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Dambreak reflection Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210908
Hogg A, Skevington E.SummaryThe unsteady reflection of dambreak flow along a horizontal channel by a remote barrier is modelled using the nonlinear shallow water equations. The interaction generates an upstream moving bore that connects the collapsing reservoir of fluid to a rapidly deepening fluid layer adjacent to the barrier. These motions are modified when the fluid is released into a channel containing a prewetted

Green’s functions for an anisotropic elastic parabolic inhomogeneity under generalised plane strain deformations Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210904
X Wang, P SchiavoneOn the basis of the Stroh sextic formalism, we propose a novel method to derive Green’s functions for a twophase composite composed of an anisotropic elastic parabolic inhomogeneity perfectly bonded to an anisotropic elastic matrix. The composite is subjected to a line force and a line dislocation, which can be located anywhere inside or outside the inhomogeneity or on the parabolic interface itself

Dynamic Green’s functions in discrete flexural systems Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210901
K H Madine, D J ColquittThe 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

Steady axisymmetric vortices in radial stagnation flows Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210818
Prabakaran Rajamanickam, Adam D WeissA class of axisymmetric vortex solutions superposed upon radial stagnation flows is described. The new vortex solutions generalize the classical Burgers’ vortex and Sullivan’s vortex solutions in the presence of a volumetric line source at the symmetry axis, the former approaching the Burgers’ vortex sheet when the source strength becomes very large. The stability of the generalized Burgers’ vortex

Integral and integrodifferential equations with an exponential kernel and applications Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210804
Y A Antipov, S M MkhitaryanA convolution integral equation of the first kind and integrodifferential equation of the second kind with the kernel $e^{\gamma y\eta}$ on a finite and semiinfinite 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 closedform representation for the solution is derived

Finding the strongest stable massless column with a follower load and relocatable concentrated masses Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210505
Oleg N Kirillov, Michael L OvertonWe consider the problem of optimal placement of concentrated masses along a massless elastic column that is clamped at one end and loaded by a nonconservative follower force at the free end. The goal is to find the largest possible interval such that the variation in the loading parameter within this interval preserves stability of the structure. The stability constraint is nonconvex and nonsmooth

Vertex Green’s Functions of a QuarterPlane: Links Between the Functional Equation, Additive Crossing and Lamé Functions Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210515
R C Assier, A V ShaninIn our previous work (R. C. Assier and A. V. Shanin, Q. J. Mech. Appl. Math., 72, 2019), we gave a new spectral formulation in two complex variables associated with the problem of planewave diffraction by a quarterplane. In particular, we showed that the unknown spectral function satisfies a condition of additive crossing about its branch set. In this article, we study a very similar class of spectral

On the electrostatic potential for the twohyperboloid and doublecone of a single sheet with elliptic crosssection Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210226
Vafeas P, Sten J, Chatjigeorgiou I.SummaryThe study of the response of divergencefree 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 singlesheeted

On the spectral asymptotics of waves in periodic media with Dirichlet or Neumann exclusions Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210315
Othman OudghiriIdrissi, Bojan B Guzina, Shixu MengWe consider homogenization of the scalar wave equation in periodic media at finite wavenumbers and frequencies, with the focus on continua characterized by: (a) arbitrary Bravais lattice in $\mathbb{R}^d$, $d \geqslant 2$, and (b) exclusions, that is, ‘voids’ that are subject to homogeneous (Neumann or Dirichlet) boundary conditions. Making use of the Blochwave expansion, we pursue this goal

A continuation method for building invisible obstacles in waveguides Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210226
Antoine Bera, AnneSophie BonnetBen Dhia, Lucas ChesnelWe 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 $\rho$ 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

Adaptive modelling of variably saturated seepage problems Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210222
Ashby B, Bortolozo C, Lukyanov A, et al.SummaryIn this article, we present a goaloriented 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 subsurfaceatmosphere boundaries. This leads to the formulation of the problem as a variational inequality

Trapped modes in a multilayer fluid Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210202
Cal F, Dias G, Pereira B, et al.SummaryIn this article, we study the existence of solutions for the problem of interaction of linear water waves with an array of threedimensional fixed structures in a densitystratified multilayer fluid, where in each layer the density is assumed to be constant. Considering timeharmonic smallamplitude motion, we present recursive formulae for the coefficients of the eigenfunctions of the spectral

On The Vibrations of Pyramidal Beams With Rectangular CrossSection and Application to Unswept Wings Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210202
Campos L, Marta A.SummaryThe 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 trailingedges, the chord is a linear function of the span; the same linear function of the span applies to thickness, in the case of constant thicknesstochord ratio. The latter is usually small, so that the beam differs

A TwoScale Analysis for a Spherical Pendulum with a Vertically Vibrating Pivot Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210301
R E GrundyIn this article, we consider the behaviour of a simple undamped spherical pendulum subject to highfrequency small amplitude vertical oscillations of its pivot. We use the method of multiple scales to derive an autonomous ordinary differential equation describing the slow time behaviour of the polar angle which generalises the Kapitza equation for the plane problem. We analyse the phase plane structure

Piezoelectric Machines: Achieving NonStandard Actuation and Sensing Properties in Poled Ceramics Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210301
Giuseppe Saccomandi, Emanuela Speranzini, Giuseppe ZurloIn the framework of linear piezoelectric ceramics, we study the deformations of a circular infinite hollow cylinder, subjected to a potential difference between the inner and outer surfaces. When the poling direction is perfectly aligned with the cylinder axis, the solution to this problem is a trivial axisymmetric antiplane state. However, when the poling direction has an offset angle with respect

Image Force on a Screw Dislocation Inside an Elastic or a Piezoelectric Inhomogeneity of Arbitrary Shape Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210202
Wang X, Yang P, Schiavone P.SummaryA novel and effective method is proposed to determine the image force acting on a screw dislocation located inside an elastic inhomogeneity of arbitrary shape perfectly bonded to an infinite elastic matrix. The basis for our representation of the image force stems from the fact that the analytic function defined inside the elastic inhomogeneity can be conveniently constructed from the continuity

Use of a Modal Model in Predicting Propagation from a Point Source Over Grooved Ground Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210202
Mellish S, Taherzadeh S, Attenborough K.SummaryRegularly spaced low walls and rectangular lattices on a hard ground have been investigated as a means for reducing noise levels from surface transport. Predictions of the insertion loss of such surfaces has involved the use of computationally intensive numerical methods such as the Boundary Element Method (BEM) or Finite difference techniques (FDTD and PSTD). By considering pointtopoint propagation

Equilibrium of Two Rods in Contact Under Pressure Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210104
Turzi S, Zoppello M, Ambrosi D.SummaryWe study the equilibrium of a mechanical system composed by two rods that bend under the action of a pressure difference; they have one fixed endpoint and are partially in contact. This system can be viewed as a bivalve made by two smooth leaflets that lean on each other. We obtain the balance equations of the mechanical system exploiting the principle of virtual work and the contact point

TwoDimensional Waves in A Chiral Elastic Chain: Dynamic Green's Matrices and Localised Defect Modes Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20210104
Jones I, Movchan N, Movchan A.SummaryThis article presents new analytical work on the analysis of waves in chiral elastic chains. The notion of dynamic chirality, well established and explored for electromagnetic waves in magnetised media, is less common for elastic solids. Indeed, it is even less common to observe vector wave problems in an elastic chain. Here, it is shown that the physical system, described by a vector formulation

The Legendre–Hadamard condition in Cosserat elasticity theory Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20201022
Shirani M, Steigmann D, Neff P.SummaryThe Legendre–Hadamard necessary condition for energy minimizers is derived in the framework of Cosserat elasticity theory.

Calculation of a key function in the asymptotic description of moving contact lines Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20201010
Scott J.SummaryAn important element of the asymptotic description of flows having a moving liquid/gas interface which intersects a solid boundary is a function denoted $Q_i \left( \alpha \right)$ by Hocking and Rivers (The spreading of a drop by capillary action, J. Fluid Mech. 121 (1982) 425–442), where $0 < \alpha < \pi$ is the contact angle of the interface with the wall. $Q_i \left( \alpha \right)$ arises

Radiation of waves by a thin cap submerged in icecovered ocean Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200919
Das A, De S, Mandal B.SummaryThe present article is concerned with the radiation of flexural gravity waves due to a thin cap submerged in the icecovered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The firstorder approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping

Four solutions of a twocylinder electrostatic problem, and identities resulting from their equivalence Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200804
Lekner J.SummaryFour distinct solutions exist for the potential distribution around two equal circular parallel conducting cylinders, charged to the same potential. Their equivalence is demonstrated, and the resulting analytical identities are discussed. The identities relate the Jacobi elliptic function $sn$, the Jacobi theta functions $\theta _1 ,~\theta _2 $ and infinite series over trigonometric and hyperbolic

Capillarygravity waves on the interface of two dielectric fluid layers under normal electric fields Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200605
A Doak, T Gao, J M VandenBroeck, J J S KandolaIn this article, we consider capillarygravity waves propagating on the interface of two dielectric fluids under the influence of normal electric fields. The density of the upper fluid is assumed to be much smaller than the lower one. Linear and weakly nonlinear theories are studied. The connection to the results in other limit configurations is discussed. Fully nonlinear computations for travelling

A Singular Nonlinear HistoryDependent Cohesive Zone Model: Is it Possible? Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200520
I I ArgatovA historydependent cohesive zone model is considered in the linear elasticity framework with the cohesive stresses governed by the fracture condition formulated in terms of a nonlinear Abeltype integral operator. A possibility for the cohesive stresses to possess a weak singularity has been examined by utilizing asymptotic modeling approach. It has been shown that the balance of the leadingterm

Regularity of Desingularized Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200520
Siran LiWe establish the regularity of weak solutions for the vorticity equation associated to a family of desingularized models for vortex filament dynamics in 3D incompressible viscous flows. These generalize the classical model ‘of an allowance for the thickness of the vortices’ due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities

Some Universal Solutions for a Class of Incompressible Elastic Body that is Not Green Elastic: The Case of Large Elastic Deformations Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200404
R BustamanteSome universal solutions are studied for a new class of elastic bodies, wherein the Hencky strain tensor is assumed to be a function of the Kirchhoff stress tensor, considering in particular the case of assuming the bodies to be isotropic and incompressible. It is shown that the families of universal solutions found in the classical theory of nonlinear elasticity, are also universal solutions for this

‘Killing Mie Softly’: Analytic Integrals for Complex Resonant States Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200320
R C Mcphedran, B StoutWe consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. These integrals arise in wave and quantum mechanical scattering problems of open systems containing cylindrical or spherical scatterers, particularly when those problems are considered in the framework of complex resonant modes. Explicit representations

Image Conditions for EllipticalCoordinate SeparationofVariables Acoustic Multiple Scattering Models with Perfectly Reflecting Flat Boundaries: Application to in Situ Tunable Noise Barriers Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200302
HoChul ShinTwodimensional timeharmonic multiple scattering problems are addressed for a finite number of elliptical objects placed in wedgeshaped acoustic domains including halfplane and rightangled corners. The method of separation of variables in conjunction with the addition theorems is employed in the elliptical coordinates. The wavefunctions are represented in terms of radial and angular Mathieu functions

Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200220
Xu Wang, Peter SchiavoneWe use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities $r^{3/4\pm i\varepsilon }$ and $r^{1/4\pm i\varepsilon }$ (where $\varepsilon $ is the oscillatory index)

Converging shock waves in a Van der Waals gas of variable density Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200215
Antim Chauhan, Rajan Arora, Amit TomarThe converging problem of cylindrically or spherically symmetric strong shock wave collapsing at the axis/centre of symmetry, is studied in a nonideal inhomogeneous gaseous medium. Here, we assume that the undisturbed medium is spatially variable and the density of a gas is decreasing towards the axis/centre according to a power law. In the present work, we have used the perturbation technique to

Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200210
E R Belden, Z A Dickman, S J Weinstein, A D Archibee, E Burroughs, N S BarlowWe demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closedform solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle $\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying $\beta\in[0.198837735, 1]$ are considered

On the Connection Between Step Approximations and DepthAveraged Models for Wave Scattering by Variable Bathymetry Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200203
R PorterTwo popular and computationally inexpensive class of methods for approximating the propagation of surface waves over twodimensional variable bathymetry are ‘step approximations’ and ‘depthaveraged models’. In the former, the bathymetry is discretised into short sections of constant depth connected by vertical steps. Scattering across the bathymetry is calculated from the product of $2 \times 2$

Hypersingular Integral Equations Arising in the Boundary Value Problems of the Elasticity Theory Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20200124
S M Mkhitaryan, M S Mkrtchyan, E G KanetsyanThe exact solutions of a class of hypersingular integral equations with kernels $\left( {sx} \right)^{2}$, $\left( {\sin \frac{sx}{2}} \right)^{2}$, $\left( {\sinh \frac{sx}{2}} \right)^{2},\cos \frac{sx}{2}\left( {\sin \frac{sx}{2}} \right)^{2}$, $\cosh \frac{sx}{2}\left( {\sinh \frac{sx}{2}} \right)^{2}$ are obtained where the integrals must be interpreted as Hadamard finitepart

Periodic Auxetics: Structure and Design. Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20180626
Ciprian S Borcea,Ileana StreinuMaterials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson's ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established

A Note on Viscous Flow Induced by HalfLine Sources Bounded by Conical Surfaces Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20191021
Prabakaran Rajamanickam, Adam D WeissIn this article, axisymmetric solutions of the Navier–Stokes equations governing the flow induced by a halfline source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in which the radial velocity along the axis is prescribed, and the other in which the radial velocity along the axis is obtained as an eigenvalue of the problem.

Time to Approach Similarity Q. J. Mech. Appl. Math. (IF 1.0) Pub Date : 20191011
Joseph J Webber, Herbert E HuppertIn a recent article, Ball and Huppert (J. Fluid Mech., 874, 2019) introduced a novel method for ascertaining the characteristic timescale over which the similarity solution to a given timedependent nonlinear differential equation converges to the actual solution, obtained by numerical integration, starting from given initial conditions. In this article, we apply this method to a range of different