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Computation of dominant energy transmission paths for ship structure using a graph theory algorithm

机译：用图论算法计算船舶结构的主要能量传递路径

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When solving a vibroacoustic problem in a physical system, a fundamental goal is to determine how energy is transmitted from a given source to any part of the system. This enables the modifications needed to reduce noise or vibration levels in each system component. Numerical techniques such as Finite Element Method (FEM) and Statistical Energy Analysis (SEA) can predict the vibroacoustic behavior of the system; yet, they do not directly reveal which part of the system shall be modified. The energy transmitted via the path that connects a source and a target subsystem component can be determined numerically. Finding the dominant paths that contribute the most to the total energy transmitted between a source and target is more art than science; finding the dominant paths usually depends on an engineer's expertise and judgement. Thus, a systematic approach to automatically identify those paths would be beneficial. Graph theory provides a solution to this problem, because powerful path algorithms for graphs have already been developed. In this study, a systematic procedure for ranking the dominant energy paths in a vibroacoustic model is developed by using existing graph theory and SEA graph approaches. To extend the use and performance of this application-specific approach which investigates the vibroacoustic behavior of a ship structure, a research ship has been modelled via a SEA model for mid- and high-frequency ranges. Then, the structure-borne energy transmission paths from a vibration source to the keel bottom (underwater hull) plates are determined and ranked by their energy output. Next, the process identifies the structural elements that need to be modified to reduce the overall energy levels. A parametric approach is then used to modify these ideal candidates using a representative FEM model. Finally, the modelling results verify that the path-modified ship structure has reduced the structural vibration energy levels. Thus, by using and extending the pre-existing graph theory algorithm, the vibroacoustic behavior of complex ship structures is predicted, the energy output of each path is found and the problematic paths are modified during the ship design phase to ensure that vibration and noise levels are minimized.
机译：解决物理系统中的振动声学问题时，基本目标是确定如何将能量从给定源传输到系统的任何部分。这样可以进行所需的修改，以减少每个系统组件中的噪声或振动水平。诸如有限元方法（FEM）和统计能量分析（SEA）之类的数字技术可以预测系统的振动声行为。但是，它们没有直接显示应修改系统的哪一部分。可以通过数值确定通过连接源和目标子系统组件的路径传输的能量。寻找对能量在源和目标之间传输的总能量贡献最大的主导路径，比科学还重要。寻找主导路径通常取决于工程师的专业知识和判断力。因此，自动识别那些路径的系统方法将是有益的。图论为这个问题提供了解决方案，因为已经开发了强大的图路径算法。在这项研究中，通过使用现有的图论和SEA图方法，开发了一种用于对振动声学模型中的主要能量路径进行排名的系统程序。为了扩展这种用于研究船舶结构的振动声行为的专用方法的用途和性能，已通过SEA模型对中高频范围的研究船进行了建模。然后，确定从振动源到龙骨底部（水下船体）板的固体传热路径，并根据其能量输出进行排序。接下来，该过程将确定需要修改以降低总体能级的结构元素。然后使用参数化方法使用代表性的FEM模型来修改这些理想的候选对象。最后，建模结果验证了路径修改后的船舶结构降低了结构振动能级。因此，通过使用和扩展预先存在的图论算法，可以预测复杂船舶结构的振动声行为，找到每条路径的能量输出，并在船舶设计阶段修改有问题的路径，以确保振动和噪声水平被最小化。

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