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1.
本文给出在非线性Rayleigh阻尼作用下,由水平地震激发的水库内动水压力变化全过程的解析解:在激发初期其幅值较小,可用小参数法使控制方程线性化,从而求得各阶渐近控制方程的解析解;当动水压力的幅值增大到小参数展开不适用时,用van derpol法求得非线性控制方程的渐近解,从而显示了动水压力的幅值从有序变化到发生突然跳跃的多值性的非线性本质。  相似文献   
2.
本文考虑在Rayleigh阻尼作用时,沿裂缝长的边界上有剪应力作用,使裂缝一端失稳而产生快速扩展(即Ⅱ型破裂)问题.应用奇异摄动理论及广义富氏级数,给出这个非线性断裂动力学问题的逐次逼近解.较之已有成果,本文考虑了非线性阻尼并给出各级近似解的显式.  相似文献   
3.
Nomenclature x , y dimensionalabscissaandordinaterespec tively (m)l halflengthofthecrack (m)δ halfwidthofthecrack (m) t dimensionaltimevariable (s) w dimensionalverticaldisplacement (m) A/ ρ oneofthedimensionalparameterinRayleighdampingformula (s- 1 ) B/ ρ theotherdi…  相似文献   
4.
This problem is solved by dividing the quadratic yielding cri-terion into two linear partial differential equations.With thehelp of Cauchy’s integral.these two linear equations can be easilysolved.An example is given to show the calculation of the stresscomponents in the plastic domain and the determination of equationof the boundary line between the plastic and elastic domains.  相似文献   
5.
This paper points out the former work does not fulfill the boundaryconditions that the concentrated force at the four corner points should notexist.Therefore,Ritz method adopted by the author concerned in the illus-trative example will not be convergent in the best way.Moreover,Garlerkinmethod which is illustrated in this paper may carry out incorrect results ifwe apply its formulae.We have proved that the boundary conditions whichgovern the concentrated force equal to zero at the four corner points areindispensable if the problem is properly set.  相似文献   
6.
固定边矩形弹性薄板卡门大挠度与大振幅方程组的逼近解   总被引:2,自引:0,他引:2  
1.大挠度问题图1所示的固定边矩形弹性薄板,其大挠度问题由下列卡门方程组定义:按文献考虑以下边界条件:当x=0及x=a 时:W=0(无挠度);((?)W)/((?)x)=0(无转角) (4)((?)~3φ)/((?)x~3) (2 μ)((?)~3φ)/((?)x(?)y~2)=0 (沿板边无法向位移) (5)((?)~2φ)/((?)x(?)y)=0 (没有阻止沿板边切向位移的力) (6)当y=0及y=b 时也有相同意义的边界条件如下:  相似文献   
7.
With non-linear Rayleigh damping formula-we describe the exciting process when therupture velocity is low and the attenuation process when the rupture velocity reachesa certain high value.Assuming the medium of the earth crust is homogeneous and isotropiclinear Voigt viscoelastic body,with small parameter perturbation method to deducethe non-linear governing partial differential equations into a system of asymptoticlinear ones,we solve them by means of generalizedfourier serier with moving coordinatesas its variables,thus transform them into non-homogeneous methieu equations.At lastMathieu equations are solved by WK3J method.  相似文献   
8.
If a plate solution is known which has the same boundary and loading conditions with ashallow shell,the solution of that shell can be reduced to a non-homogeneous Helmholtz’sequation in complex domain.Two examples are given to illustrate our method.  相似文献   
9.
非线性阻尼作用下标准线性固体粘弹性Ⅲ型破裂的解析解   总被引:3,自引:0,他引:3  
把非线性Rayleigh阻尼引入标准线性固体粘弹性介质的Ⅲ型破裂的控制方程中,此方程是一个偏微分积分方程;首先设法消去积分项,得到一个三阶非线性偏微分方程,然后用小参数摄动法,得出线性化的各阶渐近控制方程;把每一个具有变系数的三阶线性控制方程分解为弹性部分及剩余部份,而前者的解析解为已知,后者是一个二阶变系数线性偏微分方程;它化不成Mathieu方程,也化不成Hill方程,故采用WKBJ的方法得出  相似文献   
10.
用非线性Rayleigh阻尼公式描述初始破裂时有激发而加速,至一定高速时有衰减而止裂。视介质为匀质各向同性的Voigt线性粘弹性体,用小参数摄动法把滑开型(Ⅱ型)破裂定义的非线性偏微分方程组线性化,得出各次逼近解所定义的线性方程组,再用动坐标表示的广义Fourier级数把问题简化为非齐次的Mathieu方程,用WKBJ法给出问题在稳定区域的渐近解。  相似文献   
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