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1.
Lindelf’s equation is derived by using the Vakonomic model,which shows that Lindelf’s work coincides with Vakonomic model. Chaplygin’s equation is derived by using Chetaev’s model, which shows that Chaplygin’s work coincides with Chetaev’s model. On basis of these, by improving the expressions of Chaplygin’s equation and Lindelf’s equation, the reasonable transition from Chaplygin’s equation to Lindelf’s equation is realized, the reasonable transition from Lindelf’s equation to Chaplygin’s equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev’s model are complementary to each other, Lindelf’s work and Chaplygin’s work are complementary to each other too.  相似文献   

2.
I.IntroductionSinceE.T.Whittaker.proposedfoestabilit}'problellll'lofnonholononlicsystemsin1904forthefirsttime,thescholarsathomeandabroad11a\'emadealotofresearchesontheequilibriunlstabilityoflinearand11olllinearnonllolollolnicsystems,andhaveobtainedaseriesofimportantresultslZ--7].Hobbled'er,theexpositionandapplicationrelatedtoLagrange'stheorenlinthestabilityanalysisfornonholonomicsystemsisseldonlseenuptonow.Althoughitwasmentionedinreference[3].aspecialdiscussionhasnotbeencarriedoutyet.Asafam…  相似文献   

3.
The new variational principle of Gauss’s form of nonlinear nonholonomicnonpotential system relative to non-inertial reference frame is established byconstructing generalized inertial potentials.Noether’s theorem and Noether’s inversetheorem of the system above is presented and proved.Finally,one example is given toillustrate the application.  相似文献   

4.
By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given.  相似文献   

5.
I.IntroductionInl927,AmericanmathematicianG.D.Birkh0ffgaveakindofequationsofdynamicswhichweremoregeneralthantheHamilton'sequationsinhiswork"DynamicalSystems-l'].TheequationsarecalledBirkhofCsequationssuggested.byAmericanphysicianR.M.SantiIIiinl978[2j.Inl9…  相似文献   

6.
IntroductionInmodelingfordynamicsystem ,weoftengetnonlinearitymathematicalequation .Itisdifficulttogiveoutpureanalyticresolutiontotheequation ,mostanswersworkedoutaredependentuponnumericalsolution .Hence,itisextremelyimportanttofindoutasuitableapproximat…  相似文献   

7.
I.IntroductionThePade'approximationisatypeofrationalfractionapproximationtoafunction.LetfberepresentedbyapowerseriesthenUI(x)/Vm(x)issaidtobethei,mPade'approximanttof(x),denotedby[l/m],ifUI(x)isapolynomialofdegreeatmostl,Vin(x)isapolynomialofdegreeatmostnlandf(x)~UI(x)/Vm(x)=O(xl " ')(l.2)Ifl=m,thePade'approximantiscalledadiagonalone.APade'approximantisusefulinthatitmayapproximatelyrepresentafunctiononasetlargerthantheintervalofconvergenceofitsTaylorseries(l.l)if'31.Theorthogonalpolynom…  相似文献   

8.
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot’s equations for saturated porous media. The Darcy’s laws of unsaturated soil were proved. It is shown that Biot’s equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.  相似文献   

9.
The invariance and conserved quantities of the nonconservative nonholonomic systems are studied by introducing the infinitesimal transformations in phase space.The Lie’s symmetrical determining equations are establish ed.The Lie’s symmetrical structure equation is obtained.An example to illustrate the application of the result is given.  相似文献   

10.
In this paper an accurate solution for the thick rectangular plate with free edges laid onelastic foundation is presented.The superposition method of trigonometric series is used.The method can solve this kind of plates directly and simply.Its results completely satisfythe boundary conditions of the four free edges and nicely agree with the solutions by WangKe-lin and Huang Yi.  相似文献   

11.
龙门山地震带的地质背景与汶川地震的地表破裂   总被引:4,自引:0,他引:4  
龙门山位于青藏高原与扬子地台之间, 系由一系列大致平行的叠瓦状冲断带构成, 自西向东发育汶川—茂汶断裂、映秀—北川断裂和彭县—灌县断裂,并将龙门山划分为3个构造地层带,分别为变形变质构造地层带(主要由志留系—泥盆系浅变质岩和前寒武系杂岩构成)、变形变位构造地层带(主要由上古生界—三叠系沉积岩构成)、变形构造地层带(主要由侏罗系至第三系红层和第四纪松散堆积构成)。
龙门山断裂带属地震危险区,3条主干断裂皆具备发生7级左右地震的能力,其中映秀—北川断裂是引发地震的最主要断层,据对彭县—灌县断裂青石坪探槽场地的研究结果表明,在该断裂带上最晚的一次强震发生在930±40a.B.P.左右,据此,可以初步判定,这3条主干断裂的单条断裂上的强震复发间隔至少应在1000a左右,表明龙门山构造带及其内部断裂属于地震活动频度低但具有发生超强地震的潜在危险的特殊断裂,以逆冲-右行走滑为其主要运动方式。
汶川地震属于逆冲—走滑型的地震,地表破裂分布于映秀—北川断裂带和彭县—灌县断裂带上。根据近南北向的断裂(小鱼洞断层、擂鼓断层和邓家坝断层)和地表断距可将映秀—北川断层的地表破裂带划分为两个高值区和两个低值区,两个高值区分别位于南段的映秀-虹口一带和位于中北段的擂鼓—北川县城—邓家坝一带;两个低值区分别位于中南段的白水河—茶坪一带和北段的北川黄家坝至平武石坎子一带,两个高值区分别与小鱼洞断层和擂鼓断层相关。根据保存于破裂面上的擦痕,可将该地震破裂过程划分为两个阶段,早期为逆冲作用,晚期为斜向走滑作用,其与地壳增厚构造模式和侧向挤出摸式在青藏高原东缘的推论具有不吻合性。鉴于龙门山的表层运动速率与深部构造运动速率具有不一致性,初步探讨了龙门山地区的地表过程与下地壳流之间的地质动力模型,认为下地壳物质在龙门山近垂向挤出和垂向运动,从而造成导致龙门山向东的逆冲运动、龙门山构造带抬升和汶川特大地震。在此基础上,根据汶川地震所引发的地质灾害,对地震灾后重建提出了的几点建议。  相似文献   

12.
平移断层的倾角对地震产生的影响   总被引:1,自引:0,他引:1  
利用边界单元法和滑移弱化摩擦本构关系分析了平移断层上地震的产生。从依赖于速率和状态的摩擦本构关系出发,通过忽略速度的影响得到了滑移弱化摩擦本构关系。建立了两种本构关系之间的联系,使得在两种模型中可以使用共同的参数。通过将地球表面模拟成一个包含在无穷大弹性介质中的无穷大裂纹,已有的边界积分方法可以直接用来分析断层的滑移。由于断层上的摩擦本构关系的非线性,得到的方程也是非线性的,采用牛顿迭代法进行求解。通过数值计算得到了平移断层上滑移位移、速度及摩擦力的分布规律。考察了平移断层的倾角对地震产生的影响,计算结果表明断层的倾角越小,地震产生的位置离地球表面越近且地震产生所需滑移的时间越短。  相似文献   

13.
在地震作用下结构的模糊随机振动   总被引:5,自引:0,他引:5  
地震干扰不仅具有明显的随机性,而且由于地震烈度和场地土分类本身定义不明确而带来强烈的模糊性,本文在上述模糊性和随机性的基础上,建立了地震地面运动含模糊参数的平稳过程简化模型,研究了在其作用下单自由度滞后体系的模糊随机振动的分析与计算方法,由于问题的复杂性和某些数学上的困难,文中作了一些必要的简化,以作为模糊随机振动理论的初步探讨。  相似文献   

14.
Mircea Grigoriu 《Meccanica》1995,30(1):105-124
Probabilistic models of seismic ground acceleration are reviewed. The review includes uniformly modulated, oscillatory, amplitude and phase modulated, ARMA, and other processes. Moreover, a novel and general nonstationary Gaussian model is presented. The model consists of a superposition of harmonics with correlated Gaussian amplitudes. The harmonic frequencies and the amplitude probabilistic characteristics depend on the duration and the correlation of the target seismic ground motion, respectively. The model can be generalized to represent the seismic ground motion at two or more sites. Methods are also presented for generating realizations of the probabilistic models in the paper. The methods are applied to demonstrate the generation of artificial seismic ground motions and to evaluate the usefulness of various probabilistic models in earthquake engineering.Invited lecture presented at the 6th Italian National Conference on Earthquake Engineering, Perugia, 13–15 October, 1993  相似文献   

15.
地震动是工程结构地震反应研究与抗震设计的基础,要分析工程系统的性能,必须要把地震动作为随机过程来建立可靠的模型。本文通过对非平稳过程演变谱的研究,给出双调制函数,建立了双调制非平稳地震地面运动模型。结合双调制函数和三角级数法生成人工地震波,通过对人工波频率和强度的非平稳性研究验证了双调制模型的有效性。同时本文给出了双调制非平稳地震激励的结构响应虚拟激励算法,得到响应的时变功率谱。分析表明,该模型具有明确的物理意义,且更符合实际,为结构抗震可靠性分析提供了一种较好的地震动模型。  相似文献   

16.
This paper is a part of series works for discussing the “auto-destruction effects” of general nonlinear evolutional equations. The blown-up of Navier-Stockes equation is discussed in references [1,2]. Some expansion is made in this paper, and the blown-up of order-1 or 2 models and the “rebel travelling” of complex model of poly-order are discussed. The results indicate that “semi-rupture” appears for some models on specific condition: the blown-up appears during the whole evolution. For fluid, however, the weakly-nonlinear model is of more artificiality and there is much room for arguing about the smoothing scheme of the numerical integral on the basis of continuous thinking and so on.  相似文献   

17.
The purpose of this paper is to study the dynamic behavior of soft ground including a porous layer by considering the porosity change. In order to take the porosity change into account, the concept of the volume fraction, which has been proposed in continuum mechanics, is introduced. The constitutive equations presented by Bowen are applied to the analysis of the porous media. According to Bowen's theory, the porosity is considered as a variable called the volume fraction and has its own constitutive equation. The constitutive equation of the volume fraction has thermoelastic equation coefficients and is determined by the strains of the solid and the fluid. This means that the compressibilities of the solid and the fluid are considered. When the special condition is assumed, Bowen's theory can contain Biots's theory, which has been applied in earthquake engineering. The wave propagation in the ground including a porous layer, modeled by Bowen's theory, is studied and compared with that of Biot's theory. One-dimensional attenuation and surface amplitude are calculated. The effect of the volume fraction is discussed with respect to the compressibilities of the solid and the fluid.  相似文献   

18.
地震是影响斜(边)坡、滑坡稳定性的主要因素之一。白龙江上某大型滑坡经顺层斜坡发生倾倒变形而成,天然状态下处于基本稳定状态,在“5.12″汶川地震作用下,该滑坡有整体复活迹象,其后缘周界形成了连续贯通的拉裂缝、错动台阶,尤其是滑坡下游区变形拉裂较明显。本文以该滑坡在地震作用下发生复活为例,在分析滑坡所处的区域地质条件的基础上,详细研究了滑坡的基本特征以及地震作用导致滑坡复活的现象、特征,然后利用FLAC3D 软件内置动力分析模块对该滑坡复活机制进行了分析、研究。数值分析表明,地震作用下滑坡变形破坏受坡体形态的影响较显著,滑坡对地震波具有明显的放大效应; 同一地震动条件下,滑坡体相对周边处于稳定状态基岩边坡对地震更为敏感。这较好地解释了“5.12″汶川地震作用下,该滑坡的复活原因。  相似文献   

19.
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   

20.
In response to the challenge inherent in classical high-dimensional models of random ground motions, a family of simulation methods for non-stationary seismic ground motions was developed previously through employing a wave-group propagation formulation with phase spectrum model built up on the frequency components' starting-time of phase evolution. The present paper aims at extending the formulation to the simulation of non-stationary random seismic ground motions. The ground motion records associated with N—S component of Northridge Earthquake at the type-II site are investigated. The frequency components' starting-time of phase evolution of is identified from the ground motion records, and is proved to admit the Gamma distribution through data fitting. Numerical results indicate that the simulated random ground motion features zero-mean, non-stationary, and non-Gaussian behaviors, and the phase spectrum model with only a few starting-times of phase evolution could come up with a sound contribution to the simulation.  相似文献   

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