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排序方式: 共有296条查询结果,搜索用时 93 毫秒
1.
The nonlinear nonplanar response of cantilever inextensional metallic beams to a principal parametric excitation of two of its flexural modes, one in each plane, is investigated. The lowest torsional frequencies of the beams considered are much larger than the frequencies of the excited modes so that the torsional inertia can be neglected. Using this condition as well as the inextensionality condition, we develop a Lagrangian whose variation leads to two integro-partial-differential equations governing the motions of the beams. The method of time-averaged Lagrangian is used to derive four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two interacting modes. These modulation equations exhibit symmetry properties. A pseudo arclength scheme is used to trace the branches of the equilibrium solutions and an investigation of the eigenvalues of the Jacobian matrix is used to assess their stability. The equilibrium solutions experience pitchfork, saddle-node, Hopf, and codimension-2 bifurcations. A detailed bifurcation analysis of the dynamic solutions of the modulation equations is presented. Five branches of dynamic (periodic and chaotic) solutions were found. Two of these branches emerge from two Hopf bifurcations and the other three are isolated. The limit cycles undergo symmetry-breaking, cyclic-fold, and period-doubling bifurcations, whereas the chaotic attractors undergo attractor-merging and boundary crises. 相似文献
2.
考虑压电材料非线性本构关系,建立了旋转式超声电机定子的非线性动力学模型,利用解析与数值方法研究超声电机定子的主共振响应,以揭示压电材料非线性本构关系对定子振动特性的影响,为深入研究旋转行波超声电机的动力学机理奠定基础. 相似文献
3.
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
4.
The Secondary Bifurcation of an Aeroelastic Airfoil Motion: Effect of High Harmonics 总被引:6,自引:0,他引:6
The nonlinear dynamical response of a two-degree-of-freedom aeroelastic airfoil motion with cubic restoring forces is investigated. A secondary bifurcation after the primary Hopf (flutter) bifurcation is detected for a cubic hard spring in the pitch degree-of-freedom. Furthermore, there is a hysteresis in the secondary bifurcation: starting from different initial conditions the motion may jump from one limit cycle to another at different fluid flow velocities. A high-order harmonic balance method is employed to investigate the possible bifurcation branches. Furthermore, a numerical time simulation procedure is used to confirm the stable and unstable bifurcation branches. 相似文献
5.
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
6.
The most important characteristics of a nonlocal and nonlinear oscillator subject to dissipative forces are extensively studied by means of an asymptotic perturbation method, based upon temporal rescaling and harmonic balance. The conditions under which bifurcations and limit cycles appear are determined. If the parameters satisfy particular conditions, a quasi-periodic motion is predicted, because a second small frequency adds to the natural frequency of the oscillator. The analytical results are validated by numerically solving the original system. 相似文献
7.
The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit.Local active coordinate system is introduced to construct the Poincar′e returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the perioddoubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2n-homoclinic orbits. 相似文献
8.
The phenomenon of the chaotic boundary crisis and the related concept of the chaotic destroyer saddle has become recently a new problem in the studies of the destruction of chaotic attractors in nonlinear oscillators. As it is known, in the case of regular boundary crisis, the homoclinic bifurcation of the destroyer saddle defines the parameters of the annihilation of the chaotic attractor. In contrast, at the chaotic boundary crisis, the outset of the destroyer saddle which branches away from the chaotic attractor is tangled prior to the crisis. In our paper, the main point of interest is the problem of a relation, if any, between the homoclinic tangling of the destroyer saddle and the other properties of the system which may accompany the chaotic as well as the regular boundary crisis. In particular, the question if the phenomena of fractal basin boundary, indeterminate outcome, and a period of the destroyer saddle, are directly implied by the structure of the destroyer saddle invariant manifolds, is examined for some examples of the boundary crisis that occur in the mathematical models of the twin-well and the single-well potential nonlinear oscillators. 相似文献
9.
A study is made of the dynamics of oscillating systems with a slowly varying parameter. A slowly varying forcing periodically crosses a critical value corresponding to a pitchfork bifurcation. The instantaneous phase portrait exhibits a centre when the forcing does not exceed the critical value, and a saddle and two centres with an associated double homoclinic loop separatrix beyond this value. The aim of this study is to construct a Poincaré map in order to describe the dynamics of the system as it repeatedly crosses the bifurcation point. For that purpose averaging methods and asymptotic matching techniques connecting local solutions are applied. Given the initial state and the values of the parameters the properties of the Poincaré map can be studied. Both sensitive dependence on initial conditions and (quasi) periodicity are observed. Moreover, Lyapunov exponents are computed. The asymptotic expressions for the Poincaré map are compared with numerical solutions of the full system that includes small damping. 相似文献
10.
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