Annu Rani, D. K. Madan, Naveen Kumar, Mukesh Punia
This research examines the propagation of waves in a semi-infinite, isotropic magneto-thermoelastic solid, and a semi-infinite thermoelastic solid with welded contact. The study investigates the influence of a magnetic field on amplitude coefficients for the incidence of thermal, SV, and P waves in the magnetothermoelastic solid in a semi-infinite space. The incidence of these waves results in a total of six waves, including both refracted and reflected waves. The fluctuation of amplitude coefficients for various magnetic pressure values is explored for copper and aluminum as numerical constants. The study observes that the amplitude coefficients of seismic waves, occurring during the incidence of thermal, SV, and P waves in the magneto-thermoelastic solid semi-infinite space, are dependent on the incident angle, magnetic field, and material constants. Notably, the amplitude coefficients for the incidence of SV waves exhibit only a minor influence from the magnetic field. The implications of this research extend to applications in ocean acoustics, geophysics, acoustic devices, composite materials, and non-destructive testing.
本研究探讨了波在半无限各向同性磁热弹性固体和具有焊接接触的半无限热弹性固体中的传播。研究调查了磁场对半无限空间磁热弹性固体中热波、SV 波和 P 波入射振幅系数的影响。这些波的入射总共产生六种波，包括折射波和反射波。以铜和铝为数值常数，探讨了不同磁压值下振幅系数的波动。研究发现，在磁热弹性固体半无限空间中，热波、SV 波和 P 波入射时产生的地震波振幅系数取决于入射角、磁场和材料常数。值得注意的是，SV 波入射时的振幅系数仅受磁场的轻微影响。这项研究的意义延伸到海洋声学、地球物理学、声学设备、复合材料和无损检测等领域的应用。
{"title":"PLANE WAVES AT AN INTERFACE OF THERMOELASTIC AND MAGNETO-THERMOELASTIC MEDIA","authors":"Annu Rani, D. K. Madan, Naveen Kumar, Mukesh Punia","doi":"10.3846/mma.2024.18477","DOIUrl":"https://doi.org/10.3846/mma.2024.18477","url":null,"abstract":"This research examines the propagation of waves in a semi-infinite, isotropic magneto-thermoelastic solid, and a semi-infinite thermoelastic solid with welded contact. The study investigates the influence of a magnetic field on amplitude coefficients for the incidence of thermal, SV, and P waves in the magnetothermoelastic solid in a semi-infinite space. The incidence of these waves results in a total of six waves, including both refracted and reflected waves. The fluctuation of amplitude coefficients for various magnetic pressure values is explored for copper and aluminum as numerical constants. The study observes that the amplitude coefficients of seismic waves, occurring during the incidence of thermal, SV, and P waves in the magneto-thermoelastic solid semi-infinite space, are dependent on the incident angle, magnetic field, and material constants. Notably, the amplitude coefficients for the incidence of SV waves exhibit only a minor influence from the magnetic field. The implications of this research extend to applications in ocean acoustics, geophysics, acoustic devices, composite materials, and non-destructive testing.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141350143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The fractional exponential function is considered. General expansions in fractional powers are used to solve fractional population dynamics problems. Laguerretype exponentials are also considered, and an application to Laguerre-type fractional logistic equation is shown.
{"title":"A NOTE ON FRACTIONAL-TYPE MODELS OF POPULATION DYNAMICS","authors":"Diego Caratelli, P. Ricci","doi":"10.3846/mma.2024.19588","DOIUrl":"https://doi.org/10.3846/mma.2024.19588","url":null,"abstract":"The fractional exponential function is considered. General expansions in fractional powers are used to solve fractional population dynamics problems. Laguerretype exponentials are also considered, and an application to Laguerre-type fractional logistic equation is shown.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141351327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Benjamin-Bona-Mahony-Burgers equation (BBMBE) plays a fundemental role in many application scenarios. In this paper, we study a spectral method for the BBMBE with homogeneous boundary conditions. We propose a spectral scheme using the transformed generalized Jacobi polynomial in combination of the explicit fourth-order Runge-Kutta method in time. The boundedness, the generalized stability and the convergence of the proposed scheme are proved. The extensive numerical examples show the efficiency of the new proposed scheme and coincide well with the theoretical analysis. The advantages of our new approach are as follows: (i) the use of the transformed generalized Jacobi polynomial simplifies the theoretical analysis and brings a sparse discrete system; (ii) the numerical solution is spectral accuracy in space.
{"title":"SPECTRAL METHOD FOR ONE DIMENSIONAL BENJAMIN-BONA-MAHONY-BURGERS EQUATION USING THE TRANSFORMED GENERALIZED JACOBI POLYNOMIAL","authors":"Yu Zhou","doi":"10.3846/mma.2024.18595","DOIUrl":"https://doi.org/10.3846/mma.2024.18595","url":null,"abstract":"The Benjamin-Bona-Mahony-Burgers equation (BBMBE) plays a fundemental role in many application scenarios. In this paper, we study a spectral method for the BBMBE with homogeneous boundary conditions. We propose a spectral scheme using the transformed generalized Jacobi polynomial in combination of the explicit fourth-order Runge-Kutta method in time. The boundedness, the generalized stability and the convergence of the proposed scheme are proved. The extensive numerical examples show the efficiency of the new proposed scheme and coincide well with the theoretical analysis. The advantages of our new approach are as follows: (i) the use of the transformed generalized Jacobi polynomial simplifies the theoretical analysis and brings a sparse discrete system; (ii) the numerical solution is spectral accuracy in space.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141352770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we introduce a numerical approach that utilizes spline quasi-interpolation operators over a bounded interval. This method is designed to provide a numerical solution for a class of Fredholm integro-differential equations with weakly singular kernels. We outline the computational components involved in determining the approximate solution and provide theoretical findings regarding the convergence rate. This convergence rate is analyzed in relation to both the degree of the quasi-interpolant and the grading exponent of the graded grid partition. Finally, we present numerical experiments that validate the theoretical findings.
{"title":"SPLINE QUASI-INTERPOLATION NUMERICAL METHODS FOR INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS","authors":"A. Saou, D. Sbibih, M. Tahrichi, Domingo Barrera","doi":"10.3846/mma.2024.18832","DOIUrl":"https://doi.org/10.3846/mma.2024.18832","url":null,"abstract":"In this work, we introduce a numerical approach that utilizes spline quasi-interpolation operators over a bounded interval. This method is designed to provide a numerical solution for a class of Fredholm integro-differential equations with weakly singular kernels. We outline the computational components involved in determining the approximate solution and provide theoretical findings regarding the convergence rate. This convergence rate is analyzed in relation to both the degree of the quasi-interpolant and the grading exponent of the graded grid partition. Finally, we present numerical experiments that validate the theoretical findings.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141118459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a mathematical model of two-dimensional electrically driven laminar free shear flows in a straight duct under action of an applied uniform homogeneous magnetic field. The mathematical approach is based on studies by J.C.R. Hunt and W.E. Williams [10], Yu. Kolesnikov and H. Kalis [22,23]. We solve the system of stationary partial differential equations (PDEs) with two unknown functions of velocity U and induced magnetic field H. The flows are generated as a result of the interaction of injected electric current in liquid and the applied field using one or two couples of linear electrodes located on duct walls: three cases are considered. In dependence on direction of current injection and uniform magnetic field, the flows between the end walls are realized. Distributions of velocities and induced magnetic fields, electric current density in dependence on the Hartmann number Ha are studied. The solution of this problem is obtained analytically and numerically, using the Fourier series method and Matlab.
我们考虑的是在外加均匀均质磁场作用下，直管中二维电驱动层流自由剪切流的数学模型。数学方法基于 J.C.R. Hunt 和 W.E. Williams [10]、Yu.Kolesnikov 和 H. Kalis [22,23]的研究为基础。我们求解的是速度 U 和诱导磁场 H 两个未知函数的静态偏微分方程 (PDE)系统。液体中的注入电流与位于管道壁上的一个或两个线性电极耦合的外加磁场相互作用产生流动：我们考虑了三种情况。根据电流注入方向和均匀磁场，实现了端壁之间的流动。研究了速度和感应磁场的分布，以及取决于哈特曼数 Ha 的电流密度。利用傅立叶级数法和 Matlab，对该问题进行了分析和数值求解。
{"title":"MATHEMATICAL MODELLING ELECTRICALLY DRIVEN FREE SHEAR FLOWS IN A DUCT UNDER UNIFORM MAGNETIC FIELD","authors":"H. Kalis, I. Kangro","doi":"10.3846/mma.2024.19528","DOIUrl":"https://doi.org/10.3846/mma.2024.19528","url":null,"abstract":"We consider a mathematical model of two-dimensional electrically driven laminar free shear flows in a straight duct under action of an applied uniform homogeneous magnetic field. The mathematical approach is based on studies by J.C.R. Hunt and W.E. Williams [10], Yu. Kolesnikov and H. Kalis [22,23]. We solve the system of stationary partial differential equations (PDEs) with two unknown functions of velocity U and induced magnetic field H. The flows are generated as a result of the interaction of injected electric current in liquid and the applied field using one or two couples of linear electrodes located on duct walls: three cases are considered. In dependence on direction of current injection and uniform magnetic field, the flows between the end walls are realized. Distributions of velocities and induced magnetic fields, electric current density in dependence on the Hartmann number Ha are studied. The solution of this problem is obtained analytically and numerically, using the Fourier series method and Matlab.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141116996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ghizlane Zineddaine, Abdelaziz Sabiry, Said Melliani, Abderrezak Kassidi
The objective of this work is to establish the existence of entropy solutions to degenerate nonlinear elliptic problems for $L^1$-data $f$ with a Hardy potential, in weighted Sobolev spaces with variable exponent, which are represented as follows begin{gather*} -text{div}big(Phi(z,v,nabla v)big)+g(z,v,nabla v)=f+rhofrac{vert v vert^{p(z)-2}v}{|v|^{p(z)}}, end{gather*} where $-text{div}(Phi(z,v,nabla v))$ is a Leray-Lions operator from $W_{0}^{1,p(z)}(Omega,omega)$ into its dual, $g(z,v,nabla v)$ is a non-linearity term that only meets the growth condition, and $rho>0$ is a constant.
{"title":"EXISTENCE RESULTS IN WEIGHTED SOBOLEV SPACE FOR QUASILINEAR DEGENERATE P(Z)−ELLIPTIC PROBLEMS WITH A HARDY POTENTIAL","authors":"Ghizlane Zineddaine, Abdelaziz Sabiry, Said Melliani, Abderrezak Kassidi","doi":"10.3846/mma.2024.18696","DOIUrl":"https://doi.org/10.3846/mma.2024.18696","url":null,"abstract":"The objective of this work is to establish the existence of entropy solutions to degenerate nonlinear elliptic problems for $L^1$-data $f$ with a Hardy potential, in weighted Sobolev spaces with variable exponent, which are represented as follows\u0000begin{gather*}\u0000-text{div}big(Phi(z,v,nabla v)big)+g(z,v,nabla v)=f+rhofrac{vert v vert^{p(z)-2}v}{|v|^{p(z)}},\u0000end{gather*}\u0000where $-text{div}(Phi(z,v,nabla v))$ is a Leray-Lions operator from $W_{0}^{1,p(z)}(Omega,omega)$ into its dual, $g(z,v,nabla v)$ is a non-linearity term that only meets the growth condition, and $rho>0$ is a constant.\u0000","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141115282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For Volterra integro-differential equations (VIDEs) with weakly singular kernels, their solutions are singular at the initial time. This property brings a great challenge to traditional numerical methods. Here, we investigate the numerical approximation for the solution of the nonlinear model with weakly singular kernels. Due to its characteristic, we split the interval and focus on the first one to save operation. We employ the corresponding singular functions as basis functions in the first interval to simulate its singular behavior, and take the Legendre polynomials as basis functions in the other one. Then the corresponding hp-version spectral method is proposed, the existence and uniqueness of solution to the numerical scheme are proved, the hp-version optimal convergence is derived. Numerical experiments verify the effectiveness of the proposed method.
{"title":"AN EFFICIENT SPECTRAL METHOD FOR NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS","authors":"ZhiPeng Liu, Dongya Tao, Chao Zhang","doi":"10.3846/mma.2024.18354","DOIUrl":"https://doi.org/10.3846/mma.2024.18354","url":null,"abstract":"For Volterra integro-differential equations (VIDEs) with weakly singular kernels, their solutions are singular at the initial time. This property brings a great challenge to traditional numerical methods. Here, we investigate the numerical approximation for the solution of the nonlinear model with weakly singular kernels. Due to its characteristic, we split the interval and focus on the first one to save operation. We employ the corresponding singular functions as basis functions in the first interval to simulate its singular behavior, and take the Legendre polynomials as basis functions in the other one. Then the corresponding hp-version spectral method is proposed, the existence and uniqueness of solution to the numerical scheme are proved, the hp-version optimal convergence is derived. Numerical experiments verify the effectiveness of the proposed method.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140978236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the discretization method for solving three-dimensional variable-order (3D-VO) time-fractional partial differential equations. The proposed method is developed based on discrete shifted Hahn polynomials (DSHPs) and their operational matrices. In the process of method implementation, the modified operational matrix (MOM) and complement vector (CV) of integration and pseudooperational matrix (POM) of VO fractional derivative plays an important role in the accuracy of the method. Further, we discuss the error of the approximate solution. At last, the methodology is validated by well test examples in two types of space domains. In order to evaluate the accuracy and applicability of the approach, the results are compared with other methods.
我们考虑了求解三维变阶（3D-VO）时间分数偏微分方程的离散化方法。所提出的方法基于离散移位哈恩多项式（DSHPs）及其运算矩阵。在方法实施过程中，积分的修正运算矩阵（MOM）和补矢量（CV）以及 VO 分数导数的伪运算矩阵（POM）对方法的精度起着重要作用。此外，我们还讨论了近似解的误差。最后，我们通过两类空间域中的测试实例对该方法进行了验证。为了评估该方法的准确性和适用性，我们将结果与其他方法进行了比较。
{"title":"AN ACCURATE NUMERICAL SCHEME FOR THREE-DIMENSIONAL VARIABLE-ORDER TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN TWO TYPES OF SPACE DOMAINS","authors":"Haniye Dehestani, Y. Ordokhani, M. Razzaghi","doi":"10.3846/mma.2024.18535","DOIUrl":"https://doi.org/10.3846/mma.2024.18535","url":null,"abstract":"We consider the discretization method for solving three-dimensional variable-order (3D-VO) time-fractional partial differential equations. The proposed method is developed based on discrete shifted Hahn polynomials (DSHPs) and their operational matrices. In the process of method implementation, the modified operational matrix (MOM) and complement vector (CV) of integration and pseudooperational matrix (POM) of VO fractional derivative plays an important role in the accuracy of the method. Further, we discuss the error of the approximate solution. At last, the methodology is validated by well test examples in two types of space domains. In order to evaluate the accuracy and applicability of the approach, the results are compared with other methods.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140982216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is concerned with the inverse problem of recovering the time dependent source term in a time fractional diffusion equation, in the case of nonlocal boundary condition and integral overdetermination condition. The boundary conditions of this problem are regular but not strongly regular. The existence and uniqueness of the solution are established by applying generalized Fourier method based on the expansion in terms of root functions of a spectral problem, weakly singular Volterra integral equation and fractional type Gronwall’s inequality. Moreover, we show its continuous dependence on the data.
{"title":"IDENTIFICATION OF A TIME-DEPENDENT SOURCE TERM IN A NONLOCAL PROBLEM FOR TIME FRACTIONAL DIFFUSION EQUATION","authors":"M. Ismailov, Muhammed Çiçek","doi":"10.3846/mma.2024.17791","DOIUrl":"https://doi.org/10.3846/mma.2024.17791","url":null,"abstract":"This paper is concerned with the inverse problem of recovering the time dependent source term in a time fractional diffusion equation, in the case of nonlocal boundary condition and integral overdetermination condition. The boundary conditions of this problem are regular but not strongly regular. The existence and uniqueness of the solution are established by applying generalized Fourier method based on the expansion in terms of root functions of a spectral problem, weakly singular Volterra integral equation and fractional type Gronwall’s inequality. Moreover, we show its continuous dependence on the data.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140381245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article illustrates the hydroelastic interactions between surface gravity waves and a floating elastic plate in a two-layer liquid with variable bottom topography under the assumptions of small amplitude waves and potential flow theory. In this study, semi-infinite and finite-length plates are considered. The eigenfunction expansion method is applied in the fluid region with uniform bottom topography. A system of differential equations (mild-slope equations) is solved in the fluid region with variable bottom topography. From the matching and jump conditions, the solution is expressed as a linear algebraic system from which all the unknown constants are computed. We explored the effects of density ratio, depth ratio, and bottom topography on the bending moment, shear force, and the deflection of the elastic plate. Results show that when the density ratio becomes closer to one, the occurred bending moment and shear forces to the elastic plates tend to diminish. The bending moment and shear forces to the pates are higher and lower at a smaller depth ratiofor the incident surface wave and interfacial waves, respectively. The variations in the bending moment, shear force, and plate deflection, caused by surface and interfacial waves, are observed to be in opposite trends, respectively. Bottom profiles similarly affect semi-infinite and finite-length plates when they undergo free-edge conditions. These effects, however, are substantial when the plate is simply supported at the edges. Elastic plate with free edges experiences lower deflection for concave-up and plane-sloping bottoms for incident surface and interfacial waves, respectively.
{"title":"TOPOGRAPHICAL EFFECTS ON WAVE SCATTERING BY AN ELASTIC PLATE FLOATING ON TWO-LAYER FLUID","authors":"Ramanababu Kaligatla, Nagmani Prasad","doi":"10.3846/mma.2024.17539","DOIUrl":"https://doi.org/10.3846/mma.2024.17539","url":null,"abstract":"This article illustrates the hydroelastic interactions between surface gravity waves and a floating elastic plate in a two-layer liquid with variable bottom topography under the assumptions of small amplitude waves and potential flow theory. In this study, semi-infinite and finite-length plates are considered. The eigenfunction expansion method is applied in the fluid region with uniform bottom topography. A system of differential equations (mild-slope equations) is solved in the fluid region with variable bottom topography. From the matching and jump conditions, the solution is expressed as a linear algebraic system from which all the unknown constants are computed. We explored the effects of density ratio, depth ratio, and bottom topography on the bending moment, shear force, and the deflection of the elastic plate. Results show that when the density ratio becomes closer to one, the occurred bending moment and shear forces to the elastic plates tend to diminish. The bending moment and shear forces to the pates are higher and lower at a smaller depth ratiofor the incident surface wave and interfacial waves, respectively. The variations in the bending moment, shear force, and plate deflection, caused by surface and interfacial waves, are observed to be in opposite trends, respectively. Bottom profiles similarly affect semi-infinite and finite-length plates when they undergo free-edge conditions. These effects, however, are substantial when the plate is simply supported at the edges. Elastic plate with free edges experiences lower deflection for concave-up and plane-sloping bottoms for incident surface and interfacial waves, respectively.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140381059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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