On the stability and instability of linear potential systems subjected to infinitesimal circulatory forces

摘要

The stability of linear multi-degree-of-freedom stable potential systems with multiple natural frequencies under the action of infinitesimal circulatory forces is considered. Contrary to the received view that such systems are inherently unstable, a careful study shows that such systems have a much more complex behaviour than previously recognized and could exhibit an alternation of stability and instability that depends on the structure of the potential system and its interaction with the circulatory forces. The conditions under which stability or instability ensues and the nature of this alternation in stability are explicitly obtained. In low-dimensional stable potential systems, when the coefficients of the circulatory forces are proportional to an arbitrarily small scalar parameter, all the circulatory forces that cause flutter instability are described.