非保守耦合系统的统计能量分析原理

Principle of statistical energy analysis for non-conservatively coupled systems

传统的统计能量分析(SEA)理论不能解决非保守耦合系统的能量分析问题。本文在非保守耦合振子的能量分布与功率流特征的研究基础上,推导了互不相关随机激励条件下非保守耦合系统的功率平衡方程式及各有关功率项的计算式,建立了非保守耦合系统的统计能量分析理论。研究结果表明,保守耦合仅是非保守耦合的一个特例,耦合阻尼对非保守耦合系统的能量分布和功率流的特征有着显著的影响,只有在耦合阻尼远小于系统内阻尼时这种影响才可近似忽略。作为理论的一个应用实例,本文对非保守耦合板的能量问题进行了理论和实验研究。

Traditional Statistical Energy Analysis (SEA) theory can not deal with dynamic problem concerned with non-conservatively coupled systems. In this paper, based on the theory of power flow between and energy distribution in non-conservatively coupled oscillators, equations of power bal-lance and those for each concerned power flows and other power item calculations are derived to develop SEA theory for non-conservatively coupled systems. Results show that conservative coupling is only a special case in non-conservative coupling situations, the effects of coupling damping on power flow and energy distribution in non-conservatively coupled systems are not negligible unless the coupling damping is much small compared with internal damping. As an application of the theory, energy problems of non-conservatively coupled plates are studied theoretically and experimentally.