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胡海岩, H. Y. HU
Journal of Sound and Vibration (1995) 187 (3), 485-493,-0001,():
-1年11月30日
A critical phenomenon in a continuous, piecewise-linear oscillator subjected to periodic excitation is considered, in which a periodic orbit happens to graze a switching plane between two linear regions of the oscillator at zero velocity. The analysis shows that if the piecewise linearity of the oscillator changes dramatically on the switching plane, the phenomenon turns the stability trend of the periodic orbit so abruptly that it may be hard to predict an incident bifurcation, although it is of a local type, according to the concepts of smooth dynamical systems. To detect the critical phenomenon induced by the non-smooth nature of the oscillator, a numerical scheme of searching for all periodic grazing orbits is presented, as well as a test function for grazing phenomena in tracing a branch of a periodic orbit. There follows a numerical simulation based on the scheme and the test function, which reveals an abundance of grazing phenomena and incident bifurcations of the oscillator.
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【期刊论文】STABILITY ESTIMATION OF HIGH DIMENSIONAL VIBRATING SYSTEMS UNDER STATE DELAY FEEDBACK CONTROL
胡海岩, H. Y. HU, E. H. DOWELL, AND L. N. VIRGIN
Journal of Sound and Vibration (1998) 214 (3), 497-511,-0001,():
-1年11月30日
The paper presents a method of assessing the stability of high dimensional vibrating systems under state feedback control with a short time delay. It is first proved that if the time delay is sufficiently short, an n-degree-of-freedom system with feedback delay maintains 2n eigenvalues near those of the corresponding system without feedback delay. A perturbation approach is then proposed to determine the first order variation of an arbitrary eigenvalue and corresponding eigenvector of the system with feedback delay by solving a set of linear algebraic equations only. The computation in this approach can be simplified to a matrix multiplication provided that the product of the time delay and the modulus of the eigenvalue is much less than 1. Furthermore, the approach is directly related to the Newton-Raphson iteration in the continuation of eigenvalues for long time delay. The efficacy of the approach is demonstrated via a number of case studies on two feedback delay systems of two degrees of freedom and ten degrees of freedom respectively.
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【期刊论文】Simulation Complexities in the Dynamics of a Continuously Piecewise-Linear Oscillator
胡海岩, HAIYAN HU
Chaos, Solitons & Fractals Vol. 5, No.11. pp. 2201-2212, 1995,-0001,():
-1年11月30日
The vector field of a continuously piecewise-linear oscillator under periodic excitation is by nature nonsmooth. However, the nonsmoothness in studying the oscillator dynamics has drawn little attention. The paper presents the nonsmoothness effect on the differentiability of the Poincar
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胡海岩, H. Y. HU
Journal of Sound and Vibration (1998) 207 (3), 393-401,-0001,():
-1年11月30日
The primary resonance and the stability of a harmonically forced oscillator with a pair of symmetric set-up elastic stops are studied by means of the average approach. It is found that the set-up elastic stops greatly increase the complexities of the primary resonance as follows. Four kinds of persistent primary resonance and three critical cases exist. The motion of many of the persistent resonances becomes unstable when it begins to touch the set-up elastic stops with decrease of the excitation frequency. Moreover, there coexist three stable periodic motions and two unstable periodic motions at certain combinations of system parameters.
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【期刊论文】AN ADAPTIVE CONTROL SCHEME FOR RECOVERING PERIODIC MOTION OF CHAOTIC SYSTEMS
胡海岩, H. Y. HU
Journal of Sound and Vibration (1997) 199 (2), 269-274,-0001,():
-1年11月30日
The paper presents an adaptive control scheme for recovering the original dynamics of a nonlinear system after a sudden disturbance in a system parameter by controlling the system parameter through linear feedback. The key problem is to choose the control stiffness in the feedback by assigning the poles of the linearized controlled system in an extended state space, which consists of the system state and the system parameter. The paper gives the simulations of recovering the fixed point of the logistic map and the periodic orbit of a harmonically forced Duffing oscillator from the chaos due to a large disturbance in the parameter. The simulations demonstrate well the efficacy and the advantages of the proposed adaptive control scheme.
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