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梁方程
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  beam equation
     By using the degree theory on cone,the positive solutions are considered for the following elastic beam equation u~((4))(t)=f(t,u(t),u′(t),u″(t)),0≤t≤1,u(0)=u′(1)=u″(0)=u(1)=0,where nonlinear term contains first and second derivatives of unknown function.
     利用锥上的度数理论考察了非线性项含有未知函数的一、二阶导数的弹性梁方程u(4)(t)=f(t,u(t),u′(t),u″(t)),0≤t≤1,u(0)=u′(1)=u″(0)=u(1)=0的正解.
短句来源
     Abstract We discuss a particular beam equation, that is y (4) =αy-βy ″+f(y,y ″)+h(x) y(0)=y(1)=y ″(0)=y ″(1)=0 in which (α,β) is a pair of eigenvalue.
     讨论了一类非线性项比较特殊的双参共振梁方程边值问题,即y(4)=αy-βy″+f(y,y″)+h(x)y(0)=y(1)=y″(0)=y″(1)=0{其中(α,β)为特征值对。
短句来源
     Elastic Beam Equation Boundary Value Problems
     弹性梁方程边值问题
短句来源
     Initial Boundary Value Problem for an Nonlinear Beam Equation with Structural Damping
     具结构阻尼的非线性梁方程的初边值问题
短句来源
     This paper investigates the existence of one or more positive solutions of singular boundary value problems for a bending of an elastic beam equation. Sufficient conditions for the existence of one or more C~2[0,1] positive solutions as well as one or more C~3[0,1] positive solutions are given by means of a new technique which is based on the fixed point theorems on cones.
     研究了一类梁方程奇异边值问题一个正解或多个正解的存在性,利用锥上的不动点定理和新的技巧给出了C2[0,1]和C3[0,1]正解存在的充分条件.
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  beam equations
     This paper deals with the periodic Dirichlet boundary value problem for the system of semilinear beam equations with damping u tt +u xxxx +Bu t=Au+g(t,x,u)+h(t,x).
     本文讨论可能带阻尼项的半线性梁方程系统 utt+ uxxxx + But=Au + g( t,x,u) + h( t,x)的周期边值问题 .
短句来源
     The Chaotic Motion on 5 Order Nonlinear Elastic Beam Equations(Ⅰ)
     五次非线性弹性梁方程的混沌运动(Ⅰ)
短句来源
     Existence Theorems of Nonlinear Elastic Beam Equations with Fixed End and Movable End
     一端固定一端活动的非线性弹性梁方程的存在定理
短句来源
     Positive Solutions to One Class of Classical Nonlinear Elastic Beam Equations
     一类经典非线性弹性梁方程的正解
短句来源
     A Existence Result for System of Semilinear Beam Equations with Damping at Nonresonance
     非共振带阻尼半线性梁方程系统的存在性结果
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  “梁方程”译为未确定词的双语例句
     This paper deals with multiplicity results for nonlinear elastic equations of the type where e∈L ̄2(0,1), g:[0.1] ×R×R→R is a bounded continuous function,and the pair (α_1.β_1)satisfies and for all k∈N
     本文研究一类弹性梁方程边值问题的可解性及多解的存在性,其中e∈L ̄2(0.1),而g:[0,1]×R×R→R为连续有界函数,特征对(α_1,β_1)满足及
短句来源
     By using Williams\|Leggett's theorem, the existence of three positive solutions of the fourth\|order boundary value problem y″″(x)-f(y(x))=0, y(0)=y(1)=y′(0)=y′(1)=0 is obtained, which describes the deformations of elastic beam whose both end\|points are fixed.
     利用 Williams- Leggett定理 ,得到了两端固定的弹性梁方程 y″″( x) - f( y( x) ) =0 ,y( 0 ) =y( 1 ) =y′( 0 ) =y′( 1 ) =0三个正解的存在性结果 .
短句来源
     In this paper,we study the existence of the equation y″″( x) =f ( x,y( x) ) with y( 0 ) =y( 1 ) = y′( 0 ) =y′( 1 ) =0 .We show the existence of positive solutions and multiple positive solutions by a simply application of Fixed Point Theorem in cone. Which describs the deformations of an elastic beam whose both end-points are fixed.
     在边值条件 y( 0 ) =y( 1 ) =y′( 0 ) =y′( 1 ) =0下 ,研究方程 y″″( x) =f ( x,y( x) )的正解存在性 ,给出两端固定的弹性梁方程正解及多个正解存在的充分条件
短句来源
     Existence Theorems of Solution to a Class of Nonlinear Elastic-Beam Equation
     一类非线性弹性梁方程解的存在定理
短句来源
     Global Dynamics on the Equations of Nonlinear Viscous-elastic Beam
     非线性粘弹性梁方程的整体动力学
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  beam equation
Traveling wave solutions to beam equation with fast-increasing nonlinear restoring forces
      
An existence theorem of positive solutions for elastic beam equation with both fixed end-points
      
Backward wellposedness of nonuniform Timoshenko beam equation
      
Boundary feedback control of elastic beam equation with structural damping and stability
      
As an application, the existence of positive solutions for some fourth-order beam equation boundary value problems is obtained.
      
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  beam equations
In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.
      
The applications to the higher dimensional beam equations and the higher dimensional Schr?dinger equations with nonlocal smooth nonlinearity are also given in this paper.
      
The possibilities to modify the through-thickness approximations are demonstrated on the beam equations.
      
The present semi-discrete beam equations assume the form of differential-algebraic equations which are discretized in time.
      
We consider extensible beam equations, Timoshenko beam equations and the system of coupled beam equations.
      
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In this paper, the distribution of subsoil reaction of beam is illustrated by a diagram of broken-lines at equal intervals, the interfaces are taken as deformation compability points, where the subsoil settlements are denoted by the equivalent mean values obtained from the actual settlement area of the sections. The general normal equation for the subsoil reaction intensity at the interfaces under compatible deformation is established by systemizing the individual interface deflections obtained from initial...

In this paper, the distribution of subsoil reaction of beam is illustrated by a diagram of broken-lines at equal intervals, the interfaces are taken as deformation compability points, where the subsoil settlements are denoted by the equivalent mean values obtained from the actual settlement area of the sections. The general normal equation for the subsoil reaction intensity at the interfaces under compatible deformation is established by systemizing the individual interface deflections obtained from initial parameter equations of deflection, taking account of the deformation continuity condition between beam and subsoil.Some numerical tables are given for the general equations of geometrically symmetrical beams of uniform and variable cross-sections.An example is given and compared with the hinged-bar method.

本文用等区段的折线图形表示地基反力分布,并取分段点为变形协调点。协调点处的地基沉陷采取用应力面积法按梁宽范围内实际沉陷面积求得的等代均值沉陷。对梁逐段利用初参数表示的挠度曲线方程计算分段点挠度时,引入梁与地基间的变形连续条件,归纳整理后,得到解算各分段点处地基反力强度的变形协调法方程通式。文中制备了经常遇到的常截面和变截面对称情况地基梁方程通式表格,供实际使用,并附实例对本法和链杆法结果作了比较。

Based on Timoshenko's beam theory, the governing equations and boun-dary conditions of static and dynamic analysis of laminated beams, which can be reduced to the equations of Timoshenko beam in the cass of single layer, are established in this paper by using effective stiffness method and Hamilton's principle, and the analytic solution and numerical results of some problems of laminated beams are obtained by employing the governing equations.

本文在铁摩辛柯梁理论的基础上,应用迭合刚度的方法和Hamilton原理,导出了适合于层合梁静力分析和动力分析的控制方程组(在单层情况下,将退化成Timoshenko梁的方程)及边界条件。而且,利用所获得的控制方程,求得了层合梁一些问题的解析解及相应的数值结果。

On the basis of solving the lateral force of bit by using crossbar deflection continuousbeam equation at home and in the light of Chinese and foreign shareeapitals' practical drilling situation and drilling tool assembly characteristics in the Bohai Sea, this paper gives the lateral force of bit and its solution method by the combined action of transverse uniform load and axial tensile force. Through verification in practice, it is closer to the practical lateral force of bit.

本文在国内应用纵横弯曲连续梁方程求解钻头侧向力的基础上,结合渤海地区中外合资的钻井实况及钴具组合特点,提出了在横向均布载荷和轴向拉伸力联合作用下的钻头侧向力及其求解的方法。此方法通过实践验证,更接近实际的钻头侧向力。

 
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