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Natural frequencies of a Timoshenko beam with cracks 有裂缝的季莫申科梁的自然频率
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-06 DOI: 10.1016/j.wavemoti.2024.103420
{"title":"Natural frequencies of a Timoshenko beam with cracks","authors":"","doi":"10.1016/j.wavemoti.2024.103420","DOIUrl":"10.1016/j.wavemoti.2024.103420","url":null,"abstract":"<div><div>A problem of calculating of natural frequencies of a Timoshenko beam weakened by a finite number of transverse open cracks is considered. The problem is solved for both known crack models. In one model every crack is simulated by a single, massless rotational spring. In the other model every crack is simulated by two massless springs (one extensional and another one rotational). An effective method for calculation of the natural frequencies of a vibrating beam with cracks, which was previously successfully applied to Euler-Bernoulli beams, is extended to the case of Timoshenko beam. The developed method makes it possible to significantly reduce the order of the determinant, the zeros of which are natural frequencies. Numerical examples are considered. The results are compared with the known where it is possible.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rogue waves on the periodic background for a higher-order nonlinear Schrödinger–Maxwell–Bloch system 高阶非线性薛定谔-麦克斯韦-布洛赫系统的周期性背景上的游荡波
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-29 DOI: 10.1016/j.wavemoti.2024.103417
{"title":"Rogue waves on the periodic background for a higher-order nonlinear Schrödinger–Maxwell–Bloch system","authors":"","doi":"10.1016/j.wavemoti.2024.103417","DOIUrl":"10.1016/j.wavemoti.2024.103417","url":null,"abstract":"<div><div>In this paper, we construct the rogue wave solutions on the background of the Jacobian elliptic functions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system. The Jacobian elliptic function traveling wave solutions as the seed solutions are considered. Through the approach of the nonlinearization of the Lax pair and Darboux transformation method, the rogue waves and the line rogue waves on the Jacobian elliptic functions dn and cn background are obtained, respectively.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the viscoelastic-electromagnetic-gravitational analogy 关于粘弹性-电磁-引力类比
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-19 DOI: 10.1016/j.wavemoti.2024.103411
{"title":"On the viscoelastic-electromagnetic-gravitational analogy","authors":"","doi":"10.1016/j.wavemoti.2024.103411","DOIUrl":"10.1016/j.wavemoti.2024.103411","url":null,"abstract":"<div><div>The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The impact of relaxation on isothermal acoustic traveling waves: A new solvable model based on Navier–Stokes–Maxwell theory 弛豫对等温声学行波的影响：基于纳维-斯托克斯-麦克斯韦理论的新型可解模型
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103415
{"title":"The impact of relaxation on isothermal acoustic traveling waves: A new solvable model based on Navier–Stokes–Maxwell theory","authors":"","doi":"10.1016/j.wavemoti.2024.103415","DOIUrl":"10.1016/j.wavemoti.2024.103415","url":null,"abstract":"<div><div>An analysis of isothermal acoustic traveling waves in a particular sub-class of Maxwell fluids, specifically, those which behave like perfect gases and wherein the shear viscosity is proportional to the square of the mass density, is presented. Exact solutions are derived and analyzed, shock thickness results are computed, and the thermodynamic consistency of the isothermal assumption is verified vis-à-vis the Mach number values considered. It is shown that, within the range where both yield dispersed shock profiles, the Maxwell case leads to significantly smaller shock thicknesses and more asymmetric solution profiles than those admitted by the corresponding Newtonian (fluid) case.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solitary wave solutions and their limits to the fractional Schrödinger system 分数薛定谔系统的孤波解及其极限
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103416
{"title":"Solitary wave solutions and their limits to the fractional Schrödinger system","authors":"","doi":"10.1016/j.wavemoti.2024.103416","DOIUrl":"10.1016/j.wavemoti.2024.103416","url":null,"abstract":"<div><div>This study is concerned with solitary wave solutions and the dynamic behavior of the (2+1)-dimensional nonlinear fractional Schrödinger system. By exploring the dynamic properties of the equilibrium levels to the corresponding Hamiltonian, the expressions of exact solutions of the above system are obtained, including solitary wave solutions, periodic wave solutions, singular periodic wave solutions, singular wave solutions, kink wave solutions, and anti-kink wave solutions. Moreover, the linear stability, geometric characteristics, and limiting behavior of these solutions to the nonlinear fractional Schrödinger system were investigated.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New exact solutions of some (2+1)-dimensional nonlinear evolution equations and folding waves 一些 (2+1) 维非线性演化方程和折叠波的新精确解
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103414
{"title":"New exact solutions of some (2+1)-dimensional nonlinear evolution equations and folding waves","authors":"","doi":"10.1016/j.wavemoti.2024.103414","DOIUrl":"10.1016/j.wavemoti.2024.103414","url":null,"abstract":"<div><p>By means of the Hirota’s bilinear method and special multi-linear variable separation ansatz, new exact solutions with low dimensional arbitrary functions of some (2+1)-dimensional nonlinear evolution equations are constructed. That is, we propose a unified method for solving the mNNV-type equations and the Burger-type equations. The key factor to the success of this method is that we have constructed some simplified Hirota’s bilinear calculation formulas in the form of variable separation of arbitrary order. Appropriate multi-valued functions are used to construct coherent structures such as the bell-type, peak-type and loop-type folding waves.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure 具有完整科里奥利力和漩涡结构的高维地球物理流体模型
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-14 DOI: 10.1016/j.wavemoti.2024.103410
{"title":"A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure","authors":"","doi":"10.1016/j.wavemoti.2024.103410","DOIUrl":"10.1016/j.wavemoti.2024.103410","url":null,"abstract":"<div><div>Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields 强水平电场下具有恒定涡度的周期波下的流动结构
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-12 DOI: 10.1016/j.wavemoti.2024.103413
{"title":"Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields","authors":"","doi":"10.1016/j.wavemoti.2024.103413","DOIUrl":"10.1016/j.wavemoti.2024.103413","url":null,"abstract":"<div><p>While several articles have been written on Electrohydrodynamics (EHD) flows or flows with constant vorticity separately, little is known about the extent to which the combined effects of EHD and constant vorticity affect the flow. This study aims to shed light on this topic by investigating the combined influence of a horizontal electric field and constant vorticity on the free surface and the emergence of stagnation points. Using the Euler equations framework, we employ conformal mapping and pseudo-spectral numerical methods. Our findings reveal that increasing the electric field intensity eliminates stagnation points and smoothen the wave profile. This implies that a horizontal electric field acts as a mechanism for the elimination of stagnation points within the fluid body. Besides, we have identified regimes where three stagnation points appear on the free surface — something that cannot occur in purely gravity rotational waves.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wave resonances and the time-dependent capillary gravity wave motion 波共振和随时间变化的毛细管重力波运动
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-10 DOI: 10.1016/j.wavemoti.2024.103412
{"title":"Wave resonances and the time-dependent capillary gravity wave motion","authors":"","doi":"10.1016/j.wavemoti.2024.103412","DOIUrl":"10.1016/j.wavemoti.2024.103412","url":null,"abstract":"<div><p>The interconnection of time and frequency domains for capillary gravity wave motion in the presence of current is discussed in this article. The general time-dependent problem is solved using Green’s function technique, and the asymptotic solution is derived using the method of stationary phase for large time and space. Also, the frequency domain solution is derived as a special case using the Cauchy Residue theorem. Different types of wave resonances like Trapping, Blocking and Bragg resonances are discussed. The existence of the trapped mode below the cutoff frequency is justified theoretically, and numerical results are obtained using the multipole expansion method. The blocking and Bragg resonances are analyzed above the cutoff frequency. It is found that in the presence of current, when the ripple wavenumber of the bottom undulation equals twice the cosine angle of incidence of wave times the wavenumber of the wave, Bragg resonance occurs. It is found that three propagating modes exist in the case of wave blocking, and the trapped modes exist only for the first propagating mode. Furthermore, because of the negative group velocity inside the blocking zone, the Bragg reflection increases while decreasing outside. The effect of current on the wave energy propagation in the form of group velocity is analyzed and the same is verified in the case of time-dependent problem.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical treatment of the Sine-Gordon equations via a new DQM based on cubic unified and extended trigonometric B-spline functions 通过基于立方统一和扩展三角 B-样条函数的新 DQM 对正弦-戈登方程进行数值处理
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-06 DOI: 10.1016/j.wavemoti.2024.103409
{"title":"Numerical treatment of the Sine-Gordon equations via a new DQM based on cubic unified and extended trigonometric B-spline functions","authors":"","doi":"10.1016/j.wavemoti.2024.103409","DOIUrl":"10.1016/j.wavemoti.2024.103409","url":null,"abstract":"<div><p>The purpose of this work is to propose a new composite scheme based on differential quadrature method (DQM) and modified cubic unified and extended trigonometric B-spline (CUETB-spline) functions to numerically approximate one-dimensional (1D) and two-dimensional (2D) Sine-Gordon Eqs. (SGEs). These functions are modified and then applied in DQM to determine the weighting coefficients (WCs) of spatial derivatives. Using the WCs in SGEs, we obtain systems of ordinary differential equations (ODEs) which is resolved by the five-stage and order four strong stability-preserving time-stepping Runge–Kutta (SSP-RK<sub>5,4</sub>) scheme. This method's precision and consistency are validated through numerical approximations of the one-and two-dimensional problems, showing that the projected method outcomes are more accurate than existing ones as well as an incomparable agreement with the exact solutions is found. Besides, the rate of convergence (ROC) is performed numerically, which shows that the method is second-order convergent with respect to the space variable. The proposed method is straightforward and can effectively handle diverse problems. Dev-C++ 6.3 version is used for all calculations while Figs. are drawn by MATLAB 2015b.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142230239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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