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

ERI：使用统计熵增强非线性振动结构的统计能量分析

• 批准号: 2138625
• 负责人: Zahra Sotoudeh
• 金额: $ 19.98万
• 依托单位: Cal Poly Pomona Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-02-01 至 2025-01-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2138625&HistoricalAwards=false
• 关键词: ERI; Enhancing; Statistical; Energy; Analysis

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.

该奖项是根据2021年《美国救援计划法》的全部或部分资助（公共法117-2）。本工程研究启动（ERI）赠款将资助能够将统计技术用于结构优化，损害检测和噪音控制的大型和复杂工程结构的噪声控制，包括飞机，发射车辆，投资公司，船厂，船舶，货车和繁荣，繁荣的繁荣和繁荣的繁荣，对于在频率紧密的频率下引起共鸣的大量振动程度的结构，标准的分析和计算技术由于对不确定性的高敏感性而易于不准确，因此在迭代设计过程中无效。在振动的情况下，一种称为统计能量分析的技术克服了这些局限性，这些局限性与输入功率线性响应，并确保对结构不同部分以及结构中消散的功率之间的能量交换进行准确的预测。该项目将通过解释非线性的限制，这些非线性在大幅度振动中占主导地位，或者是由于材料特性并影响所有运动量表。理解统计能量分析的新理论框架将技术从启发式工程工具转移到严格的理论，对可靠性，可验证性和对现代工程结构的可扩展性具有实际影响。通过这个项目，在西班牙裔服务机构中拥有大量的低收入学生，来自潜水员背景的多组本科生将参与为期一年的多学科研究活动，为他们为传统工程工作以外的研究或工业职业做好准备。这项研究旨在为统计能量分析的新颖且数学上严格的热力学解释做出基本贡献，该解释不受线性假设的不受限制，因此也可能扩展到非线性系统。它将通过基于统计熵，经典熵和克劳西乌斯定律而不是基于能量保护的传统类比来开发相应的理论来实现这一结果。 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.参数研究将用于根据非线性的强度来确定理论的有效性上限。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响来审查标准，通过评估诚实地认为支持了支持。