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81.
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction. 相似文献
82.
One of the most well-known situations in which nonlinear effects must be taken into account to obtain realistic results is
the rotating beam problem. This problem has been extensively studied in the literature and has even become a benchmark problem
for the validation of nonlinear formulations. Among other approaches, the substructuring technique was proven to be a valid
strategy to account for this problem. Later, the similarities between the absolute nodal coordinate formulation and the substructuring
technique were demonstrated. At the same time, it was found the existence of a critical angular velocity, beyond which the
system becomes unstable that was dependent on the number of substructures. Since the dependence of the critical velocity was
not so far clear, this paper tries to shed some light on it. Moreover, previous studies were focused on a constant angular
velocity analysis where the effects of Coriolis forces were neglected. In this paper, the influence of the Coriolis force
term is not neglected. The influence of the reference conditions of the element frame are also investigated in this paper. 相似文献
83.
Haixia Wang Qishao Lu Qingyun Wang 《Communications in Nonlinear Science & Numerical Simulation》2008,13(8):1668-1675
Bursting is an important electrical behavior in neuron’s firing. In this paper, based on the fast/slow dynamical bifurcation analysis and the phase plane analysis, two types of bursting are presented in the modified Morris–Lecar neuronal model, and the associated bifurcation mechanisms of switching between the active phase and the silent phase are analyzed. For two coupled bursters, it is found that the same type of coupled bursters may have different synchronization transition path from that of two different types of coupled bursters. The analysis of bursting types and the transition to synchronization may provide us with better insight into neuronal encoding and information transmission. 相似文献
84.
Passively Q-switched microchip lasers generate strongly pulsating intensity oscillations that emerge from a Hopf bifurcation point. We show that this bifurcation is nearly vertical and explain why strongly pulsating oscillations are immediately observed as we pass the Hopf bifurcation point. The laser dynamical problem is mathematically a singular perturbation problem which we investigate. The leading order problem is conservative and corresponds to Lotka–Volterra equations. 相似文献
85.
To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic. 相似文献
86.
87.
88.
Consider a one-mass system with two degrees of freedom, non-linearly coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable, a stable periodic solution may emerge, there are also cases where the trivial solution is stable and co-exists with a stable periodic solution; if both the trivial solution and the periodic solution(s) are unstable, we find an attracting torus with large amplitudes by a Neimark-Sacker bifurcation. The results of the harmonic balance method and averaging are compared, as well as the results on the Neimark-Sacker bifurcation obtained by the numerical software package CONTENT and by averaging. In all cases we have good agreement. 相似文献
89.
汽轮机转子在气流力和油膜力作用下的非线性动力学特性 总被引:2,自引:0,他引:2
为了分析转子在油膜力和气流激振力共同作用下的非线性振动特性,本文以短轴承支撑的不平衡刚性对称Jeffcott转子系统为研究对象,首先分析转子在非稳态油膜力作用下的振动特性,然后分析转子在油膜力和气流激振力共同作用下的非线性振动特性。采用数值模拟的方法研究了系统的分岔和混沌特性,计算结果表明,考虑气流激振力和油膜力共同作用下的转子系统与仅考虑油膜力的转子系统相比,在相对进气速度v=30m/s时,随着无量纲转速ω的增加。二者都出现了周期运动和混沌运动多次交替出现的复杂运动特性,但是前者首次出现倍周期分岔和混沌运动时的转运提前,在定转速情况下,随着v的增大,系统最终在经历周期运动之后进入混沌运动,而且圆盘中心的最大振幅随着v的增大而增大。 相似文献
90.
Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions
Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions. 相似文献