The quarterly journal of mechanics and applied mathematics最新文献

The steady-state response of a three-phase elliptical inhomogeneity with interface slip and diffusion under an edge dislocation in the matrix 具有界面滑移和扩散的三相椭圆不均匀性在基体边缘位错作用下的稳态响应

The quarterly journal of mechanics and applied mathematics Pub Date : 2024-09-14 DOI: 10.1093/qjmam/hbae010

Xu Wang, Peter Schiavone

{"title":"The steady-state response of a three-phase elliptical inhomogeneity with interface slip and diffusion under an edge dislocation in the matrix","authors":"Xu Wang, Peter Schiavone","doi":"10.1093/qjmam/hbae010","DOIUrl":"https://doi.org/10.1093/qjmam/hbae010","url":null,"abstract":"We study the steady-state response of a three-phase elliptical inhomogeneity in which the internal elliptical elastic inhomogeneity is bonded to the surrounding infinite matrix through an interphase layer with two confocal elliptical interfaces permitting simultaneous interface slip and diffusion. The matrix is subjected to an edge dislocation at an arbitrary position and uniform remote in-plane stresses. An analytical solution to the steady-state problem is derived using Muskhelishvili’s complex variable formulation. The effect of the edge dislocation and remote loading on the elastic fields in the inhomogeneity and the interphase layer is exhibited through a single loading parameter. More specifically, when divided by this loading parameter, the expressions for the stresses and strains in the inhomogeneity and the interphase layer are uninfluenced by the specific loading applied in the matrix. After excluding a particular common factor, the stresses and strains in the inhomogeneity and the interphase layer are also unaffected by the mismatch in shear moduli between the interphase layer and the matrix.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269272","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: 0

Second-order water wave properties over Roseau’s three-parameter bottom topography 罗索三参数海底地形的二阶水波特性

The quarterly journal of mechanics and applied mathematics Pub Date : 2024-05-28 DOI: 10.1093/qjmam/hbae004

Ulf Ehrenmark

{"title":"Second-order water wave properties over Roseau’s three-parameter bottom topography","authors":"Ulf Ehrenmark","doi":"10.1093/qjmam/hbae004","DOIUrl":"https://doi.org/10.1093/qjmam/hbae004","url":null,"abstract":"Summary In his book Asymptotic Wave Theory (North-Holland 1976), Roseau develops the only known exact solution for linear wave propagation over a shoal. Remarkably, almost half a century later, the only properties of that solution which appear to have been used to validate more wide-ranging models are the limiting values of wave height in the far field. The primary aim of this work is to remedy this situation by providing a robust computational setting where the solution may be fully evaluated randomly both on the surface and the interior, speedily and to a high degree of accuracy. Such ‘benchmark’ solutions will facilitate a much more rigorous approach to validation of more general alternative approximation models. One such has some of its numerical results here examined and subsequently largely vindicated by the present calculations. Computation of the absolutely convergent solution integrals is supported by cubic spline approximation of an integrand component which satisfies a certain difference equation and the work is extended to cover bottom profiles with overhang including the extreme case where the overhang degenerates to a semi-infinite flat plate. The further development of solutions at second-order reveals details of mean Eulerian current and the attendant Stokes drift enabling mass transport computations; all illustrated through the entire depth with a range of contouring and arrows plots. The force field that drives a second harmonic component is calculated and shows excellent agreement with its equivalent in the more general modal expansion model applied to a non-identical but somewhat similar profile. This further validates the modelling approach and application described in that work.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171689","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: 0

A numerical investigation on the vibration of a two-deck Euler–Bernoulli beam flooded by a potential flow 势流淹没双层欧拉-伯努利梁的振动数值研究

The quarterly journal of mechanics and applied mathematics Pub Date : 2024-05-28 DOI: 10.1093/qjmam/hbae006

Zihua Liu, Tao Gao, Choi-Hong Lai, Wenxing Guo

{"title":"A numerical investigation on the vibration of a two-deck Euler–Bernoulli beam flooded by a potential flow","authors":"Zihua Liu, Tao Gao, Choi-Hong Lai, Wenxing Guo","doi":"10.1093/qjmam/hbae006","DOIUrl":"https://doi.org/10.1093/qjmam/hbae006","url":null,"abstract":"This work concerns the structural vibration of a bladeless wind turbine, modelled by a two-deck Euler–Bernoulli beam, due to a surrounding potential flow. The deflection is governed by the Euler–Bernoulli equation which is studied first by a linear theory and then computed numerically by a finite difference method in space with a collocation method over the arc length, and an implicit Euler method in time. The fluid motion in the presence of gravity is governed by the full Euler equations and solved by the time-dependent conformal mapping technique together with a pseudo-spectral method. Numerical experiments of excitation by a moving disturbance on the fluid surface with/without a stochastic noise are carried out. The random process involved in generating the noise on the water surface is driven by a Wiener Process. A Monte Carlo method is used for stochastic computations. The generated surface waves impinge on the beam causing structural vibration which is presented and discussed in detail. By elementary statistical analysis, the structural response subject to the stochastic hydrodynamic disturbance caused by white noise is found to be Gaussian.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"2016 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171688","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: 0

Linear stability of a compressible flow in a channel 通道中可压缩流的线性稳定性

The quarterly journal of mechanics and applied mathematics Pub Date : 2023-12-20 DOI: 10.1093/qjmam/hbad010

M Deka, G Tomar, V Kumaran

{"title":"Linear stability of a compressible flow in a channel","authors":"M Deka, G Tomar, V Kumaran","doi":"10.1093/qjmam/hbad010","DOIUrl":"https://doi.org/10.1093/qjmam/hbad010","url":null,"abstract":"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, are compared with boundary layer and Couette flows that have been previously studied. The dominant compressible instabilities in a channel flow are shown to be viscous in nature, in contrast to compressible boundary layer modes. For general compressible bounded-domain flows, a necessary condition for the existence of neutral modes in the inviscid limit is obtained, and this criterion is used to determine critical Mach numbers below which the compressible modes remain stable. This criterion also delineates a range of wave-angles which could go unstable at a specified Mach number. Asymptotic analysis is carried out for the lower and upper branches of the stability curve in the limit of high Reynolds number for both the T-S and the compressible modes. A common set of relations are identified for the scaling exponents, and the leading order eigenvalues for the unstable modes are obtained through an adjoint-based procedure. The asymptotic analysis shows that the stability boundaries for 3D perturbations at high Reynolds numbers can be calculated from the strain rate and the temperature of the base flow at the wall.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"486 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138824198","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: 0

The behaviour of a forced spherical pendulum operating in a weightless environment 在失重环境下工作的受迫球摆的行为

The quarterly journal of mechanics and applied mathematics Pub Date : 2023-11-30 DOI: 10.1093/qjmam/hbad008

R E Grundy

{"title":"The behaviour of a forced spherical pendulum operating in a weightless environment","authors":"R E Grundy","doi":"10.1093/qjmam/hbad008","DOIUrl":"https://doi.org/10.1093/qjmam/hbad008","url":null,"abstract":"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 coordinates centred at the pivot, we show that the motion of such a pendulum has fast and slow-scale components which we analyse using the method of multiple scales. The slow scale equation for the polar angle is autonomous, and a phase plane analysis reveals the essential orbital structure including the existence of conical solutions analogous to the terrestrial fixed pivot conical pendulum. In the absence of an azimuthal velocity component, its behaviour can provide a direct simulation of a plane terrestrial simple fixed pivot pendulum with a correspondingly simple form for the small amplitude period. We can also use a two-scale analysis to examine the effects of damping. Here, the slow scale polar equation has two asymptotically stable states, and we employ a combination of numerical and asymptotic analyses to elicit the slow scale orbital trajectories.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528022","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: 0

Large Amplitude Non-Spherical Bubbles 大振幅非球形气泡

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-12-12 DOI: 10.1093/qjmam/hbac019

Madeleine Cockerill, L. Forbes, A. Bassom

引用次数: 0

Superhydrophobicity Can Enhance Convective Heat Transfer in Pressure-Driven Pipe Flow 超疏水性可以增强压力驱动管道流动中的对流换热

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-11-17 DOI: 10.1093/qjmam/hbac016

Henry Rodriguez-Broadbent, Darren G Crowdy

引用次数: 0

On The Power Series Solution to The Nonlinear Pendulum 非线性摆的幂级数解

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-09-09 DOI: 10.1093/qjmam/hbac013

W. Reinberger, M. S. Holland, N. Barlow, S. J. Weinstein

{"title":"On The Power Series Solution to The Nonlinear Pendulum","authors":"W. Reinberger, M. S. Holland, N. Barlow, S. J. Weinstein","doi":"10.1093/qjmam/hbac013","DOIUrl":"https://doi.org/10.1093/qjmam/hbac013","url":null,"abstract":"\u0000 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 pendulum equation can be analytically solved exactly by the power series solution method. Although recursive formulae for the series coefficients were provided in V. Fairén et al., the series itself—as well as the optimal location about which an expansion should be chosen to maximize the domain of convergence—has not yet been examined, and this is provided here. By virtue of its representation as an elliptic function, the pendulum function has singularities that lie off of the real axis in the complex time plane. This, in turn, imposes a radius of convergence on the power series solution in real time. By choosing the expansion point at the top of the trajectory, the power series converges all the way to the bottom of the trajectory without being affected by these singularities. We provide an exact resummation of the pendulum series that accelerates the series’ convergence uniformly from the top to the bottom of the trajectory. We also provide the formulae needed to extend the pendulum series for all time via symmetry. The pendulum problem, in its relative simplicity, provides an explicit demonstration of the effect of singularity structure and initial condition location on convergence properties of power series solutions.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89154299","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

Exact Solution to Axisymmetric Interface Crack Problem in Magneto-Piezo-Electric Transversely Isotropic Materials 磁-压电横向各向同性材料轴对称界面裂纹问题的精确解

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-08-24 DOI: 10.1093/qjmam/hbac009

V I Fabrikant

{"title":"Exact Solution to Axisymmetric Interface Crack Problem in Magneto-Piezo-Electric Transversely Isotropic Materials","authors":"V I Fabrikant","doi":"10.1093/qjmam/hbac009","DOIUrl":"https://doi.org/10.1093/qjmam/hbac009","url":null,"abstract":"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 transform. We derive first the governing equations, which are valid for a crack of arbitrary shape. The usual approach leads to five hypersingular integral equations, we arrive at four integro-differential equations (one of them being complex). While the coefficients of the governing equations in existing publications are presented in terms of the results of the solution of a set of linear algebraic equations and are too cumbersome to be written explicitly in terms of the basic constants, our choice of the basic constants leads to quite elegant explicit expressions for these coefficients and reveals certain symmetry, which was noticed only numerically in previous publications or not noticed at all. In the particular case of axial symmetry, the problem is reduced to just one singular equation, for which an exact closed-form solution is known. We are not aware of any other publication with which our results can be compared.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528013","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: 0

Steady Normal-Mode Vortices in Circular Cavities 圆腔中的稳定正态涡

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-08-08 DOI: 10.1093/qjmam/hbac010

P. Tyvand

{"title":"Steady Normal-Mode Vortices in Circular Cavities","authors":"P. Tyvand","doi":"10.1093/qjmam/hbac010","DOIUrl":"https://doi.org/10.1093/qjmam/hbac010","url":null,"abstract":"\u0000 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 is to let one of them have circular streamlines, trivially satisfying the kinematic boundary condition at the circle boundary. The requirement for steady flow is that the wavenumber eigenvalues for the Helmholtz equations are identical. This eigenvalue has to be dictated by a normal-mode vortex that is fully 2D. In a circle sector with a designed angle, it is possible to add two fully 2D normal-mode vortices so that their superposed flow is steady. One such example is demonstrated, where the circle sector has an angle of $63.77^circ$. While conventional stability analysis does not apply to these families of steady normal-mode vortices, there is a latent algebraic instability in terms of linearly growing offspring vortices evolving from an initial state where a small initial perturbation is added to the steady normal-mode vortex.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72999326","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: 0