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The quarterly journal of mechanics and applied mathematics最新文献

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A note on the two-dimensional electrostatic field produced by a line charge near a dielectric wedge 介电楔附近的线电荷所产生的二维静电场的注释
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-08-01 DOI: 10.1093/QJMAM/HBZ007
A. Rawlins
{"title":"A note on the two-dimensional electrostatic field produced by a line charge near a dielectric wedge","authors":"A. Rawlins","doi":"10.1093/QJMAM/HBZ007","DOIUrl":"https://doi.org/10.1093/QJMAM/HBZ007","url":null,"abstract":"\u0000 We shall consider the problem of determining the correct electrostatic field produced when an infinite two-dimensional line source is influenced by an adjacent infinite dielectric wedge. This result corrects a number of previous attempts at this problem, which are shown to be in error. The method avoids using the Mellin transform which has lead to some of these earlier errors. The method is used to solve a more general problem of the electrostatic field produced by an arbitrary number of line sources located in an arbitrary number of contiguous dielectric wedges.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73372447","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
Size-Dependent elastic response in functionally graded microbeams considering generalized first strain gradient elasticity 考虑广义第一应变梯度弹性的功能梯度微梁的尺寸相关弹性响应
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-08-01 DOI: 10.1093/QJMAM/HBZ005
Sai Sidhardh, M. Ray
{"title":"Size-Dependent elastic response in functionally graded microbeams considering generalized first strain gradient elasticity","authors":"Sai Sidhardh, M. Ray","doi":"10.1093/QJMAM/HBZ005","DOIUrl":"https://doi.org/10.1093/QJMAM/HBZ005","url":null,"abstract":"\u0000 In this article, the size-dependent mechanical response of an isotropic functionally graded (FG) microbeam has been investigated. The size-effects over the elastic response have been modeled by the Mindlin–Toupin strain gradient theory, with the coefficients evaluated from the generalized first strain gradient theory of elasticity. In order to facilitate the derivation of the exact solutions to the governing differential equations of equilibrium, an exponentially graded FG beam is chosen. These exact solutions are derived for a simply supported beam subjected to a sinusoidally distributed mechanical load. Following this, an element-free Galerkin (EFG) model involving moving least squares interpolations across the domain is also developed here. The EFG model is validated with the exact solutions for the exponentially graded beam. Finally, the EFG model is extended to the more general case of a power law-graded beam. The mechanical responses for the power law-graded beams under various loading and boundary conditions are presented here. These results may serve as benchmark for further studies over size-effects in FG beams.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78183597","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: 4
Displacements representations for the problems with spherical and circular material surfaces 球面和圆形材料表面问题的位移表示
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-06-11 DOI: 10.1093/QJMAM/HBZ013
S. Mogilevskaya, V. Kushch, A. Zemlyanova
{"title":"Displacements representations for the problems with spherical and circular material surfaces","authors":"S. Mogilevskaya, V. Kushch, A. Zemlyanova","doi":"10.1093/QJMAM/HBZ013","DOIUrl":"https://doi.org/10.1093/QJMAM/HBZ013","url":null,"abstract":"\u0000 The displacements representations of the type used by Christensen and Lo (J. Mech. Phys. Solids27, 1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations are used to derive closed-form expressions for the local elastic fields and effective moduli of macroscopically isotropic composite materials containing spherical and circular inhomogeneities with the interfaces described by the complete Gurtin–Murdoch and Steigmann–Ogden models.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83255183","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: 21
Dynamics of Nonlinear Thermoelastic Double-Beam Systems 非线性热弹性双梁系统动力学
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-05-01 DOI: 10.1093/QJMAM/HBZ004
M. Campo, José R. Fernández, M. G. Naso, E. Vuk
{"title":"Dynamics of Nonlinear Thermoelastic Double-Beam Systems","authors":"M. Campo, José R. Fernández, M. G. Naso, E. Vuk","doi":"10.1093/QJMAM/HBZ004","DOIUrl":"https://doi.org/10.1093/QJMAM/HBZ004","url":null,"abstract":"","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72843075","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
Homogenization of elastic materials containing self-similar microcracks 含有自相似微裂纹的弹性材料的均匀化
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-05-01 DOI: 10.1093/QJMAM/HBY023
M. Jarroudi, M. Er-Riani
{"title":"Homogenization of elastic materials containing self-similar microcracks","authors":"M. Jarroudi, M. Er-Riani","doi":"10.1093/QJMAM/HBY023","DOIUrl":"https://doi.org/10.1093/QJMAM/HBY023","url":null,"abstract":"","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"5 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72599090","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: 4
Rayleigh surface waves in functionally graded materials — long-wave limit 功能梯度材料中的瑞利表面波——长波极限
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-05-01 DOI: 10.1093/QJMAM/HBZ002
I. Argatov, A. Iantchenko
{"title":"Rayleigh surface waves in functionally graded materials — long-wave limit","authors":"I. Argatov, A. Iantchenko","doi":"10.1093/QJMAM/HBZ002","DOIUrl":"https://doi.org/10.1093/QJMAM/HBZ002","url":null,"abstract":"A first-order asymptotic model for describing waves propagating along the surface of a functionally graded isotropic elastic half-space is constructed in the long-wave limit under the assumption of ...","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74132607","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: 12
The Kapitza equation for the inverted pendulum 倒立摆的Kapitza方程
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-05-01 DOI: 10.1093/QJMAM/HBZ006
R. E. Grundy
{"title":"The Kapitza equation for the inverted pendulum","authors":"R. E. Grundy","doi":"10.1093/QJMAM/HBZ006","DOIUrl":"https://doi.org/10.1093/QJMAM/HBZ006","url":null,"abstract":"","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84713746","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: 5
Dynamic stability and instability of nanobeams based on the higher-order nonlocal strain gradient theory 基于高阶非局部应变梯度理论的纳米梁的动态稳定性和不稳定性
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-05-01 DOI: 10.1093/QJMAM/HBY024
I. Pavlović, R. Pavlović, G. Janevski
{"title":"Dynamic stability and instability of nanobeams based on the higher-order nonlocal strain gradient theory","authors":"I. Pavlović, R. Pavlović, G. Janevski","doi":"10.1093/QJMAM/HBY024","DOIUrl":"https://doi.org/10.1093/QJMAM/HBY024","url":null,"abstract":"","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86737024","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: 6
Alternating Strain Regimes for Failure Propagation in Flexural Systems 弯曲系统中破坏传播的交变应变形式
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-04-18 DOI: 10.1093/QJMAM/HBZ008
M. Garau, M. Nieves, I. Jones
{"title":"Alternating Strain Regimes for Failure Propagation in Flexural Systems","authors":"M. Garau, M. Nieves, I. Jones","doi":"10.1093/QJMAM/HBZ008","DOIUrl":"https://doi.org/10.1093/QJMAM/HBZ008","url":null,"abstract":"\u0000 We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler–Bernoulli beams. A fault inside the structure is assumed to propagate with a constant speed and this occurs as a result of the action of a remote sinusoidal, mechanical load. The established regime of fracture corresponds to the case of an alternating generalised strain regime. The model is reduced to a Wiener–Hopf equation and its solution is presented. We determine the minimum feeding wave energy required for the steady-state fracture process to occur. In addition, we identify the dynamic features of the structure during the steady-state fracture regime. A transient analysis of this problem is also presented, where the existence of steady-state fracture regimes, revealed by the analytical model, are verified and the associated transient features of this process are discussed.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79441032","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: 3
Wave response to a submerged wedge-shaped rubble mound breakwater 楔形碎石丘防波堤的波浪响应
The quarterly journal of mechanics and applied mathematics Pub Date : 2019-02-01 DOI: 10.1093/qjmam/hby020
U T Ehrenmark
{"title":"Wave response to a submerged wedge-shaped rubble mound breakwater","authors":"U T Ehrenmark","doi":"10.1093/qjmam/hby020","DOIUrl":"https://doi.org/10.1093/qjmam/hby020","url":null,"abstract":"The action of a wedge-shaped breakwater similar to that at Ramsgate harbour, UK, is investigated by means of an idealised analytical model which permits a solution process involving a pair of singular integral equations of the second kind where the integrals are of the Cauchy Principal Value type. It is found that an integrable singularity in velocity components emerges at the tip of the breakwater wedge assumed coincident with the mean free surface. Nevertheless, the wave profile is continuous across the breakwater though, because of the singularity, it steepens significantly near the tip. The absence of other parameters facilitates an investigation of the intrinsic relationship between friction and dissipation in wedge-shaped breakwaters. Expressions are derived for total energy dissipation measured against the friction term which is, in common with other investigations, linearised according to the Lorentz law of equivalent work. That dissipation is found to have a maximum at a relatively low critical value of the friction parameter, an outcome which could jeopardise the strategy of increasing the parameter to mimic wave breaking losses over trapezoidal breakwaters as suggested by Sollit and Cross (Proc. 13th Coastal Eng. Conf. (Vancouver, ASCE 1972) 1827–1846).","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"72 1","pages":"25-50"},"PeriodicalIF":0.0,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hby020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49986335","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
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