高损耗和无损元件组成系统的拉格朗日框架
Lagrangian Framework for Systems Composed of High-Loss and Lossless Components
摘要：
利用拉格朗日力学方法，我们构建了一个框架来研究由两个组成部分组成的系统的耗散特性，其中一个是高损耗的，另一个是无损的。我们已经表明，在我们以前的工作中，这样一个复合系统的模式分为两个不同的类，高损耗和低损耗，根据他们的耗散行为。本文的一个主要结果是，对于任何这样的耗散拉格朗日系统，其损耗由瑞利耗散函数来解释，都会出现一个相当普遍的现象，即选择性过阻尼：高损耗模式都是过阻尼的，即，非振荡的，同样数量的低损耗模式也是如此，但是其余的低损耗模式保持振荡，每个模式具有极高的品质因数，该品质因数实际上随着损耗分量的损耗增加而增加。我们证明了这一结果使用一个新的时间动力学表征的过阻尼的维里定理耗散系统和能量均分的突破。
英文摘要：
Using a Lagrangian mechanics approach, we construct a framework to study the dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. We have shown in our previous work that for such a composite system the modes split into two distinct classes, high-loss and low-loss, according to their dissipative behavior. A principal result of this paper is that for any such dissipative Lagrangian system, with losses accounted by a Rayleigh dissipative function, a rather universal phenomenon occurs, namely, selective overdamping: The high-loss modes are all overdamped, i.e., non-oscillatory, as are an equal number of low-loss modes, but the rest of the low-loss modes remain oscillatory each with an extremely high quality factor that actually increases as the loss of the lossy component increases. We prove this result using a new time dynamical characterization of overdamping in terms of a virial theorem for dissipative systems and the breaking of an equipartition of energy.
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