The quarterly journal of mechanics and applied mathematics最新文献_第3页

Green's functions for an anisotropic elastic parabolic inhomogeneity under generalised plane strain deformations 广义平面应变变形下各向异性弹性抛物不均匀性的格林函数

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-03-01 DOI: 10.1093/qjmam/hbab008

X Wang;P Schiavone

引用次数: 0

Steady axisymmetric vortices in radial stagnation flows 径向停滞流动中的稳定轴对称涡

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-03-01 DOI: 10.1093/qjmam/hbab009

Prabakaran Rajamanickam;Adam D Weiss

引用次数: 1

Integral and integro-differential equations with an exponential kernel and applications 具有指数核的积分和积分微分方程及其应用

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-03-01 DOI: 10.1093/qjmam/hbab007

Y A Antipov;S M Mkhitaryan

{"title":"Integral and integro-differential equations with an exponential kernel and applications","authors":"Y A Antipov;S M Mkhitaryan","doi":"10.1093/qjmam/hbab007","DOIUrl":"https://doi.org/10.1093/qjmam/hbab007","url":null,"abstract":"A convolution integral equation of the first kind and integro-differential equation of the second kind with the kernel \u0000<tex>$e^{-gamma |y-eta|}$</tex>\u0000 on a finite and semi-infinite interval are analyzed. For the former equation necessary and sufficient conditions for the existence and uniqueness of the solution are obtained, and when the solution exists, a closed-form representation for the solution is derived. On the basis of these results new integral relations for the spheroidal functions and Laguerre polynomials are obtained. The integro-differential equations on a finite and semi-infinite interval are transformed into a vector and scalar Riemann–Hilbert problem, respectively. Both problems are solved in closed-form. An application of these solutions to bending problems of a strip-shaped and a half-plane-shaped plate contacting with an elastic linearly deformable three-dimensional foundation characterized by the Korenev kernel \u0000<tex>$AK_0(delta r)$</tex>\u0000 (\u0000<tex>$A$</tex>\u0000 and \u0000<tex>$delta$</tex>\u0000 are parameters, \u0000<tex>$K_0(cdot)$</tex>\u0000 is the modified Bessel function, and \u0000<tex>$r=sqrt{(x-xi)^2+(y-eta)^2}$</tex>\u0000) is considered.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"74 3","pages":"297-322"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49978820","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: 1

Dynamic Green's functions in discrete flexural systems 离散弯曲系统中的动态格林函数

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-03-01 DOI: 10.1093/qjmam/hbab006

K H Madine;D J Colquitt

{"title":"Dynamic Green's functions in discrete flexural systems","authors":"K H Madine;D J Colquitt","doi":"10.1093/qjmam/hbab006","DOIUrl":"https://doi.org/10.1093/qjmam/hbab006","url":null,"abstract":"The article presents an analysis of the dynamic behaviour of discrete flexural systems composed of Euler–Bernoulli beams. The canonical object of study is the discrete Green's function, from which information regarding the dynamic response of the lattice under point loading by forces and moments can be obtained. Special attention is devoted to the interaction between flexural and torsional waves in a square lattice of Euler–Bernoulli beams, which is shown to yield a range of novel effects, including extreme dynamic anisotropy, asymmetric wave propagation, wave-guiding, filtering and the ability to create localised defect modes, all without the need for additional resonant elements or interfaces. The analytical study is complimented by numerical computations and finite element simulations, both of which are used to illustrate the effects predicted. A general algorithm is provided for constructing Green's functions as well as defect modes. This algorithm allows the tuning of the lattice to produce pass bands, band gaps, resonant modes, wave-guides and defect modes, over any desired frequency range.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"74 3","pages":"323-350"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016817/9579149/09579152.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49978819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Vertex Green's Functions of a Quarter-Plane: Links Between the Functional Equation, Additive Crossing and Lamé Functions 四分之一平面的顶点格林函数:泛函方程、加性交叉与lam<s:1>函数之间的联系

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-03-01 DOI: 10.1093/qjmam/hbab004

R C Assier;A V Shanin

引用次数: 5

Adaptive modelling of variably saturated seepage problems 变饱和渗流问题的自适应建模

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-02-01 DOI: 10.1093/qjmam/hbab001

B Ashby;C Bortolozo;A Lukyanov;T Pryer

{"title":"Adaptive modelling of variably saturated seepage problems","authors":"B Ashby;C Bortolozo;A Lukyanov;T Pryer","doi":"10.1093/qjmam/hbab001","DOIUrl":"https://doi.org/10.1093/qjmam/hbab001","url":null,"abstract":"In this article, we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a nonlinear Darcy–Buckingham law with physical constraints on subsurface-atmosphere boundaries. This leads to the formulation of the problem as a variational inequality. The solutions to this problem are investigated using an adaptive finite element method based on a dual-weighted a posteriori error estimate, derived with the aim of reducing error in a specific target quantity. The quantity of interest is chosen as volumetric water flux across the seepage face, and therefore depends on an a priori unknown free boundary. We apply our method to challenging numerical examples as well as specific case studies, from which this research originates, illustrating the major difficulties that arise in practical situations. We summarise extensive numerical results that clearly demonstrate the designed method produces rapid error reduction measured against the number of degrees of freedom.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"74 1","pages":"55-81"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbab001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49986252","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: 1

On The Vibrations of Pyramidal Beams With Rectangular Cross-Section and Application to Unswept Wings 矩形截面金字塔梁的振动及其在无翼机翼上的应用

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-02-01 DOI: 10.1093/qjmam/hbaa017

L M B C Campos;A C Marta

{"title":"On The Vibrations of Pyramidal Beams With Rectangular Cross-Section and Application to Unswept Wings","authors":"L M B C Campos;A C Marta","doi":"10.1093/qjmam/hbaa017","DOIUrl":"10.1093/qjmam/hbaa017","url":null,"abstract":"The bending frequencies of an unswept wing are calculated based on the model of a beam clamped at the root and free at the tip. For a tapered wing with straight leading- and trailing-edges, the chord is a linear function of the span; the same linear function of the span applies to thickness, in the case of constant thickness-to-chord ratio. The latter is usually small, so that the beam differs from the more frequent cases of a conical beam with a circular cross-section or a prismatic beam with a square cross-section. Thus, the bending modes of a non-uniform beam are considered, with mass and area moment of inertia which are respectively quadratic and quartic functions of the span. There is no exact solution expressible in finite terms using elementary functions, and thus power series expansions are used. The bending frequencies are calculated for a delta wing and compared with a rectangular wing, with the same span, mean chord and thickness, mass density and Young’s modulus. It is shown that the fundamental frequency is higher by a factor 4.96 for the delta wing; it is also shown that the general case of the tapered wing is intermediate between the delta and the rectangular wing. Lastly, the analytical results obtained for the bending modes are compared with numerical modal analyses of general tapered wing beams using high-fidelity finite-element model software.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"74 1","pages":"1-31"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbaa017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43085483","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: 2

Trapped modes in a multi-layer fluid 多层流体中的俘获模式

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-02-01 DOI: 10.1093/qjmam/hbaa019

F S Cal;G A S Dias;B M M Pereira;J H Videman

引用次数: 4

A continuation method for building invisible obstacles in waveguides 在波导中建立不可见障碍物的连续方法

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-02-01 DOI: 10.1093/qjmam/hbaa020

Antoine Bera;Anne-Sophie Bonnet-Ben Dhia;Lucas Chesnel

{"title":"A continuation method for building invisible obstacles in waveguides","authors":"Antoine Bera;Anne-Sophie Bonnet-Ben Dhia;Lucas Chesnel","doi":"10.1093/qjmam/hbaa020","DOIUrl":"https://doi.org/10.1093/qjmam/hbaa020","url":null,"abstract":"We consider the propagation of acoustic waves in a waveguide which is unbounded in one direction. We explain how to construct at a given wavenumber penetrable obstacles characterised by a physical coefficient \u0000<tex>$rho$</tex>\u0000 which are invisible in various ways. In particular, we focus our attention on invisibility in reflection (the reflection matrix is zero), invisibility in reflection and transmission (the scattering matrix is the same as if there were no obstacle) and relative invisibility (two different obstacles have the same scattering matrix). To study these problems, we use a continuation method which requires to compute the scattering matrix \u0000<tex>$mathbb{S}(rho)$</tex>\u0000 as well as its differential with respect to the material index \u0000<tex>$dmathbb{S}(rho)$</tex>\u0000. The justification of the method also needs for the proof of abstract results of surjectivity of well-chosen functionals constructed from the terms of \u0000<tex>$dmathbb{S}(rho)$</tex>\u0000. We provide a complete proof of the results in monomode regime when the wavenumber is such that only one mode can propagate. And we give all the ingredients to implement the method in multimode regime. We end the article by presenting numerical results to illustrate the analysis.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"74 1","pages":"83-116"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbaa020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49979206","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: 1

On the electrostatic potential for the two-hyperboloid and double-cone of a single sheet with elliptic cross-section 椭圆截面单片双双曲面和双锥的静电势

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-02-01 DOI: 10.1093/qjmam/hbaa021

Panayiotis Vafeas;Johan C -E Sten;Ioannis K Chatjigeorgiou

{"title":"On the electrostatic potential for the two-hyperboloid and double-cone of a single sheet with elliptic cross-section","authors":"Panayiotis Vafeas;Johan C -E Sten;Ioannis K Chatjigeorgiou","doi":"10.1093/qjmam/hbaa021","DOIUrl":"10.1093/qjmam/hbaa021","url":null,"abstract":"The study of the response of divergence-free electric fields near corners and edges, resembling singularities that accumulate charges, is significant in modern engineering technology. A sharp point can mathematically be modelled with respect to the tip of the one sheet of a double cone. Here, we investigate the behaviour of the generated harmonic potential function close to the apex of a single-sheeted two-hyperboloid with elliptic cross-section, whose asymptote is the corresponding elliptic double cone with one sheet present. Hence, the electrostatic potential problem, involving a single sheet of a two-hyperboloid, is developed using the theory of ellipsoidal-hyperboloidal harmonics, wherein the particular consideration enforces as solution in terms of generalised Lamé functions of non-integer order. A numerical method to determine these functions is outlined and tested. We demonstrate our technique to the solution of a classical boundary value problem in electrostatics, referring to a metallic and charged single-sheeted elliptic two-hyperboloid and its double-cone limit. Semi-analytical expressions for the related fields are derived, all cases being accompanied by the necessary numerical implementation.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"74 1","pages":"117-135"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbaa021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46689786","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: 2