共查询到20条相似文献,搜索用时 15 毫秒
1.
In the present paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate, yet highly accurate secular equation of fourth-order in terms of the dimensionless thickness of the layer is derived. From the secular equation obtained, an approximate formula of third-order for the velocity of Rayleigh waves is established. The approximate secular equation and the formula for the velocity obtained in this paper are potentially useful in many practical applications. 相似文献
2.
加权残数配点法解正交各向异性板的积分方程 总被引:1,自引:0,他引:1
本文推导了一般各向异性板弯曲的积分方程,运用加权残数配点法求解了正交各向异性板弯曲的积发方程,本文将部分配点取在边界上,另一部分配点取在域外,只用关于找度的基本积分方程,而不用关于转角的补充积分方程,简化了方程求解和计算程序,由于正交各向异性板没有争析形式的、实用的基本解,本文提出了两种新的近似基本解;加权双三角级数;广义各向同性板解析形式的基本解和加权双三角级数的叠加,算例表明,本文提出的解法和近似基本解适用于各类边界条件的正交各向异性板,具有简单、可靠、精度高等优点。 相似文献
3.
考虑粘性作用情况下船在船厢中运动的水动力学分析 总被引:1,自引:1,他引:0
从根据浅水特性在垂直方向所平均化的N-S方程出发,利用有限元计算船舶进出船厢时的水动力学过程和船舶运动过程中的升沉、纵倾及船舶与厢底的最小间隙.由于在平均过程中保留了粘性项,同时产生了底摩擦项,使得到的数学方程更接近真实物理问题,另一方面也增加数值计算的稳定性.本文提出了随非惯性系一起运动的开边界的辐射条件.关于压力的求解,在船底与自由表面分别利用压力泊松方程求压力及自由表面利用连续方程求波高的求解方法.由针对三峡升船机的数值模拟的计算结果看,计算结果合理,计算方法稳定. 相似文献
4.
5.
LIQUID-SOLID COUPLED SYSTEM OF MICROPUMP 总被引:1,自引:0,他引:1
WU Jiankang Lu Lijun 《Acta Mechanica Solida Sinica》2006,19(1):40-49
This paper employs the integral-averaged method of thickness to approximate the periodical flows in a piezoelectric micropump, with a shallow water equation including nonlinearity and viscous damp presented to characterize the flows in micropump. The finite element method is used to obtain a matrix equation of fluid pressure. The fluid pressure equation is combined with the vibration equation of a silicon diaphragm to construct a liquid-solid coupled equation for reflecting the interaction between solid diaphragm and fluid motion in a micropump. Numerical results of a mode analysis of the coupled system indicate that the natural frequencies of the coupled system are much lower than those of the non-coupled system. The influence of additional mass and viscous damp of fluid on the natural frequencies of the coupled system is more significant as the pump thickness is small. It is found that the vibration shape functions of silicon diaphragm of the coupled system are almost the same as those of the non-coupled system. This paper also gives the first-order amplitude-frequency relationship of the silicon diaphragm, which is necessary for the flow-rate-frequency analysis of a micropump. 相似文献
6.
In a recent paper Gresho and Sani showed that Dirichlet and Neumann boundary conditions for the pressure Poisson equation give the same solution. The purpose of this paper is to confirm this (for one case at least) by numerically solving the pressure equation with Dirichlet and Neumann boundary conditions for the inviscid stagnation point flow problem. The Dirichlet boundary condition is obtained by integrating the tangential component of the momentum equation along the boundary. The Neumann boundary condition is obtained by applying the normal component of the momentum equation at the boundary. In this work solutions for the Neumann problem exist only if a compatibility condition is satisfied. A consistent finite difference procedure which satisfies this condition on non-staggered grids is used for the solution of the pressure equation with Neumann conditions. Two test cases are computed. In the first case the velocity field is given from the analytical solution and the pressure is recovered from the solution of the associated Poisson equation. The computed results are identical for both Dirichlet and Neumann boundary conditions. However, the Dirichlet problem converges faster than the Neumann case. In the second test case the velocity field is computed from the momentum equations, which are solved iteratively with the pressure Poisson equation. In this case the Neumann problem converges faster than the Dirichlet problem. 相似文献
7.
8.
The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper,
the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then
solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no
exact solution. Travelling wave solutions are also obtained. 相似文献
9.
Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations (PDEs) derived from the Landau-Ginzburg-Higgs equation. The numerical re- sults for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors. 相似文献
10.
变深度浅水域中非定常船波 总被引:1,自引:0,他引:1
以Green—Naghdi(G—N)方程为基础,采用波动方程/有限元法计算船舶经过变深度浅水域时非定常波浪特性.把运动船舶对水面的扰动作为移动压强直接加在Green-Naghdi方程里,以描述运动船体和水面的相互作用.以Series60 CB=0.6船为算例,给出自由面坡高,波浪阻力在船舶经过一个水下凸包时变化规律,并与浅水方程的结果进行了比较.计算结果表明,当船舶经过凸包时,波浪阻力先增加,后减少,并逐渐趋于正常.同时发现,当船速小于临界速度时(Fr=√gh<1.0),G—N方程给出的船后尾波比浅水方程的结果明显,波浪阻力也比浅水方程的结果有所提高,频率散射必须考虑.当船速大于临界速度时(Fr=√gh>1.0),G—N方程的计算结果与浅水方程差别不大,频率散射的影响可以忽略. 相似文献
11.
R.I. Leine 《International Journal of Non》2012,47(9):1020-1032
The aim of this paper is to give a Lyapunov stability analysis of a parametrically excited impact oscillator, i.e. a vertically driven pendulum which can collide with a support. The impact oscillator with parametric excitation is described by Hill's equation with a unilateral constraint. The unilaterally constrained Hill's equation is an archetype of a parametrically excited non-smooth dynamical system with state jumps. The exact stability criteria of the unilaterally constrained Hill's equation are rigorously derived using Lyapunov techniques and are expressed in the properties of the fundamental solutions of the unconstrained Hill's equation. Furthermore, an asymptotic approximation method for the critical restitution coefficient is presented based on Hill's infinite determinant and this approximation can be made arbitrarily accurate. A comparison of numerical and theoretical results is presented for the unilaterally constrained Mathieu equation. 相似文献
12.
S.
. Wille 《国际流体数值方法杂志》1994,18(12):1135-1151
In the present work a new iterative method for solving the Navier-Stokes equations is designed. In a previous paper a coupled node fill-in preconditioner for iterative solution of the Navier-Stokes equations proved to increase the convergence rate considerably compared with traditional preconditioners. The further development of the present iterative method is based on the same storage scheme for the equation matrix as for the coupled node fill-in preconditioner. This storage scheme separates the velocity, the pressure and the coupling of pressure and velocity coefficients in the equation matrix. The separation storage scheme allows for an ILU factorization of both the velocity and pressure unknowns. With the inner-outer solution scheme the velocity unknowns are eliminated before the resulting equation system for the pressures is solved iteratively. After the pressure unknown has been found, the pressures are substituted into the original equation system and the velocities are also found iteratively. The behaviour of the inner-outer iterative solution algorithm is investigated in order to find optimal convergence criteria for the inner iterations and compared with the solution algorithm for the original equation system. The results show that the coupled node fill-in preconditioner of the original equation system is more efficient than the coupled node fill-in preconditioner of the reduced equation system. However, the solution technique of the reduced equation system revals properties which may be advantageous in future solution algorithms. 相似文献
13.
Exact solutions to the KdV-Burgers'' equation 总被引:3,自引:0,他引:3
A. Jeffrey 《Wave Motion》1991,14(4):369-375
This paper presents two different methods for the construction of exact solutions to the KdVB equation. The first is a direct one based on a combination of solutions to the KdV equation and Burgers' equation. In this approach a number of unknown constants are involved, and it is shown that the equations leading to their determination are properly determined and are capable of solution.
The second method involves a series, and is essentially an extension of Hirota's method. This approach is capable of solving the KdVB equation exactly, and also of generalization to higher order equations with a KdVB-type nonlinearity. 相似文献
14.
This paper studies the partial differential equation with a small coefficient in the highest-order item. This kind of equation
is also named as boundary layer problem. The Burgers equation and modified Burgers equation are analyzed in this approach.
First, these equations are transferred into the strong nonlinear ones, and then the corresponding strong nonlinear equations
are solved based on the perturbation method. The results from the asymptotic method are comparable with those obtained from
numerical computation.
An erratum to this article is available at . 相似文献
15.
We consider in this paper the numerical solution of the Falkner-Skan differential equation, modelling under some similarity assumptions the boundary layer equation. We look for the extremal solution of this third order differential equation. The methods we use are basically the Newton method with a shooting process, which is coupled with a continuation method: they allow us to follow the solution arcs which contain regular and turning point solutions. 相似文献
16.
Axisymmetric problem of a nonhomogeneous elastic layer 总被引:3,自引:0,他引:3
Summary The paper deals with a theoretical treatment of elastic behavior for a medium with nonhomogeneous materials property, which
is defined by the relation , i.e., shear modulus of elasticity G varies with the dimensionless axial coordinate by the power product form, arbitrarily. Fundamental differential equation for such nonhomogeneous medium has been already
proposed in [5]. It is given by a second-order partial differential equation. However, it was found that the fundamental equation
is not sufficient in general to solve several kinds of boundary-value problems. On the other hand, it is shown in the present
paper making use of the fundamental equations system for a nonhomogeneous medium, which has been proposed in our previous
paper [7], it is possible to solve axisymmetric problems for a thick plate (layer) subjected to an arbitrarily distributed
load or a concentrated load on its surfaces. Numerical calculations are carried out for several cases, taking into account
the variation of the nonhomogeneous parameter m. The numerical results for displacements stress and components are shown in graphical form.
Accepted for publication 25 March 1997 相似文献
17.
Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading
《European Journal of Mechanics - A/Solids》2001,20(3):485-500
In this paper, the buckling problem of non-uniform columns subjected to axial concentrated and distributed loading is studied. The expression for describing the distribution of flexural stiffness of a non-uniform column is arbitrary, and the distribution of axial forces acting on the column is expressed as a functional relation with the distribution of flexural stiffness and vice versa. The governing equation for buckling of a non-uniform column with arbitrary distribution of flexural stiffness or axial forces is reduced to a second-order differential equation without the first-order derivative by means of functional transformations. Then, this kind of differential equation is reduced to Bessel equations and other solvable equations for 12 cases, several of which are important in engineering practice. The exact solutions that represent a class of exact functional solutions for the buckling problem of non-uniform columns subjected to axial concentrated and distributed loading are obtained. In order to illustrate the proposed method, a numerical example is given in the last part of this paper. 相似文献
18.
Propagation of SH waves in an irregular monoclinic crustal layer 总被引:2,自引:0,他引:2
A. Chattopadhyay S. Gupta V. K. Sharma Pato Kumari 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(12):989-999
The present paper discusses the dispersion equation for SH waves in a monoclinic layer over a semi-infinite elastic medium
with an irregularity. In the absence of the irregularity, the dispersion equation reduces to standard dispersion equation
for SH waves in a monoclinic layer over an isotropic semi-infinite medium. The dispersion curves for different size of the
irregularity are computed and compared for the half-space without any irregularity. It can be seen that the phase velocity
is strongly influenced by the wave number and the depth of the irregularity. 相似文献
19.
朱勇 《应用数学和力学(英文版)》1997,18(10):957-962
I.IntroductionZabuskyandKruskal(l965)foundthattwoKdVsolitarywavesofthesamemodekeeptheiroriginalshapesandspeedsafterstronginteractions,andcalledthesewavessolitons.However,solitaryx"avessometimestravelintwodimensionalspace,otherthaninonedimensionalspace.Mil… 相似文献
20.
Multi-symplectic method for generalized Boussinesq equation 总被引:1,自引:0,他引:1
The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations (PDEs) derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations. 相似文献