Mid-Frequency Vibration Analysis of Complex Structures

本研究计画的主要重点是发展分析与预测复杂结构中的中频振动传递的方法，复杂结构是由连接的子结构所组成。复结构是周期结构和近周期结构的推广。 在复杂结构振动的中频范围内，振动波长足够小，使得结构中的不确定性和缺陷对全局动力学具有显著影响。目前限制高频统计能量方法的假设进行了系统的检查和放松。这将它们的适用性扩展到更一般的系统，例如具有强组件间耦合的系统。这项研究工作的一个主要推动力是消除限制分析高频范围的假设。这项研究的成果是复杂结构振动分析的新方法的层次。这些新的方法是有效的中频和高频范围内，再现模式本地化和相关现象所造成的不确定性，处理中度和强耦合的情况下，是相对简单的。所开发的方法进行了验证，通过系统的比较与实验数据。简单的基准实验（例如， 振动在两个耦合板中的传递）在实验室中进行。

The main emphasis of this research project is to develop methods for analyzing and predicting mid-frequency vibration transmission in complex structures, which are assemblages of connected substructures. Complex structures are a generalization of periodic and nearly periodic structures. In the mid-frequency range of vibration for a complex structure, the vibration wavelengths are small enough for uncertainties and flaws in the structure to have significant impact on the global dynamics. The assumptions which currently limit high-frequency statistical energy methods are systematically examined and relaxed. This extends their applicability to more general systems such as those with strong inter-component coupling. A major thrust in this research effort is on the elimination of assumptions which restrict the analysis to the high-frequency range. The outcome of this research is a hierarchy of new methods for the vibration analysis of complex structures. These new methods are valid for both mid-and high-frequency ranges, reproduce mode localization and related phenomena caused by uncertainties, which handle moderate and strong coupling situations, and are relatively simple. The methods developed are validated through systematic comparison with experimental data. Simple benchmark experiments (e.g., vibration transmission in two coupled plates) are carried out in the laboratory.