弦振动方程

弦振动方程Cauchy问题广义解的结构

Structure of the Generalized Solution of the Cauchy Problem to the Vibrating String Equation

然后以求解非线性弦振动方程和组合KdV方程为例，指出其中的展开函数应该满足的两个条件。

That two conditions of the expansion functions should be satisfied was presented by solving the nonlinear vibrating string equation and the combined KdV equation .

一般弦振动方程GAUCHY问题的Fourier级数解法

The Fourier Series Solution of the CAUCHY Problem for General Chord Oscilating Equations

进而，应用不涉及群论的CK直接方法得到了非线性弦振动方程的更为一般的相似约化。

The more general similarity reductions are obtained by the CK direct method , this method does not require the Lie group theoretic techniques .

本文利用Fourier分析方法，讨论了一类由混合边界弦振动方程决定的分布参数控制系统的控制函数集。

By means of Fourier analysis , the control function sets of a kind of distributed parameter control systems , which are determined by mixed-end points string vibration equation were discussed .

利用改进的tanh函数法，将非线性弦振动方程化为一阶非线性常微分方程组。

With the improved tanh-function method , the equations of nonlinear vibrating string are reduced to first-order nonlinear ordinary differential equations .

非线性弦振动方程的精确解

The exact solutions to the equation of nonlinear vibrating string

非线性弦振动方程的新类孤子解

New Soliton-like Solutions for the Equation of Nonlinear Vibrating String

有界弦振动方程与有界杆热传导方程三类边界问题的研究

Equations of Bounded sinusoidal vibrations Equations of Bounded Thermal Conduction in strips or Bars

解弦振动方程初始条件的反问题

Solution of the inverse problem for an initial condition in a string vibrating equation

作为应用，特别研究了拟线性弦振动方程带第三类边界条件的精确边界能控性。

Especially , using a boundary control on one end , we get exact boundary controllability for the quasilinear vibrating equation with boundary condition of the third type on another end .

利用改进的双曲函数法，研究了非线性弦振动方程，得到了若干其它方法不曾给出的多种新形式的类孤子解。

With the further improved hyperbolic functions method , the new exact soliton solutions for the equation of nonlinear vibrating string are obtained , which include kink soliton solution and new soliton-like solutions .

本文就有界弦振动方程与有界杆热传导方程的第三类边界问题进行讨论。

This paper devotes discussions pertaining to the equations of bounded sinusoidal vibrations and the equations of bounded thermal conduction along a strip with respect to the category of the third boundary value problems .

在现行的数学物理方法教材中，数理方程只涉及到一维的弦振动方程、杆振动方程和热传导方程等，对二维薄膜的振动只作了扼要的介绍。

However , the current teaching materials of mathematical equations only include 1D string vibration equation , pole vibration equation and heat conductivity equation while only a brief introduction is given to 2D thin film vibration .

在对拟线性弦振动方程带第三类边界条件的精确边界能控性研究中，出现了一种带非局部边界条件的一阶拟线性双曲组的混合初-边值问题。

In the study of exact boundary controllability for the quasilinear vibrating string equation with boundary condition of the third type , we meet a kind of nonlocal mixed initial-boundary value problem of first order quasilinear hyperbolic system .

解析函数的实部和虚部均满足拉普拉斯方程，本文仿效利用弦振动方程的达朗伯解法来求解二维拉普拉斯方程，得出了由给定解析函数的实部或虚部求对应解析函数的十分简便的方法。

In this paper , we Solve two-dimension Laplace equation by the Similar way of Solving d ' Alembert spring-Vibrating equation , through given real or image Part of analytic function which Satisfies Laplace equation and therefore , a simpler method is obtained .

基于轴向运动弦线横向振动方程和边界条件，通过Laplace变换导出频率域中的控制方程，并将该控制方程和边界条件用状态变量表示。

The Laplace transform was applied to change the governing equation of the transverse vibration of axially moving strings from time domain into frequency domain . The transformed governing equation and boundary conditions were expressed in terms of the state variables .

研究了一类关于受摩擦力作用且具有固定端点的有界弦振动的波动方程，证明了在满足一定条件时其能量的衰减性，并由此推导出在外力作用下方程解的性态。

To bounded vibrating string equation by friction and have fixed end point , satisfied certainty condition of wave equation , proved that its energy was reduced , and pushed out the properties of equation solutions .

由哈密顿最小作用量原理导出弦的大挠度振动方程，用奇异摄动理论求出挠度频率的第二阶近似解，并对频率的相对误差进行讨论。

Big Amount of deflection vibration equation of chord is educed from Hamilton smallest function theory , Use singular ingestion theory to get the second approximate explanation of amount of deflection frequency , and analysis the relation error of frequency .