共查询到20条相似文献,搜索用时 125 毫秒
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针对薄板弯曲大变形问题, 运用变分原理, 建立了薄板弯曲大变形问题的高阶非线性偏微分方程. 运用有限差分法和动态设计变量优化算法原理, 以离散坐标点的上未知挠度为设计变量, 以离散坐标点的差分方程组构建目标函数, 提出了薄板弯曲大变形挠度求解的动态设计变量优化算法, 编制了相应的优化求解程序. 分析了具有固定边界、均布载荷下的矩形薄板挠度的典型算例. 通过与有限元的结果对比, 表明了本文求解算法的有效性和精确性, 提供了直接求解实际工程问题的基础. 相似文献
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矩形板高阶模式超声振动辐射器的研究 总被引:1,自引:0,他引:1
在耦合振动理论以及矩形截面细棒弯曲振动的基础上,本文对矩形薄板的弯曲振动进行了研究,推出了自由边界矩形薄板的弯曲振动频率方程,研究了薄板的振动模式及其与共振频率的关系.实验表明,矩形薄板弯曲振动共振频率的测量值与计算值符合很好.用共振式矩形薄板作为超声清洗等液体中超声应用技术的声波辐射器具有声场分布均匀,换能器频率调节容易,声波辐射面大等优点,是一种很有前途的新型超声源. 相似文献
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从最小势能原理出发,使用变分-差分方法构造带有弯曲边梁的薄板的小挠度弯曲问题的差分格式,所得格式仅依赖板面网格结点,从而避免了由于引入虚拟网格结点而带来的问题;编制求解差分方程组的MATLAB程序,给出数值模拟结果. 相似文献
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The initial and boundary value problem for the fractional diffusion equation in half-space with the Robin boundary condition is considered. The solution is comprised of two parts: the contribution of the initial value and the contribution of the boundary value, for which the respective fundamental solutions are given. Finally, the solution formula of the considered problem is obtained. 相似文献
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On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow 下载免费PDF全文
D. Lesnic 《advances in applied mathematics and mechanics.》2009,1(1):140-150
In this paper, the two-dimensional slowly rotating highly viscous
fluid flow in small cavities is modelled by the triharmonic equation
for the streamfunction. The Dirichlet problem for this triharmonic
equation is recast as a set of three boundary integral equations
which however, do not have a unique solution for three exceptional
geometries of the boundary curve surrounding the planar solution
domain. This defect can be removed either by using modified
fundamental solutions or by adding two supplementary boundary
integral conditions which the solution of the boundary integral
equations must satisfy. The analysis is further generalized to
polyharmonic equations. 相似文献
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Burde GI 《Chaos (Woodbury, N.Y.)》2012,22(1):013138
Some new effects in the soliton dynamics governed by higher order Korteweg-de Vries (KdV) equations are discussed based on the exact explicit solutions of the equations on the positive half-line. The solutions describe the process of generation of a soliton that occurs without boundary forcing and on the steady state background: the boundary conditions remain constant and the initial distribution is a steady state solution of the problem. The time moment when the soliton generation starts is not determined by the parameters present in the problem formulation, the additional parameters imbedded into the solution are needed to determine that moment. The equations found capable of describing those effects are the integrable Sawada-Kotera equation and the KdV-Kaup-Kupershmidt (KdV-KK) equation which, albeit not proven to be integrable, possesses multi-soliton solutions. 相似文献
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A unified compatibility method of differential equations is employed to solve some nonlinear two-point boundary value problems arising in the study of the classical model of viscous (Newtonian) fluid flow due to impermeable shrinking and stretching sheets. The solution procedure allows us to find the exact solution of the nonlinear models in the form of a closed-form exponential function. The solution methodology is easy as well as systematic and provides a unified treatment to already known ad hoc solutions of these models found in the literature before. Moreover, some new exact solutions of the various extended versions of this classical engineering boundary layer problem under different physical considerations are discussed. Hence, several misrepresented solutions related to this boundary layer model which are discussed before in the literature are identified, corrected, and clarified in this paper. 相似文献
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Carlos Gay 《Journal of Quantitative Spectroscopy & Radiative Transfer》1984,31(5):423-438
The problem of the dissipation of temperature perturbations in a finite homogeneous atmosphere is solved for the situation in which the temperature at one boundary is maintained constant (that is, the temperature perturbation is zero for all times) while energy can be freely radiated to space through the other boundary. Exact solutions are shown for the exponential-sum fit to the kernel of the basic integral equation. These solutions constitute the set of radiative eigenfunctions. Also, approximate solutions in terms of the radiative eigenfunctions in the diffusion approximation (one exponential term in the expansion of the kernel) are obtained. These, in turn, are used in the solution of an initial value problem. The constant temperature boundary condition simulates the interface between two regions in one of which the relaxation processes are much more rapid than the purely radiative relaxation of the other. 相似文献
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研究了一类非线性奇摄动方程的激波问题.利用Sinc-Galerkin方法,构造出边值问题的激波解,并由Newton法得到其近似解.
关键词:
非线性方程
激波
Sinc-Galerkin方法
Newton法 相似文献
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We show how to construct low energy solutions to the Randall-Sundrum II (RSII) model by using an associated five-dimensional anti-de Sitter space (AdS(5)) and/or four-dimensional conformal field theory (CFT(4)) problem. The RSII solution is given as a perturbation of the AdS(5)-CFT(4) solution, with the perturbation parameter being the radius of curvature of the brane metric compared to the AdS length ?. The brane metric is then a specific perturbation of the AdS(5)-CFT(4) boundary metric. For low curvatures the RSII solution reproduces 4D general relativity on the brane. Recently, AdS(5)-CFT(4) solutions with a 4D Schwarzschild boundary metric were numerically constructed. We modify the boundary conditions to numerically construct large RSII static black holes with radius up to ~20?. For a large radius, the RSII solutions are indeed close to the associated AdS(5)-CFT(4) solution. 相似文献
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V. S. Buslaev Ya. Yu. Koptelov S. B. Levin D. A. Strygina 《Physics of Atomic Nuclei》2013,76(2):208-218
Based on a new method of the numerical construction of the three-body Schrödinger operator continuous spectrum eigenfunctions an analysis of the solutions of the problem of three identical particles on the axis with quickly decreasing repulsive pair potentials is offered. The initial problem is reduced to solving an inhomogeneous boundary problem for an elliptical partial differential equation in a twodimensional domain as a circle with radiation boundary conditions, with a ray approximation of the solution with diffraction corrections, contributing to a smoothness of a solution sought, being used. The approach offered allows a natural generalization for a case of slowly decreasing potentials of the Coulomb type and higher configuration space dimensions. 相似文献
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The asymptotic behavior of solutions of the Burgers equation and its generalizations with initial value-boundary problem on a finite interval with constant boundary conditions is studied. Since it describes a dissipative medium, any initial profile will evolve to a time-invariant solution with the same boundary values. Yet there are three distinctive asymptotic processes: the initial profile may regularly decay to a smooth invariant solution; or a Heaviside-type gap develops through a dispersive shock and multi-oscillations; or an asymptotic limit is a stationary ‘sawtooth’ solution with periodical breaks of derivative. 相似文献
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C.M. JUNGB.F. FEENY 《Journal of sound and vibration》2002,252(3):409-428
A one-dimensional elastic system with distributed contact under fixed boundary conditions is investigated in order to study dynamic behavior under sliding friction. A partial differential equation of motion is established and its exact solution is presented. Due to the friction the eigenvalue problem is non-self-adjoint. Mathematical methods for handling the non-self-adjoint system, such as the non-self-adjoint eigenvalue problem and the eigenvalue problem with a proper inner product, are reviewed and applied. The exact solution showed that the undamped elastic system under fixed boundary conditions is neutrally stable when the coefficient of friction is a constant. The assumed mode approximation and the lumped-parameter discretization method are evaluated and their solutions are compared with the exact solution. As a cautionary example the assumed modes approximation leads to false conclusions about stability. The lumped-parameter discretization algorithm generates reliable results. 相似文献