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81.
82.
参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉 总被引:4,自引:0,他引:4
在本文里我们首先研究了具有Z_2-对称性的范式理论和退化向量场的普适开折理论。然后利用上述理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,从而解决了当解具有两个零特征值时解的稳定性问题。最后利用Melnikov方法求出了参数平面上的同宿分叉曲线,讨论了全局分叉的存在性。 相似文献
83.
本文应用Normal Form理论和退化向量场的普适开折理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,用Melnikov方法讨论了全局分叉的存在性. 相似文献
84.
This paper presents stability and convergence results on a novel approach for imposing holonomic constraints for a class of multibody system dynamics. As opposed to some recent techniques that employ a penalty functional to approximate the Lagrange multipliers, the method herein defines a penalized dynamical system using penalty-augmented kinetic and potential energies, as well as a penalty dependent constraint violation dissipation function. In as much as the governing equations are not typically cocreive, the usual convergence criteria for linear variational boundary value problems are not directly applicable. Still numerical simulations by various researchers suggest that the method is convergent and stable. Despite the fact that the governing equations are nonlinear, the theoretical convergence of the formulation is guaranteed if the multibody system is natural and conservative. Likewise, stability and asymptotic stability results for the penalty formulation are derived from well-known stability results available from classical mechanics. Unfortunately, the convergence theorem is not directly applicable to dissipative multibody systems, such as those encountered in control applications. However, it is shown that the approximate solutions of a typical dissipative system converge to a nearby collection of trajectories that can be characterized precisely using a Lyapunov/Invariance Principle analysis. In short, the approach has many advantages as an alternative to other computational techniques:
Just as importantly, these results for nonlinear systems can be sharpened considerably for linear systems:
相似文献
(1) | Explicit constraint violation bounds can be derived for a large class of nonlinear multibody dynamics problems |
(2) | Sufficient conditions for the Lyapunov stability, and asymptotic stability, of the penalty formulation are derived for a large class of multibody systems |
(3) | The method can be shown to be relatively insensitive to singular configurations by selecting the penalty parameters to dissipate constraint violation energy |
(4) | The Invariance Principle can be employed in the method, in certain cases, to derive the asymptotic behavior of the constraint violation for dissipative multibody systems by identifying constraint violation limit cycles |
(5) | Explicit spectral error estimates can be obtained for substructure synthesis |
(6) | The penalty equations can be shown to be optimal in the sense that the terms represent feedback that minimizes a measure of the constraint violation |
85.
<正> 1、引言 流体运动总是同时受动力学和热力学规律的约制,通常处理流动问题时这两方面的考虑也总是交织在一起,例如,为了定义描述流动现象的诸流动变量,首先要假定每个流体质点微团是处于热力学平衡态,即假定流动系统满足“局域热平衡”条件。这样才可以定义各“点”的压力、密度、熵等变量。由于流动系统同时又是一个热力学系统,因此它的 相似文献
86.
We prove the existence of a unique weak solution to the quasistatic problem of frictional contact between a deformable body
and a rigid foundation. The material is assumed to have nonlinear viscoelastic behavior. The contact is modeled with normal
compliance and the associated version of Coulomb's law of dry friction. We establish the continuous dependence of the solution
on the normal compliance function. Moreover, we prove the existence of a unique solution to the problem of sliding contact
with wear.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
87.
Stability of a geothermal system is considered in a case when the water layer lies over the layer of superheated vapor in a stratum having relatively low permeability. This stratum locates between two parallel high permeable layers. Under the assumption of smallness of advective energy transfer as compared with the conductive one, the stationary distribution of the characteristics in the stratum with an interface of phase transition is obtained. The interface separates the domains occupied by water and vapor. Investigation of normal stability of the interface shows, that stable configurations in the geothermal system under consideration exist within the range of permeability values bounded by k 0.6 × 10–15 m2 from above. The most unstable configurations occur to be the quiescent states when the permeability exceeds a certain threshold. A sufficiently high value of permeability, satisfying the criterion of smallness of the advective energy transfer as compared with the conductive one makes it possible to explain the existence of a wide class of stable natural geothermal reservoirs, where the vapor layer underlies the water one. 相似文献
88.
A sphere in air will roll down a plane that is tilted away from the vertical. The only couple acting about the point of contact between the sphere and the plane is due to the component of the weight of the sphere along the plane, provided that air friction is negligible. If on the other hand the sphere is immersed in a liquid, hydrodynamic forces will enter into the couples that turn the sphere, and the rotation of the sphere can be anomalous, i.e., as if rolling up the plane while it falls. In this paper we shall show that anomalous rolling is a characteristic phenomenon that can be observed in every viscoelastic liquid tested so far. Anomalous rolling is normal for hydrodynamically levitated spheres, both in Newtonian and viscoelastic liquids. Normal and anomalous rolling are different names for dry and hydrodynamic rolling. Spheres dropped at a vertical wall in Newtonian liquids are forced into anomalous rotation and are pushed away from the wall while in viscoelastic liquids, they are forced into anomalous rotation, but are pushed toward the wall. If the wall is inclined and the fluid is Newtonian, the spheres will rotate normally for dry rolling, but the same spheres rotate anomalously in viscoelastic liquids when the angle of inclination from the vertical is less than some critical value. The hydrodynamic mechanisms underway in the settling of circular particles in a Newtonian fluid at a vertical wall are revealed by an exact numerical simulation based on a finite-element solution of the Navier-Stokes equations and Newton's equations of motion for a rigid body. 相似文献
89.
The phase-space kinetic theory for polymeric liquid mixtures is used to obtain an expression for the polymer contribution to the thermal conductivity of a nonflowing, dilute solution of polymers, where the polymer molecules are modeled as Fraenkel dumbbells. This theory takes into account three mechanisms for the energy transport: diffusion of kinetic energy (including the Öttinger-Petrillo term), diffusion of intramolecular energy, and the work done against the intramolecular forces. This paper is an extension of previous developments for the Hookean dumbbell model and the finitely-extensible dumbbell model. A comparison among the dumbbell results suggests that the thermal conductivity increases with chain stiffness. In addition, the zero-shear-rate viscosity and first normal-stress coefficient are also given for the Fraenkel dumbbell model.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday. 相似文献
90.
Alexander F. Vakakis 《Nonlinear dynamics》1992,3(2):123-143
The fundamental and subharmonic resonances of a two degree-of-freedom oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-seales averaging analysis. The system is in a 1–1 internal resonance, i.e., it has two equal linearized eigenfrequencies, and it possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies. The analytical results are verified by a numerical integration of the equations of motion, and a discussion of the effects of the mode bifurcation on the dynamics of the system is given. 相似文献