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Quarterly Journal of Mechanics and Applied Mathematics最新文献

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Active cloaking of inclusions for flexural waves in thin elastic plates 薄弹性板中弯曲波夹杂物的主动隐身
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-08-01 DOI: 10.1093/QJMAM/HBV007
J. O'Neill, Ö. Selsil, R. McPhedran, A. Movchan, N. Movchan
{"title":"Active cloaking of inclusions for flexural waves in thin elastic plates","authors":"J. O'Neill, Ö. Selsil, R. McPhedran, A. Movchan, N. Movchan","doi":"10.1093/QJMAM/HBV007","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV007","url":null,"abstract":"We present a new method to create an active cloak for a single clamped inclusion in a Kirchhoff plate in the presence of flexural waves. In order to cloak this inclusion, we place control sources in the exterior of the scatterer and choose their intensities to eliminate propagating components of the scattered wave, thus reconstructing the incident wave. Our initial discussion is on the canonical problem of active cloaking of a clamped circular cylinder for which a closed form analytic solution is derived, and exemplified in a number of illustrative cases. We then consider a clamped scatterer of arbitrary shape with a smooth boundary and describe a method for solving the active cloaking problem.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"263-288"},"PeriodicalIF":0.9,"publicationDate":"2015-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 33
A low-order model for slamming in a flexible-channel flow 柔性通道流中撞击的低阶模型
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-08-01 DOI: 10.1093/QJMAM/HBV009
F. Xu, O. Jensen
{"title":"A low-order model for slamming in a flexible-channel flow","authors":"F. Xu, O. Jensen","doi":"10.1093/QJMAM/HBV009","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV009","url":null,"abstract":"In simulations, large-amplitude self-excited oscillations of high-Reynolds-number flow in a finite-length flexible channel often exhibit vigorous repetitive ’slamming’ motion, during which the channel briefly becomes almost completely occluded over a very short lengthscale near its downstream end before rapidly reopening. Here we analyse this near-singular behaviour using an established one-dimensional PDE model of the two-dimensional physical system. Working in a distinguished asympotic limit, we systematically derive a low-order differential/algebraic model for the flow when it is close to the slamming state. The shape of the channel near the constriction is determined by a balance between membrane tension and fluid inertia; this region is also the predominant site of viscous dissipation, which balances energy changes distributed along the channel. The reduced model accurately captures a set of steady solution branches and their stability and shows how slamming is strongly coupled to the properties of the rigid channel downstream of the membrane. A singularity is identified in the low-order model which may explain the violent readjustment of the flow at the end of a slamming event.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"299-319"},"PeriodicalIF":0.9,"publicationDate":"2015-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
CORRIGENDUM AND ADDENDUM: MODELING WEAKLY NONLINEAR ACOUSTIC WAVE PROPAGATION 修正和补充:模拟弱非线性声波传播
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-05-01 DOI: 10.1093/QJMAM/HBU023
I. Christov, C. Christov, P. Jordan
{"title":"CORRIGENDUM AND ADDENDUM: MODELING WEAKLY NONLINEAR ACOUSTIC WAVE PROPAGATION","authors":"I. Christov, C. Christov, P. Jordan","doi":"10.1093/QJMAM/HBU023","DOIUrl":"https://doi.org/10.1093/QJMAM/HBU023","url":null,"abstract":"This article presents errors, corrections, and additions to the research outlined in the following citation: Christov, I., Christov, C. I., & Jordan, P. M. (2007). Modeling weakly nonlinear acoustic wave propagation. The Quarterly Journal of Mechanics and Applied Mathematics, 60(4), 473-495.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"231-233"},"PeriodicalIF":0.9,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Influence of boundary elasticity on a couple stress elastic solid with a mode-III crack 边界弹性对含ⅲ型裂纹的耦合应力弹性固体的影响
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-05-01 DOI: 10.1093/QJMAM/HBV004
T. Sigaeva, P. Schiavone
{"title":"Influence of boundary elasticity on a couple stress elastic solid with a mode-III crack","authors":"T. Sigaeva, P. Schiavone","doi":"10.1093/QJMAM/HBV004","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV004","url":null,"abstract":"In this article, we develop a linear theory of elastic boundary reinforcement of a couple stress elastic solid subjected to anti-plane deformations. The reinforcement is represented by a thin couple stress elastic coating perfectly bonded to the boundary of the solid. The elastic properties of the coating are taken to be separate from those of the surrounding bulk material. In this context, the model developed here can also be viewed as a more comprehensive representation of the deformation of a couple stress material in which the separate role of surface mechanics is incorporated into the model of deformation. As an example of our theory, we consider the classical problem of a semi-infinite crack in a couple stress material and examine the contribution of the reinforcement to the stress distributions in the vicinity of the crack tip. Our results indicate that the presence of the reinforcing layer on the crack faces eliminates the well-known stress singularity at the crack tip demonstrating the influence of surface and couple stress effects in the model of deformation.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"195-202"},"PeriodicalIF":0.9,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Motion of a spherical particle in a viscous fluid along a slip wall 粘滞流体中球形粒子沿滑动壁的运动
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-05-01 DOI: 10.1093/QJMAM/HBV001
H. Loussaief, L. Pasol, F. Feuillebois
{"title":"Motion of a spherical particle in a viscous fluid along a slip wall","authors":"H. Loussaief, L. Pasol, F. Feuillebois","doi":"10.1093/QJMAM/HBV001","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV001","url":null,"abstract":"Summary The motion of a solid spherical particle in the flow of a viscous fluid is calculated in the framework of Stokes equations, when the Navier condition of slippage applies on the wall and the no-slip condition applies on the particle. The problem for the flow around a sphere translating and rotating in a pure shear flow is solved, from the linearity of Stokes equations, as the sum of elementary problems: a sphere held fixed in a shear flow close to a wall, a sphere translating and rotating along a wall in a fluid at rest. The creeping flow is calculated analytically using the bispherical coordinates technique that provides the fluid velocity and pressure as series. The unknown coupled infinite series of coefficients are reduced by combinations from seven to four. This simplifies the formulation compared with earlier works on the translation and rotation problems. The infinite linear system for the coefficients is then solved using an extension of Thomas algorithm that allows to calculate O(10 5 ) terms in the series. Such a high number is necessary to obtain a good accuracy at small sphere to wall gaps down to 10 −5 sphere radius, in particular for a large slip on the wall. Accurate results for the force and torque on the particle are then obtained for each of the three elementary problems. On this basis, results are provided for the diffusion coefficient of a dilute suspension of freely rotating spheres parallel to a slipping wall and for the translational and rotational velocities of a freely moving sphere in a pure shear flow along such a wall. Simplified formulae are provided for application to various physical problems, like for instance the interpretation of velocity measurements at micro-scales by tracking of particles close to a hydrophobic wall.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"115-144"},"PeriodicalIF":0.9,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Computation of higher order ellipsoidal harmonics with an application in electroencephalography 高阶椭球谐波的计算及其在脑电图中的应用
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-05-01 DOI: 10.1093/QJMAM/HBV002
G. Dassios, I. Chatjigeorgiou
{"title":"Computation of higher order ellipsoidal harmonics with an application in electroencephalography","authors":"G. Dassios, I. Chatjigeorgiou","doi":"10.1093/QJMAM/HBV002","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV002","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"145-172"},"PeriodicalIF":0.9,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Acoustic wave propagation through a triply periodic lattice of arbitrary shape scatterers 声波通过任意形状散射体的三周期晶格传播
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-02-01 DOI: 10.1093/QJMAM/HBU020
S. Guo
{"title":"Acoustic wave propagation through a triply periodic lattice of arbitrary shape scatterers","authors":"S. Guo","doi":"10.1093/QJMAM/HBU020","DOIUrl":"https://doi.org/10.1093/QJMAM/HBU020","url":null,"abstract":"Summary Acoustic wave propagation through a triply periodic array of arbitrary shape scatterers is considered by the method of matched asymptotic expansions. It is assumed that the scatterer size is much smaller than both the wavelength and the array periodicity but no restriction on the wavelength relative to the periodicity. Therefore, it is possible to examine the phenomena associated with periodic media such as band gaps. This is illustrated with simple cubic and body-centred cubic lattices.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"1-22"},"PeriodicalIF":0.9,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Stability of a helicoidal surface inside a cylinder with pinned diameters 螺旋面在直径固定圆柱内的稳定性
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-02-01 DOI: 10.1093/QJMAM/HBU026
R. Whittaker, S. Cox
{"title":"Stability of a helicoidal surface inside a cylinder with pinned diameters","authors":"R. Whittaker, S. Cox","doi":"10.1093/QJMAM/HBU026","DOIUrl":"https://doi.org/10.1093/QJMAM/HBU026","url":null,"abstract":"A mathematical analysis is presented of the stability of a soap film with uniform surface tension when stretched between two diameters on the inside of a circular cylinder. The stability boundary is found as a critical twist angle θ between the two diameters, as a function of the aspect ratio l of the cylinder. Numerical and asymptotic results agree well with previous numerical simulations and experiments by Cox & Jones (J. Engr Math, 2014, 86, 1-7). Their hypothesis that the stability boundary for the multiple-vane case is identical to the single film case is confirmed. It is also shown that two distinct instability mechanisms operate. For moderate and small θ/l, the instability is driven by the decrease in area caused by the film moving to an off-diameter position. But for larger θ/l (more twisted films), the decrease in area is dominated by an internal rearrangement of the surface. The latter mechanism is more relevant to Plateau borders in foams, and our results indicate that straight Plateau borders should be stable at any length provided the total twist is less than π/√2.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"23-52"},"PeriodicalIF":0.9,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Absence of localisation in ocean wave interactions with a rough seabed in intermediate water depth 在中等水深中，海浪与粗糙海床的相互作用缺乏局域性
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-02-01 DOI: 10.1093/QJMAM/HBU024
L. Bennetts, M. Peter, Hyuck Chung
{"title":"Absence of localisation in ocean wave interactions with a rough seabed in intermediate water depth","authors":"L. Bennetts, M. Peter, Hyuck Chung","doi":"10.1093/QJMAM/HBU024","DOIUrl":"https://doi.org/10.1093/QJMAM/HBU024","url":null,"abstract":"The possibility of a rough seabed causing localisation of ocean waves in intermediate water depth is considered. A numerical and analytical study of the localisation phenomenon is conducted using a transect model and linear potential theory. It is shown that although the effective wave field is strongly attenuated by the roughness, leading to previous predictions of localisation, individual wave fields are not localised.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"97-113"},"PeriodicalIF":0.9,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Solvability of the integrodifferential equation of Eshelby's equivalent inclusion method Eshelby等效包含法积分微分方程的可解性
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2015-02-01 DOI: 10.1093/QJMAM/HBU025
D. Gintides, K. Kiriaki
{"title":"Solvability of the integrodifferential equation of Eshelby's equivalent inclusion method","authors":"D. Gintides, K. Kiriaki","doi":"10.1093/QJMAM/HBU025","DOIUrl":"https://doi.org/10.1093/QJMAM/HBU025","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"85-96"},"PeriodicalIF":0.9,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
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