论文标题
非线性阻尼对退化参数扩增的影响
The effects of nonlinear damping on degenerate parametric amplification
论文作者
论文摘要
本文认为，单个自由度系统具有非线性刚度和非线性阻尼的动态响应，该系统受到共振直接激发和共振参数激发的影响，两者之间具有一般阶段。这概括并扩展了先前对非线性对参数扩增的影响的研究，尤其是包括在包括微型和纳米级共振器在内的各种系统中通常观察到的非线性阻尼的影响。使用平均方法，进行了彻底的参数研究，描述了两种激发形式的幅度和相对相的影响。非线性阻尼对参数增益的影响首先得出。确定频率响应曲线的各种拓扑形式之间的跃迁，这些曲线可以包括隔离，双峰和环，并在感兴趣的参数空间中进行分叉分析。通常，这些结果提供了系统响应的完整图片，并允许人们在具有非线性阻尼的系统中选择最大幅度增益，最大相位灵敏度或平坦的共振峰，从而避免双重驱动条件。
This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase between the two. This generalizes and expands on previous studies of nonlinear effects on parametric amplification, notably by including the effects of nonlinear damping, which is commonly observed in a large variety of systems, including micro- and nano-scale resonators. Using the method of averaging, a thorough parameter study is carried out that describes the effects of the amplitudes and relative phase of the two forms of excitation. The effects of nonlinear damping on the parametric gain are first derived. The transitions among various topological forms of the frequency response curves, which can include isolae, dual peaks, and loops, are determined, and bifurcation analyses in parameter spaces of interest are carried out. In general, these results provide a complete picture of the system response and allow one to select drive conditions of interest that avoid bistability while providing maximum amplitude gain, maximum phase sensitivity, or a flat resonant peak, in systems with nonlinear damping.
