组合激励下振动系统自共振捕获的渐近分析
Asymptotic analysis of the autoresonance capture in oscillating systems with combined excitation
摘要：
研究了参数激励和外部啁啾激励联合作用下非线性系统的自共振数学模型。具有不断增长的振幅和有界相位失配的解决方案与自谐振捕获相关联。应用李雅普诺夫函数方法，我们研究了自共振模的存在性和稳定性条件，并构造了稳定解的长期渐近性。特别是，我们表明，不稳定的制度变得稳定时，系统参数通过一定的阈值。
英文摘要：
A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the autoresonant capture. By applying Lyapunov function method we investigate the conditions for the existence and stability of autoresonant modes and construct long-term asymptotics for stable solutions. In particular, we show that unstable regimes become stable when the system parameters pass through certain threshold values.
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