在模態分析中，為了能夠使用正規模態矩陣解耦系統方程，吾人會假設系統含比例阻尼，解耦後的系統會具有實模態的形式。然而一般含阻尼的線性結構系統會呈現複模態的形式而不是實模態的形式，而複模態形式的產生與阻尼的非比例性有關，因此了解系統阻尼的非比例性程度便成為一個工程上重要的課題。本文主要探討如何定義出可以有效的描述系統中阻尼非比例性的量化指標，首先針對前人所提出的非比例阻尼指標，進行模擬與分析，進而提出兩個新指標，以有效反映系統中阻尼的非比例性程度。再以數值模擬的方式，比較各個指標之間的優劣，驗證本文所提出的新指標之可行性。

In conventional modal analysis of damped systems, the equations of motion can be diagonalized using the undamped modal matrix when the damping matrix is known as proportional damping or classical damping. In general, however, damped linear systems possess complex modes instead of classical normal modes due to non-proportionality of damping, and therefore it is of great interest to study the non-proportionality of damping of general structural systems. This thesis studies how to define appropriate indices to quantify the non-proportionality of damping , which are referred to as the indices of non-proportional damping in the present study. Two new indices measuring the non-proportionality of damping are proposed, the applicability of the proposed indices is demonstrated by numerical simulations. The examples also show the performance of the proposed indices in comparison with existing indices.

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