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51.
Anthony N. Kounadis 《International Journal of Non》2007,42(1):24-35
The local dynamic instability of autonomous conservative, lumped-mass (discrete) systems, is thoroughly discussed when negligibly small dissipative forces are included. It is shown that such small forces may change drastically the response of these systems. Hence, existing, widely accepted, findings based on the omission of damping could not be valid if damping, being always present in actual systems, is included. More specifically the conditions under which the above systems may experience dynamic bifurcations associated either with a degenerate or a generic Hopf bifurcation are examined in detail by studying the effect of the structure of the damping matrix on the Jacobian eigenvalues. The case whereby this phenomenon may occur before divergence is discussed in connection with the individual or coupling effect of non-uniform mass and stiffness distribution. Jump phenomena in the critical dynamic loading at a certain mass distribution are also assessed. Numerical results verified by a non-linear dynamic analysis using 2-DOF and 3-DOF models confirm the validity of the theoretical findings as well as the efficiency of the technique proposed herein. 相似文献
52.
Analytic Approximation of the Homoclinic Orbits of the Lorenz System at σ = 10, b = 8/3 and ρ = 13.926... 总被引:1,自引:0,他引:1
We present an iterative technique to analytically approximate the homoclinic loops of the Lorenz system for = 10, b = 8/3 and = H = 13.926.... First, the local structure of the homoclinic solution for t 0 ± and t ± is analyzed. Then, global approximants are used to match the local expansions. The matching procedure resembles the one used in Padé approximations. The accuracy of the approximation is improved iteratively, with each iteration providing estimates for the initial conditions of the homoclinic orbit, the value of H, and three undetermined constants in the local expansions. Within three iterations the error in H falls to the order of 0.1%. Comparisons with numerical integrations are made, and a discussion on ways to extend the technique to other types of homoclinic or heteroclinic orbits, and to improve its accuracy, is given. 相似文献
53.
The second-order closure method is used to analyze the nonlinear response of two-degree-of-freedom systems with quadratic nonlinearities. The excitation is assumed to be the sum of a deterministic harmonic component and a random component. The case of primary resonance of the second mode in the presence of a two-to-one internal (autoparametric) resonance is investigated. The method of multiple scales is used to obtain four first-order ordinary-differential equations that describe the modulation of the amplitudes and phases of the two modes. Applying the second-order closure method to the modulation equations, we determine the stationary mean and mean-square responses. For the case of a narrow-band random excitation, the results show that the presence of the nonlinearity causes multi-valued mean-square responses. The multi-valuedness is responsible for a jump phenomenon. Contrary to the results of the linear analysis, the nonlinear analysis reveals that the directly excited second mode takes a small amount of the input energy (saturates) and spills over the rest of the input energy into the first mode, which is indirectly excited through the autoparametric resonance. 相似文献
54.
Two homoclinic solutions for a nonperiodic fourth‐order differential equation without coercive condition 下载免费PDF全文
In this paper, we investigate the existence of homoclinic solutions for a class of fourth‐order nonautonomous differential equations where w is a constant, and . By using variational methods and the mountain pass theorem, some new results on the existence of homoclinic solutions are obtained under some suitable assumptions. The interesting is that a(x) and f(x,u) are nonperiodic in x,a does not fulfil the coercive condition, and f does not satisfy the well‐known (AR)‐condition. Furthermore, the main result partly answers the open problem proposed by Zhang and Yuan in the paper titled with Homoclinic solutions for a nonperiodic fourth‐order differential equations without coercive conditions (see Appl. Math. Comput. 2015; 250:280–286). Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
55.
The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations 下载免费PDF全文
We consider the problem of the periodic solutions bifurcated from a homoclinic orbit for a pair of coupled ordinary differential equations in . Assume that the autonomous system has a degenerate homoclinic solution γ in . A functional analytic approach is used to consider the existence of periodic solution for the autonomous system with periodic perturbations. By exponential dichotomies and the method of Lyapunov–Schmidt, the bifurcation function defined between two finite dimensional subspaces is obtained, where the zeros correspond to the existence of periodic solutions for the coupled ordinary differential equations near . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
56.
Friction plays a key role in the efficiency and stability of the slip-controlled torque converter clutches. The effects of
friction on the dynamics and stability of a slip-controlled torque converter clutch system using a bifurcation-analysis-based
approach is presented in this paper. A three degree-of-freedom nonlinear driveline model with integral feedback action to
control the clutch slip speed has been utilized for this study. The clutch interface friction is dependent on the slip speed
and is a function of the static friction constant, μ
0, the low velocity friction constant μ
1, and the low velocity exponential rate, γ. Using one-parameter numerical continuation, local Hopf bifurcations of the subcritical type are observed as the friction
parameters μ
1 and γ were varied at low slip speeds. The continuation results are verified using simulations of the full nonlinear model. Stick-slip
and undesirable oscillations of the model inertia elements are observed for certain parameter values. As the slip speed is
increased, the bifurcation instability occurs at an increasingly higher value of μ
1 signifying an improved tolerance of negative friction gradient at higher slip speeds. Smaller exponential rates γ are tolerated at higher slip speeds before the bifurcation instability occurs. For the range of parameter values considered,
no bifurcations occur for a slip speeds higher than 3.4 and 4.5 rad/s with μ
1 and γ as the continuation parameters, respectively. These values of slip speeds are much lower than the system’s first mode of
torsional vibration of 16 Hz (≈100 rad/s). 相似文献
57.
58.
2000MathematicsSubjectClassification:35Q Introduction ContinueRef.[1],inthispart,weapplythegeneralizedConley Moserconditions[2]toshowtheexistenceofSmalehorseshoesinbelowthediscreteNLSsystems(1).Considerthefollowingn particle(any2相似文献
59.
This paper investigates multiple modeling choices for analyzing the rich and complex dynamics of high-speed milling processes.
Various models are introduced to capture the effects of asymmetric structural modes and the influence of nonlinear regeneration
in a discontinuous cutting force model. Stability is determined from the development of a dynamic map for the resulting variational
system. The general case of asymmetric structural elements is investigated with a fixed frame and rotating frame model to
show differences in the predicted unstable regions due to parametric excitation. Analytical and numerical investigations are
confirmed through a series of experimental cutting tests. The principal results are additional unstable regions, hysteresis
in the bifurcation diagrams, and the presence of coexisting periodic and quasiperiodic attractors which is confirmed through
experimentation. 相似文献
60.
利用一维扩展过程的奇点理论并结合能量包络的随机平均法,考查“隐藏在余维2分岔点之后”的同宿分岔系统受参激白噪声影响的分岔行为。 相似文献