The quarterly journal of mechanics and applied mathematics最新文献_第2页

On a Qualitative and Lie Symmetry Analysis for a Pendulum with Two Reaction Wheels 双反力轮摆的定性和李氏对称性分析

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-08-04 DOI: 10.1093/qjmam/hbac012

A. Ruiz, C. Basquerotto, J. Trentin, S. da Silva

引用次数: 0

Meso-scale method of asymptotic analysis of elastic vibrations in periodic and non-periodic multi-structures 周期和非周期多结构弹性振动渐近分析的细观尺度方法

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-08-01 DOI: 10.1093/qjmam/hbac011

M. Nieves, A. Movchan

{"title":"Meso-scale method of asymptotic analysis of elastic vibrations in periodic and non-periodic multi-structures","authors":"M. Nieves, A. Movchan","doi":"10.1093/qjmam/hbac011","DOIUrl":"https://doi.org/10.1093/qjmam/hbac011","url":null,"abstract":"\u0000 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 of its individual constituents. The main mathematical challenge comes from the analysis of the junction regions assigned to the multi-structure itself. Attention is given to problems of vibration and on the coupling of vibration modes corresponding to displacements of different orientations. The method is demonstrated through the dynamic analysis of infinite or finite multi-scale asymmetric flexural systems consisting of a heavy beam connected to a non-periodic array of massless flexural resonators within some interval. In modelling the interaction between the beam and the resonators, we derive a vectorial system of partial differential equations through which the axial and flexural motions of the heavy beam are coupled. The solution of these equations is written explicitly in terms of Green’s functions having intensities determined from a linear algebraic system. The influence of the resonators on the heavy beam is investigated within the framework of scattering and eigenvalue problems. For large collections of resonators, dynamic homogenization approximations for the medium within the location of the resonant array are derived, leading to (i) the classical Rayleigh beam for symmetric systems and (ii) a generalized Rayleigh beam for asymmetric structures that support flexural–longitudinal wave coupling. Independent numerical simulations are also presented that demonstrate the accuracy of the analytical results.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72519253","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

Large-time asymptotics to solutions of a generalized Burgers equation with linear damping on half-line 半线上具有线性阻尼的广义Burgers方程解的大时渐近性

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-07-30 DOI: 10.1093/qjmam/hbac008

P. Samanta, C. S. Rao

引用次数: 0

Analytical solutions for Bloch waves in resonant phononic crystals: deep-subwavelength energy splitting and mode steering between topologically protected interfacial and edge states 共振声子晶体中布洛赫波的解析解:深亚波长能量分裂和拓扑保护界面和边缘状态之间的模式转向

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-07-22 DOI: 10.1093/qjmam/hbad001

R. Wiltshaw, J. D. Ponti, R. Craster

{"title":"Analytical solutions for Bloch waves in resonant phononic crystals: deep-subwavelength energy splitting and mode steering between topologically protected interfacial and edge states","authors":"R. Wiltshaw, J. D. Ponti, R. Craster","doi":"10.1093/qjmam/hbad001","DOIUrl":"https://doi.org/10.1093/qjmam/hbad001","url":null,"abstract":"\u0000 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 per primitive cell, over Bragg to deep-subwavelength scales; we cross-verify against finite element numerical simulations to gain further confidence in our approach, which relies upon the hypothesis of Euler–Bernoulli beam theory considerably simplifying continuity conditions such that each beam can be replaced by point forces and moments applied to the neutral plane of the plate. The representations of Green’s functions by Fourier series or Fourier transforms readily follows, yielding rapid and accurate analytical schemes. The accuracy and flexibility of our solutions are demonstrated by engineering topologically non-trivial states, from primitive cells with broken spatial symmetries, following the phononic analogue of the Quantum Valley Hall Effect. Topologically protected states are produced and coexist along: interfaces between adjoining chiral-mirrored bulk media, and edges between one such chiral bulk and the surrounding bare elastic plate, allowing topological circuits to be designed with robust waveguiding. Our topologically protected interfacial states correspond to zero-line modes, and our topological edgestates are produced in accordance with the bulk-edge correspondence. These topologically non-trivial states exist within near flexural resonances of the constituent beams of the phononic crystal and hence can be tuned into a deep-subwavelength regime.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84898540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

On the Smallest Number of Functions Representing Isotropic Functions of Scalars, Vectors and Tensors 关于表示标量、向量和张量各向同性函数的最小数量的函数

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-07-20 DOI: 10.1093/qjmam/hbac022

M. Shariff

引用次数: 5

Global bifurcation of capillary-gravity dark solitary waves on the surface of a conducting fluid under normal electric fields 正常电场作用下导电流体表面毛细重力暗孤立波的全局分岔

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-06-03 DOI: 10.1093/qjmam/hbac007

A. Doak, T. Gao, J. Vanden-Broeck

引用次数: 3

CORRECTION to: Theory of perturbation of electrostatic field by an anisotropic dielectric sphere 修正:各向异性介电球对静电场的扰动理论

The quarterly journal of mechanics and applied mathematics Pub Date : 2022-02-26 DOI: 10.1093/qjmam/hbac001

Lakhtakia A, Tsitsas N, Alkhoori H.

引用次数: 0

Theory of Perturbation of Electrostatic Field by an Anisotropic Dielectric Sphere 各向异性介电球对静电场的扰动理论

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-12-01 DOI: 10.1093/qjmam/hbab013

Akhlesh Lakhtakia;Nikolaos L Tsitsas;Hamad M Alkhoori

引用次数: 3

On wave generation by a submerged oscillating source over Roseau's beach profile with outline application to a scattering problem 浸没振荡源在罗索海滩剖面上产生的波浪及其在散射问题上的概要应用

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-12-01 DOI: 10.1093/qjmam/hbab011

Ulf Ehrenmark

{"title":"On wave generation by a submerged oscillating source over Roseau's beach profile with outline application to a scattering problem","authors":"Ulf Ehrenmark","doi":"10.1093/qjmam/hbab011","DOIUrl":"https://doi.org/10.1093/qjmam/hbab011","url":null,"abstract":"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. In particular, the one where the wave field at infinity is devoid of incoming waves allows Sretenski's (Prikl. Mat. Meh. 27 (1963) 1012–1025) established discovery on how the source is made invisible at long distances by its strategic placement, to be verified by the asymptotic theory. Meanwhile, the opportunity is taken to construct the solution in the form of a Green's function and its use is exemplified with a detailed guide to solving a problem of waves attacking a finite floating dock above the Roseau profile. The symmetry property of the Green's function is verified numerically thereby providing a robust check on the validity of the procedures used in computation and leaving the reader with a tool to explore a number of different problems over this curved beach such as might be required from time to time to validate and calibrate more detailed computational models ultimately designed for application with a wide variety of bottom profiles.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"74 4","pages":"379-409"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49964452","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 Life Cycle Effects of Corporate Takeover Defenses 企业收购防御的生命周期效应

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-10-15 DOI: 10.1093/qjmam/hhab113

William C Johnson, Jonathan M Karpoff, Sangho Yi

引用次数: 0