The Effect of Infinitesimal Damping on the Dynamic Instability Mechanism of Conservative Systems
The Effect of Infinitesimal Damping on the Dynamic Instability Mechanism of Conservative Systems
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DOI：
10.1155/2008/471080
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发表时间：
2008-05
影响因子：
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通讯作者：
D. Sophianopoulos;G. Michaltsos;A. Kounadis
中科院分区：
文献类型：
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作者：
D. Sophianopoulos;G. Michaltsos;A. Kounadis
利用Lienard-Chipart稳定性判据，讨论了2自由度弱阻尼系统的局部失稳问题。研究了质量和刚度分布对主要由无穷小阻尼引起的动力渐近稳定性的个别和耦合影响。这些系统可能如下：(a)卸载（自由运动）和(b)承受恒定大小和方向、持续时间无限的突然施加的载荷（强迫运动）。上述参数与阻尼矩阵的代数结构（正半定或不定）结合在一起，在一定条件下可能对这些自治系统的雅可比特征值产生巨大的影响，进而对这些自治系统的局部稳定性产生巨大的影响。结果表明，当系统处于卸载状态时，系统可能表现为周期运动或发散运动，而当系统受到上述阶跃载荷时，系统可能表现为简并Hopf分岔或由一般Hopf分岔引起的周期吸引子。充分评估了导致全局渐近稳定的纯虚特征值存在的条件。通过非线性动力学分析，验证了理论结果的有效性。
The local instability of 2 degrees of freedom (DOF) weakly damped systems is thoroughly discussed using the Lienard-Chipart stability criterion. The individual and coupling effect of mass and stiffness distribution on the dynamic asymptotic stability due to mainly infinitesimal damping is examined. These systems may be as follows: (a) unloaded (free motion) and (b) subjected to a suddenly applied load of constant magnitude and direction with infinite duration (forced motion). The aforementioned parameters combined with the algebraic structure of the damping matrix (being either positive semidefinite or indefinite) may have under certain conditions a tremendous effect on the Jacobian eigenvalues and then on the local stability of these autonomous systems. It was found that such systems when unloaded may exhibit periodic motions or a divergent motion, while when subjected to the above step load may experience either a degenerate Hopf bifurcation or periodic attractors due to a generic Hopf bifurcation. Conditions for the existence of purely imaginary eigenvalues leading to global asymptotic stability are fully assessed. The validity of the theoretical findings presented herein is verified via a nonlinear dynamic analysis.