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In this paper we solve axisymmetric problems by stress and deduce a series of valuable general solutions by unified method.
Some of them are well-known solutions, and others have not appeared in the literature. We also prove the completeness of these
general solutions. 相似文献
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The influence of the different distributed phase-randomized on the experimental data obtained in dynamic analysis 总被引:4,自引:0,他引:4
I.IntroductionSince1980manyscholarsaroundtheworldhavepaidmoreattentiontothequestionsoftimeseries.Inthereallifesometimeseriesrepresentthecharacterthatisdeterminedasrandomprocesstimeseries,andothersrepresentthecharacterthatisdeterminedasnonlinearchaotictilneseries.Soitisveryimportanttodistinguishthepropertyoftherealtimeseries.Ref.[11gaveustheftlndamentalmethodtodifferentiatethenonlinearchaotictimeseriesfromrandomtimeseries(thatiscalledphase-randomizedmethod).Ref.[2]gaveusthecalculatingmethodofc… 相似文献
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The matric algorithm of Lyapunov exponent for the experimental data obtained in dynamic analysis 总被引:2,自引:0,他引:2
IntroductionChaosisanirregularphenomenongeneratedbynonlinearmodels.Itextensivelyexistsinnature.Whenarealirregulartimeseriesisgiven,peoplewillspontaneouslyaskthequestion:whetherthetimeseriesisprocessasrandomorasdeterministicchaos.Ifthetimeseriesisther… 相似文献
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Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control 总被引:5,自引:0,他引:5
The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincaré maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries. 相似文献
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Alexey Bobtsov Nikolay Nikolaev Olga Slita 《应用数学和力学(英文版)》2007,28(7):893-900
Analytical conditions and practical methods of their realization are proposed to solve a problem of a command signal tracking for a nonlinear disturbed system.Non- linear disturbed plants consisting of linear dynamic block and nonlinear block in feedback are considered.Nonlinear part of the plant and disturbance are unknown and bounded. The paper illustrates a possibility of applications of proposed algorithms to control libra- tion angle of satellite. 相似文献
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Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis 总被引:2,自引:0,他引:2
In this paper, the planar dynamics of a nonlinearly constrained pipe conveying fluid is examined numerically, by considering the full nonlinear equation of motions and a refined trilinear-spring model for the impact constraints—completing the circle of several studies on the subject. The effect of varying system parameters is investigated for the two-degree-of-freedom (N=2) model of the system, followed by less extensive similar investigations forN=3 and 4. Phase portraits, bifurcation diagrams, power spectra and Lyapunov exponents are presented for a selected set of system parameters, showing some rather interesting, and sometimes unexpected, results. The numerical results are compared with experimental ones obtained previously. It is found that in the parameter space that includesN, there exists a subspace wherein excellent qualitative, and reasonably good (N=2) to excellent (N=4) quantitative agreement with experiment. In the latter case, excellent agreement is not only obtained in the threshold flow velocities (u) for the key bifurcations, but the inclusion of the nonlinear terms improves agreement with experiment in terms of amplitudes of motion and by capturing features of behaviour not hitherto predicted by theory. 相似文献
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黄蔚章 《应用数学和力学(英文版)》1997,18(6):575-584
I.Intr0ducti0n'Manyresultshavebeeng0tinstudyingthesingu1arperturbation0fboundaryvalueproblemfornonlinearsystemeg#=j(t,g,y',8)(l.l)bythemethodandthetechniqueofdiagonalizationl'~'l.Thepapersarebasedonsucha.conditionthattheeigenvaluesofJacobimatrixlu'offwit… 相似文献
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陈松林 《应用数学和力学(英文版)》1996,17(11):1095-1100
SINGULARPERTURBATIONFORANONLINEARBOUNDARYVALUEPROBLEMOFFIRSTORDERSYSTEMChenSonglin(陈松林)(ReceivedApril8,1984;RevisedApril15,19... 相似文献
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Threshold value for diagnosis of chaotic nature of the data obtained in nonlinear dynamic analysis 总被引:8,自引:0,他引:8
I.IntroductionInreallife,inengineering,innature,andinthesociety,thereexisteverykindoftimeseriesproblems.Becausenonlinearfactorsareextensivelyimplicatedilltiledynamicsystemsofvariousfields,thebehaviourofthesystemscantakethecomplicatedanddiverseforms.Atpresent,twodifferentmethodsareusedtostudytheproblemoftinleseries.Ollemethodistoadoptthetheoryofrandomprocessonthebasisofprobabilitytheory.Andthistheoryisusedtofoundthesystemlinearmodel.Thismethodhasalreadybeenstudiedperfectly.Forexample,determin… 相似文献
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The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion. 相似文献
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The state space reconstruction technology of different kinds of chaotic data obtained from dynamical system 总被引:7,自引:0,他引:7
Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the
practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the
ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical
data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate
the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the
basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors
of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different
kinds of chaotic data obtained from dynamical system has also been discussed in detail.
The project supported by the National Natural Science Foundation of China (19672043) 相似文献
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The dynamics of a panel forced by transverse loads and undergoing limit cycle oscillations and chaos is investigated. The nonlinear von Karman plate theory is used to obtain a model for healthy and damaged panels. Damage is modeled by a loss of stiffness in a portion of the plate. The presence of low levels of damage is identified by using an external nonlinear excitation and analyzing the attractor of the resulting dynamics in state space. Most of the current studies of such problems are based on linear theories and linear structures. In contrast, the results presented are obtained by using and enhancing nonlinear and chaotic dynamics, and have the advantage of an increased accuracy in detecting damage and monitoring structural health.An earlier version of this paper was presented at the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, California, April 2004. 相似文献
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为了克服粒子退化现象,将奇异值分解Unscented卡尔曼滤波(SVD-UKF)和粒子滤波相结合,利用SVD-UKF得到粒子滤波的重要性分布,提出了一种改进的粒子滤波算法。该算法将最新观测信息引入到状态估计中,不但使估计精度优于常规的粒子滤波,而且继承了奇异值分解数值稳定性好的优点,因而具有较强的鲁棒性。将该算法应用到列车组合定位系统,与经典粒子滤波进行仿真比较,结果表明,提出的改进粒子滤波算法导航定位精度高,算法稳定性好。 相似文献
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一类弱非线性振动问题的插值摄动解法 总被引:8,自引:0,他引:8
用插值摄动法[1]求解一类有阻尼的弱非线性振动问题。算例表明,当小参数很小时,本文结果和多尺度法的一级近似结果十分接近。当小参数不是很小时(即接近于强非线性振动时),本文结果,仍然相当准确,并优于多尺度法的一级近似结果。 相似文献
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IntroductionDynamicsanalysisofcrackedrotorwhenignoringnonlinearwhirlingcouldbefoundinmanyReferences [1 -3 ] .Nonlineardynamicsofcrackedrotorwithwhirlinghavebeenstudiedbasedonformerscholar’swork[4 ]andthewhirlingequationsofacrackedshafthavebeenestablished .Th… 相似文献
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IntroductionOscillationisanimportantfactortosecurityofpowertransmissionsystems.Exceptforperiodicoscillationwhentheyarerunningnormally,sometimespowersystemsdisplaychaoticphenomena[1],oscillatingirregularly,suddenly,andwithoutperiodicity.Seriouscasesco… 相似文献