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

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。这项工程研究启动（ERI）拨款将资助研究，使统计技术能够用于结构优化，损伤检测和大型复杂工程结构的噪声控制，包括飞机，运载火箭，船舶和汽车，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的结构，在紧密间隔的频率上共振，标准的分析和计算技术是昂贵的，而且由于对不确定性的高度敏感性，容易产生不准确性，使它们在迭代设计过程中无效。一种被称为统计能量分析的技术克服了这些限制，在振动与输入功率线性响应的情况下，并确保准确预测结构不同部分之间的能量交换，以及结构中耗散的能量。该项目将通过考虑在大振幅振动中占主导地位的非线性，或由于材料特性而影响所有运动尺度，从而消除对线性体系的限制。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具有可靠性，可验证性和可扩展性的现代工程结构实践意义的严格理论。通过这个项目，在一个拥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做好准备。本研究旨在为统计能量分析的一种新颖的、数学上严格的热力学解释做出基本贡献，这种解释不受线性假设的限制，因此也有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离散结构以及耦合杆-杆和板-板系统中捕获能量传递的线性和非线性效应的程度，从而也提供一系列可用于测试相关理论的基准示例和验证度量。参数研究将用于确定理论在非线性强度方面有效性的上限。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.