a half-plane containing a nearby nanosized hole, it is customary to assume that the edge of the half-plane is traction free. In the context of nanomechanics, however, the more realistic scenario is to incorporate surface effects not only on the edge of the hole but also on the edge of the half-plane. Our results indicate that the incorporation of surface effects on the edge of the half-plane indeed plays a significant role, in particular as the distance between the hole and the half-plane decreases. In fact, we show that the absence of the corresponding surface effect on the edge of the half-plane induces a significant error in the stress concentration around an arbitrary-shaped hole when the distance between the hole and the edge reaches a critical value. We illustrate our results with a variety of examples including circular, elliptical, triangular and square-shaped holes.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"69 3","pages":"215-229"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49954116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Solutions of some boundary value problems for a class of constitutive relations for non-linear elastic bodies that is not Green elastic 非格林弹性非线性弹性体的一类本构关系边值问题的解
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-08-01 DOI: 10.1093/qjmam/hbw007
R. Bustamante
{"title":"Solutions of some boundary value problems for a class of constitutive relations for non-linear elastic bodies that is not Green elastic","authors":"R. Bustamante","doi":"10.1093/qjmam/hbw007","DOIUrl":"https://doi.org/10.1093/qjmam/hbw007","url":null,"abstract":"Several boundary value problems are solved for a new class of constitutive equation, where the left Cauchy–Green stretch tensor is given as a non-linear function of the Cauchy stress tensor. Some constitutive inequalities and restrictions are proposed as well.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"69 3","pages":"257-279"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49954117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Asymptotic modelling of the JKR adhesion contact for a thin elastic layer 薄弹性层JKR粘着接触的渐近建模
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-03-01 DOI: 10.1093/qjmam/hbw002
I. I. Argatov;G. S. Mishuris;V. L. Popov
{"title":"Asymptotic modelling of the JKR adhesion contact for a thin elastic layer","authors":"I. I. Argatov;G. S. Mishuris;V. L. Popov","doi":"10.1093/qjmam/hbw002","DOIUrl":"https://doi.org/10.1093/qjmam/hbw002","url":null,"abstract":"The Johnson–Kendall–Roberts model of frictionless adhesive contact is extended to the case of a thin transversely isotropic elastic layer bonded to a rigid base. The leading-order asymptotic models are obtained for both compressible and incompressible elastic layers. The boundary conditions for the contact pressure approximation on the contour of the contact area have been derived from the boundary-layer solutions, which satisfy the condition that the stress intensity factor of the contact pressure density should have the same value all around the contact area boundary. In the incompressible case, a perturbation solution is obtained for a slightly perturbed circular contact area.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"69 2","pages":"161-179"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49959018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 21
Scattering of water waves by an inclined porous plate submerged in ocean with ice cover 有冰覆盖的海洋中倾斜多孔板对水波的散射
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-03-01 DOI: 10.1093/qjmam/hbw004
Dibakar Mondal;Sudeshna Banerjea
{"title":"Scattering of water waves by an inclined porous plate submerged in ocean with ice cover","authors":"Dibakar Mondal;Sudeshna Banerjea","doi":"10.1093/qjmam/hbw004","DOIUrl":"https://doi.org/10.1093/qjmam/hbw004","url":null,"abstract":"In the present article, we have studied the problem of scattering of water waves by a porous plate submerged in the ocean and inclined at an angle to the vertical. The problem is formulated in terms of a hypersingular integral equation of the second kind. The hypersingular integral equation is then solved by a collocation method by representing the unknown function using Tchebychev polynomials. The reflection and transmission coefficients are then obtained and presented graphically. It is observed that porosity of the plate dissipates the wave energy and thereby reduces the reflection and transmission of wave energy. However, it is found that the presence of ice cover reduces the dissipation of energy and also the reflection of wave energy and thereby increases the transmission of wave energy. Also, the increase in angle of inclination of porous plate reduces the energy dissipation as well as the reflection of waves.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"69 2","pages":"195-213"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49959020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
Effective properties of periodic tubular structures 周期管状结构的有效性能
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-03-01 DOI: 10.1093/qjmam/hbw003
Yuri A. Godin
{"title":"Effective properties of periodic tubular structures","authors":"Yuri A. Godin","doi":"10.1093/qjmam/hbw003","DOIUrl":"https://doi.org/10.1093/qjmam/hbw003","url":null,"abstract":"A method is described to calculate effective tensor properties of a periodic array of two-phase dielectric tubes embedded in a host matrix. The method uses Weierstrass' quasiperodic functions for representation of the potential that considerably facilitates the problem and allows us to find an exact expression for the effective tensor. For weakly interacting tubes, we obtain Maxwell-like approximation of the effective parameter which is in very good agreement with numerical results in considered examples.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"69 2","pages":"181-193"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49959019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Active cloaking of resonant coated inclusions for waves in membranes and Kirchhoff plates 膜和基尔霍夫板中波的共振包覆物的主动隐身
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-03-01 DOI: 10.1093/qjmam/hbw001
J. O'Neill;Ö. Selsil;R. C. McPhedran;A. B. Movchan;N. V. Movchan;C. Henderson Moggach
{"title":"Active cloaking of resonant coated inclusions for waves in membranes and Kirchhoff plates","authors":"J. O'Neill;Ö. Selsil;R. C. McPhedran;A. B. Movchan;N. V. Movchan;C. Henderson Moggach","doi":"10.1093/qjmam/hbw001","DOIUrl":"https://doi.org/10.1093/qjmam/hbw001","url":null,"abstract":"The dynamic response of a coated inclusion is considered in the context of active cloaking. The active cloak is achieved for a coated inclusion in the presence of flexural and membrane waves. In this article, we investigate the design of an active cloak for a coated inclusion in three frequency regimes: the low-frequency range, the intermediate range and the higher frequency range in which scattering resonances occur. In the first of these ranges, we extend previous work, which resulted in a simple mass-compensation design for the monopole scatterer, while in the second and third ranges, a combination of the use of an appropriate coating and the appropriate choice of the amplitudes of the active cloaking sources is necessary. We show that such cloaking can indeed be effective in the region of strong scattering resonances. We give closed form analytic expressions for the required amplitudes of the active cloaking sources in the three frequency regions and provide asymptotic estimates and numerical illustrations.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"69 2","pages":"115-159"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49959017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
Back matter 背景材料
The quarterly journal of mechanics and applied mathematics Pub Date : 2016-03-01
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引用次数: 0
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