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Linear stability of a compressible flow in a channel Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-12-20 M Deka, G Tomar, V Kumaran
Summary Modal instabilities in a compressible flow through a channel at high Reynolds numbers are studied for three-dimensional (3D) perturbations. In addition to the Tollmien–Schlichting (TS) mode, there exist compressible modes in a channel flow that do not have a counterpart in the incompressible limit. The stability characteristics of these compressible modes, obtained through numerical calculations
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The behaviour of a forced spherical pendulum operating in a weightless environment Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-11-30 R E Grundy
Summary In this article, we show that by subjecting the pivot of a simple inextensible pendulum to small amplitude high frequency rectilinear oscillations it is possible to make it operate in a weightless environment. The axis of vibration of the pivot defines a preferred direction in space and a consequential dynamical structure which is completely absent when the pivot is fixed. Using spherical polar
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Theory of Perturbation of Electrostatic Field By A Coated Anisotropic Dielectric Sphere Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-09-10 Nikolaos L Tsitsas, Hamad M Alkhoori, Akhlesh Lakhtakia
Summary A boundary-value problem was formulated for perturbation of an electrostatic field by a coated dielectric sphere made of two distinct linear anisotropic dielectric (LAD) materials. Specific affine transformations were employed to represent the electric potential inside the core and the coating in terms of the solutions of the Laplace equation. A transition matrix was found to relate the source
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Homogenisation of Nonlinear Heterogeneous Thin Plate When the Plate Thickness and In-Plane Heterogeneities are of the Same Order of Magnitude Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-07-26 E Pruchnicki
Summary In this work, we propose a new two-scale finite-strain thin plate theory for highly heterogeneous plates described by a repetitive periodic microstructure. For this type of theory, two scales exist, the macroscopic one is linked to the entire plate and the microscopic one is linked to the size of the heterogeneity. We consider the case when the plate thickness is comparable to in-plane heterogeneities
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Scattering by a Perforated Sandwich Panel: Method of Riemann Surfaces Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-06-22 Y A Antipov
Summary The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is exactly solved. The model is governed by two Helmholtz equations for the velocity potentials in the upper and lower half-planes coupled by the Leppington effective
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Analytical solutions for Bloch waves in resonant phononic crystals: deep-subwavelength energy splitting and mode steering between topologically protected interfacial and edge states Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-04-07 R Wiltshaw, J M De Ponti, R V Craster
Summary We derive analytical solutions based on singular Green’s functions, which enable efficient computations of scattering simulations or Floquet–Bloch dispersion relations for waves propagating through an elastic plate, whose surface is patterned by periodic arrays of elastic beams. Our methodology is versatile and allows us to solve a range of problems regarding arrangements of multiple beams
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On the Smallest Number of Functions Representing Isotropic Functions of Scalars, Vectors and Tensors Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-01-12 M H B M Shariff
Summary In this article, we prove that for isotropic functions that depend on $P$ vectors, $N$ symmetric tensors and $M$ non-symmetric tensors (a) the minimal number of irreducible invariants for a scalar-valued isotropic function is $3P+9M+6N-3,$ (b) the minimal number of irreducible vectors for a vector-valued isotropic function is $3$ and (c) the minimal number of irreducible tensors for a tensor-valued
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A New Solution for the Deformations of an Initially Elliptical Elastic-Walled Tube Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-01-09 D J Netherwood, R J Whittaker
Summary We investigate the small-amplitude deformations of a long thin-walled elastic tube having an initially axially uniform elliptical cross-section. The tube is deformed by a (possibly non-uniform) transmural pressure. At leading order, its deformations are shown to be governed by a single partial differential equation (PDE) for the azimuthal displacement as a function of the axial and azimuthal
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Solitary Waves on Flows with an Exponentially Sheared Current and Stagnation Points Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2023-01-09 Marcelo V Flamarion, Roberto-J R Ribeiro
Summary While several articles have been written on water waves on flows with constant vorticity, little is known about the extent to which a non-constant vorticity affects the flow structure, such as the appearance of stagnation points. In order to shed light on this topic, we investigate in detail the flow beneath solitary waves propagating on an exponentially decaying sheared current. Our focus
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Large Amplitude Non-Spherical Bubbles Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-12-12 Madeleine C Cockerill, Lawrence K Forbes, Andrew P Bassom
Summary We consider the long-term evolution of an axisymmetric bubble and explore the ways in which it may develop. Linearised inviscid analysis is used to predict the stability of the bubble with a small disturbance while a nonlinear inviscid extension shows that the growth of unstable modes is ultimately limited by the formation of axisymmetric curvature singularities. The addition of surface tension
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Superhydrophobicity Can Enhance Convective Heat Transfer in Pressure-Driven Pipe Flow Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-11-17 Henry Rodriguez-Broadbent, Darren G Crowdy
Summary Theoretical evidence is given that it is possible for superhydrophobicity to enhance steady laminar convective heat transfer in pressure-driven flow along a circular pipe or tube with constant heat flux. Superhydrophobicity here refers to the presence of adiabatic no-shear zones in an otherwise solid no-slip boundary. Adding such adiabatic no-shear zones reduces not only hydrodynamic friction
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On The Power Series Solution to The Nonlinear Pendulum Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-09-10 W C Reinberger, M S Holland, N S Barlow, S J Weinstein
Summary The exact solution to the simple pendulum problem has long been known in terms of Jacobi elliptic functions, of which an efficient numerical evaluation is standard in most scientific computing software packages. Alternatively, and as done in V. Fairén, López and L. Conde (Power series approximation to solutions of nonlinear systems of differential equation, Am. J. Phys. 56 (1988) 57–61], the
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Exact Solution to Axisymmetric Interface Crack Problem in Magneto-Piezo-Electric Transversely Isotropic Materials Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-08-24 V I Fabrikant
Summary This seems to be the first exact closed-form solution to the problem of a penny-shaped interface crack, subjected to an axisymmetric normal and tangential loading. The crack is located at the boundary between two bonded magneto-piezo-electric transversely isotropic half-spaces, made of different materials. We use the combination of Green’s functions for two different half-spaces and Fourier
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Meso-scale method of asymptotic analysis of elastic vibrations in periodic and non-periodic multi-structures Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-08-24 M J Nieves, A B Movchan
Summary The method of meso-scale asymptotic approximations has proved to be very effective for the analysis of models of solids containing large clusters of defects, such as small inclusions or voids. Here, we present a new avenue where the method is extended to elastic multi-structures. Geometrically, a multi-structure makes a step up in the context of overall dimensions, compared to the dimensions
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Steady Normal-Mode Vortices in Circular Cavities Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-08-08 Peder A Tyvand
Summary This article establishes elementary families of steady two-dimensional (2D) vortices in circular enclosures filled with inviscid fluid. A normal-mode vortex is a continuous vortex that satisfies a Helmholtz equation for the streamfunction. An individual normal-mode vortex satisfies the steady 2D vorticity equation. A way to satisfy the vorticity equation with two superposed normal-mode vortices
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On a Qualitative and Lie Symmetry Analysis for a Pendulum with Two Reaction Wheels Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-08-04 A Ruiz, C H C C Basquerotto, J F S Trentin, S Da Silva
Summary In this article, it is studied the mechanical system formed by a pendulum with two reaction wheels in which the friction torque is assumed to follow a Coulomb law. A qualitative analysis of the system is performed for the damped case. Specifically, the equilibrium points for the unforced pendulum are analyzed. Also, in the forced case, the conditions for which there exist asymptotically stable
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Large-time asymptotics to solutions of a generalized Burgers equation with linear damping on half-line Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-07-30 P Samanta, Ch. Srinivasa Rao
Summary In this article, we investigate an initial-boundary value problem posed for generalized Burgers equation (GBE) with linear damping via the method of matched asymptotic expansions. Asymptotic solutions are constructed for different sub-regions of the domain $x > 0,~ t > 0$. A special solution is derived, and it describes the large-time asymptotic behavior of the solutions of the GBE for certain
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Global bifurcation of capillary-gravity dark solitary waves on the surface of a conducting fluid under normal electric fields Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-06-03 A Doak, T Gao, J -M Vanden-Broeck
Summary This article is concerned with capillary-gravity waves travelling on the interface of a dielectric gas and a conducting fluid under the effect of a vertical electric field. A boundary integral equation method is employed to compute fully nonlinear steady travelling wave solutions. The global bifurcation diagram of periodic waves, solitary waves, generalised solitary waves and dark solitary
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CORRECTION to: Theory of perturbation of electrostatic field by an anisotropic dielectric sphere Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-02-26 Lakhtakia A, Tsitsas N, Alkhoori H.
The Quarterly Journal of Mechanics and Applied Mathematics, 74 (2021) 467—490, https://doi.org/10.1093/qjmam/hbab013
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Carreau law for non-newtonian fluid flow through a thin porous media Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-02-01 María Anguiano,Matthieu Bonnivard,Francisco J Suárez-Grau
Summary We consider the flow of generalized Newtonian fluid through a thin porous media. The media under consideration is a bounded perforated three dimensional domain confined between two parallel plates, where the distance between the plates is described by a small parameter $\varepsilon$. The perforation consists in an array of solid cylinders, which connect the plates in perpendicular direction
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Chiral waves in structured elastic systems: dynamics of a meta-waveguide Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-02-01 I S Jones,N V Movchan,A B Movchan
Summary The notion of meta-surfaces is well established for waves interacting with arrays of periodic resonators. Here, an infinite elastic rod, attached to a system of gyroscopic spinners, is considered. This forms a waveguide with unusual dispersion properties and will be referred to as a chiral meta-waveguide. A class of transient and time-harmonic formulations describing waves in elastic chiral
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On the parameterisation of a class of doubly periodic lattices of equally strong holes Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-02-01 J S Marshall
Summary We construct an exact, explicit parameterisation of a class of doubly periodic lattices of equally strong holes in an infinite elastic plate that is in a state of plane stress. This parameterisation assumes no symmetries of the lattices’ holes and allows for any finite number of holes per period cell. It is stated in terms of a conformal map from a circular domain. We construct this map in
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Investigation of buckling of rectilinear beams with additional constraint at an arbitrary internal point Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2022-02-01 E I Ryzhak
Summary The problems of stability and instability (buckling) of compressed rectilinear beams are considered. The beams are treated as one-dimensional elastic bodies possessing stiffnesses of two kinds: the stiffness with respect to extension–compression and the stiffness with respect to bending. The ends of beams are hinged, but along with traditional setting of a problem, characterized by one movable
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The Life Cycle Effects of Corporate Takeover Defenses Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-10-15 William C Johnson, Jonathan M Karpoff, Sangho Yi
We document that the relation between firm value and the use of takeover defenses is positive for young firms but becomes negative as firms age. This value reversal pattern reflects specific changes in the costs and benefits of takeover defenses as firms age and arises because defenses are sticky and rarely removed. Firms can attenuate the value reversal by removing defenses, but do so only when the
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Coupling Stokes Flow with Inhomogeneous Poroelasticity Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-10-11 Matteo Taffetani, Ricardo Ruiz-Baier, Sarah Waters
Summary We investigate the behaviour of flux-driven flow through a single-phase fluid domain coupled to a biphasic poroelastic domain. The fluid domain consists of an incompressible Newtonian viscous fluid while the poroelastic domain consists of a linearly elastic solid filled with the same viscous fluid. The material properties of the poroelastic domain, that is permeability and elastic parameters
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On wave generation by a submerged oscillating source over Roseau’s beach profile with outline application to a scattering problem Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-09-08 Ulf Ehrenmark
Summary The exact solution for linearised water wave motion over a specific curved bottom beach profile, developed by Roseau in his book Asymptotic Wave Theory (North-Holland 1976) is here generalised to account also for the insertion of a submerged oscillating line source randomly placed above the beach. An explicit expression is obtained for the associated velocity potential in various scenarios
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Theory of Perturbation of Electrostatic Field by an Anisotropic Dielectric Sphere Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-09-08 Akhlesh Lakhtakia, Nikolaos L Tsitsas, Hamad M Alkhoori
Summary The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and tesseral harmonics, as is standard for the Laplace equation. A bijective transformation of space was carried out to formulate a series representation of the
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Hypersingular Integral Equation Formulation of the Problem of Water Wave Scattering by A Circular Arc Shaped Impermeable Barrier Submerged in Water of Finite Depth Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-08-20 Dibakar Mondal, Anushree Samanta, Sudeshna Banerjea
Summary In this article, we study the problem of scattering of water waves by a thin impermeable circular arc shaped barrier submerged in ocean of finite depth under the assumption of linearised theory of water waves. The problem is formulated in terms of a hypersingular integral equation of an unknown function representing the difference of potential function across the curved barrier. The hypersingular
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Dam-break reflection Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-08-11 Andrew J Hogg, Edward W G Skevington
Summary The unsteady reflection of dam-break 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 pre-wetted
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Steady axisymmetric vortices in radial stagnation flows Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-07-23 Prabakaran Rajamanickam, Adam D Weiss
Summary A 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’
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Green’s functions for an anisotropic elastic parabolic inhomogeneity under generalised plane strain deformations Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-07-20 X Wang, P Schiavone
Summary On the basis of the Stroh sextic formalism, we propose a novel method to derive Green’s functions for a two-phase 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
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Integral and integro-differential equations with an exponential kernel and applications Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-06-30 Y A Antipov, S M Mkhitaryan
Summary A convolution integral equation of the first kind and integro-differential equation of the second kind with the kernel $e^{-\gamma |y-\eta|}$ 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
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Dynamic Green’s functions in discrete flexural systems Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-03-18 K H Madine, D J Colquitt
Summary 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
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On the electrostatic potential for the two-hyperboloid and double-cone of a single sheet with elliptic cross-section Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-02-26 Vafeas P, Sten J, Chatjigeorgiou I.
SummaryThe 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
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Finding the strongest stable massless column with a follower load and relocatable concentrated masses Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-03-15 Oleg N Kirillov, Michael L Overton
Summary We 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
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Vertex Green’s Functions of a Quarter-Plane: Links Between the Functional Equation, Additive Crossing and Lamé Functions Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-03-05 R C Assier, A V Shanin
Summary In 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 plane-wave diffraction by a quarter-plane. 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
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A continuation method for building invisible obstacles in waveguides Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-02-26 Antoine Bera, Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel
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 |$\rho$| 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
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Trapped modes in a multi-layer fluid Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-02-02 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 three-dimensional fixed structures in a density-stratified multi-layer fluid, where in each layer the density is assumed to be constant. Considering time-harmonic small-amplitude motion, we present recursive formulae for the coefficients of the eigenfunctions of the spectral
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On The Vibrations of Pyramidal Beams With Rectangular Cross-Section and Application to Unswept Wings Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-02-02 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 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
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A Two-Scale Analysis for a Spherical Pendulum with a Vertically Vibrating Pivot Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-03-01 R E Grundy
In this article, we consider the behaviour of a simple undamped spherical pendulum subject to high-frequency 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
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Image Force on a Screw Dislocation Inside an Elastic or a Piezoelectric Inhomogeneity of Arbitrary Shape Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-02-02 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
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Use of a Modal Model in Predicting Propagation from a Point Source Over Grooved Ground Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-02-02 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 point-to-point propagation
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Equilibrium of Two Rods in Contact Under Pressure Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-01-04 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 bi-valve 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
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Two-Dimensional Waves in A Chiral Elastic Chain: Dynamic Green's Matrices and Localised Defect Modes Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-01-04 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
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On the spectral asymptotics of waves in periodic media with Dirichlet or Neumann exclusions Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-01-19 Othman Oudghiri-Idrissi, Bojan B Guzina, Shixu Meng
Summary We 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 Bloch-wave expansion, we pursue this goal
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Piezoelectric Machines: Achieving Non-Standard Actuation and Sensing Properties in Poled Ceramics Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-01-17 Giuseppe Saccomandi, Emanuela Speranzini, Giuseppe Zurlo
Summary In 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 anti-plane state. However, when the poling direction has an offset angle with
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Adaptive modelling of variably saturated seepage problems Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2021-01-14 B Ashby, C Bortolozo, A Lukyanov, T Pryer
Summary 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
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The Legendre–Hadamard condition in Cosserat elasticity theory Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-10-22 Shirani M, Steigmann D, Neff P.
SummaryThe Legendre–Hadamard necessary condition for energy minimizers is derived in the framework of Cosserat elasticity theory.
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Calculation of a key function in the asymptotic description of moving contact lines Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-10-10 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
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Radiation of waves by a thin cap submerged in ice-covered ocean Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-09-19 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 ice-covered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The first-order approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping
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Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-08-04 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
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Capillary-gravity waves on the interface of two dielectric fluid layers under normal electric fields Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-06-05 A Doak, T Gao, J -M Vanden-Broeck, J J S Kandola
In this article, we consider capillary-gravity 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
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A Singular Nonlinear History-Dependent Cohesive Zone Model: Is it Possible? Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-05-20 I I Argatov
A history-dependent 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 Abel-type 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 leading-term
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Regularity of Desingularized Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-05-20 Siran Li
We 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
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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 0.9) Pub Date : 2020-04-04 R Bustamante
Some 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
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‘Killing Mie Softly’: Analytic Integrals for Complex Resonant States Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-03-20 R C Mcphedran, B Stout
We 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
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Image Conditions for Elliptical-Coordinate Separation-of-Variables Acoustic Multiple Scattering Models with Perfectly Reflecting Flat Boundaries: Application to in Situ Tunable Noise Barriers Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-03-02 Ho-Chul Shin
Two-dimensional time-harmonic multiple scattering problems are addressed for a finite number of elliptical objects placed in wedge-shaped acoustic domains including half-plane and right-angled 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
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Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-02-20 Xu Wang, Peter Schiavone
We 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 $| is the oscillatory index)
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Converging shock waves in a Van der Waals gas of variable density Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-02-15 Antim Chauhan, Rajan Arora, Amit Tomar
The converging problem of cylindrically or spherically symmetric strong shock wave collapsing at the axis/centre of symmetry, is studied in a non-ideal inhomogeneous gaseous medium. Here, we assume that the undisturbed medium is spatially variable and the density of a gas is decreasing towards the axis/centre according to a power law. In the present work, we have used the perturbation technique to
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Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation Q. J. Mech. Appl. Math. (IF 0.9) Pub Date : 2020-02-10 E R Belden, Z A Dickman, S J Weinstein, A D Archibee, E Burroughs, N S Barlow
We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle |$\beta\pi/2$| to the horizontal. A wide range of wedge angles satisfying |$\beta\in[-0.198837735, 1]$| are considered