ERI: Enhancing Statistical Energy Analysis for Nonlinear Vibrating Structures Using Statistical Entropy

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。这项工程研究启动(ERI)拨款将资助能够使用统计技术对大型和复杂工程结构(包括飞机、运载火箭、船舶和汽车)进行结构优化、损伤检测和噪音控制的研究，从而促进科学进步，促进繁荣和福利。对于具有大量振动自由度且频率间隔很近的结构，由于对不确定性高度敏感，标准的分析和计算方法昂贵且容易产生不准确，这使得它们在迭代设计过程中无效。在振动与输入功率线性响应的情况下，一种称为统计能量分析的技术克服了这些限制，并确保准确预测结构不同部分之间的能量交换以及结构中消耗的功率。这个项目将通过考虑成为大振幅振动的主导或由于材料特性而影响所有运动尺度的非线性来消除对线性区域的限制。理解统计能量分析的新理论框架将该技术从启发式工程工具提升为严格的理论，对现代工程结构的可靠性、可验证性和可扩展性具有实际意义。通过这个项目，在一个有大量低收入学生的西班牙裔服务机构，来自不同背景的多组本科生将参与为期一年的多学科研究活动，为他们在传统工程工作之外的研究或工业职业生涯做好准备。这项研究旨在为统计能量分析的一种新的、数学上严格的热力学解释做出根本贡献，这种解释不受线性假设的限制，因此也可能扩展到非线性系统。它将通过发展基于统计熵、经典熵和克劳修斯定律的相应理论来实现这一结果，而不是基于能量守恒的传统类比。该项目将使用物理实验和数值模拟，包括结合蒙特卡罗技术的高保真有限元分析，以表征统计能量分析在多大程度上捕捉到离散结构以及杆-杆和板-板耦合系统中能量传递的线性和非线性影响，从而还提供了一系列基准实例和验证指标，可用于测试相关理论。参数研究将被用来确定该理论在非线性强度方面的有效性上限。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).This Engineering Research Initiation (ERI) grant will fund research that enables the use of statistical techniques for structural optimization, damage detection, and noise control of large and complex engineering structures, including aircraft, launch vehicles, ships, and cars, thereby promoting the progress of science and advancing prosperity and welfare. For structures with very large numbers of vibrational degrees of freedom that resonate at closely spaced frequencies, standard analytical and computational techniques are expensive and prone to inaccuracies due to high sensitivity to uncertainties, making them ineffective in an iterative design process. A technique known as statistical energy analysis overcomes these limitations in the case of vibrations that respond linearly with input power, and ensures accurate predictions of the energy exchange between different parts of the structure, as well as of the power dissipated in the structure. This project will remove the restriction to the linear regime by accounting for nonlinearities that become dominant for large-amplitude vibrations or are due to material properties and affect all scales of motion. The new theoretical framework for understanding statistical energy analysis elevates the technique from a heuristic engineering tool to a rigorous theory with practical implications for reliability, verifiability, and extensibility to modern engineering structures. Through this project, housed at a Hispanic-Serving Institution with a significant population of low-income students, multiple groups of undergraduates from diverse backgrounds will be engaged in year-long multidisciplinary research activities, preparing them for research or industrial careers beyond traditional engineering jobs. This research aims to make fundamental contributions to a novel and mathematically rigorous thermodynamic interpretation of statistical energy analysis that is unrestricted by assumptions of linearity and therefore potentially extensible also to nonlinear systems. It will achieve this outcome by developing a corresponding theory based on statistical entropy, classical entropy, and Clausius’s law, rather than the traditional analogy based on conservation of energy. The project will use physical experiments and numerical simulations, including high-fidelity finite-element analysis combined with Monte Carlo techniques, to characterize the degree to which the statistical energy analysis captures both linear and nonlinear effects of energy transfer in discrete structures, as well as coupled rod-rod and plate-plate systems, thereby also providing a series of benchmark examples and verification metrics that may be used to test related theories. Parameter studies will be used to determine an upper limit of validity of the theory in terms of the strength of nonlinearity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.