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资助（公法117-2）。这项工程研究启动（ERI）赠款将资助研究，使统计技术的使用，结构优化，损伤检测和大型复杂的工程结构，包括飞机，运载火箭，船舶和汽车的噪音控制，从而促进科学的进步，促进繁荣和福利。对于具有非常大的振动自由度的结构，在紧密间隔的频率下共振，标准的分析和计算技术是昂贵的，并且由于对不确定性的高度敏感性而容易产生不准确性，使得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，在振动的情况下，线性响应与输入功率，并确保准确预测的能量交换之间的不同部分的结构，以及在结构中耗散的功率。该项目将通过考虑非线性来消除对线性状态的限制，这些非线性对于大振幅振动或由于材料特性而成为主导，并影响所有运动尺度。理解统计能量分析的新的理论框架提升了技术从一个启发式的工程工具，一个严格的理论与现代工程结构的可靠性，可验证性和可扩展性的实际影响。通过这个项目，住在一个西班牙裔服务机构与低收入学生的显着人口，来自不同背景的本科生的多个群体将从事为期一年的多学科研究活动，准备他们的研究或工业生涯超越传统的工程工作。这项研究的目的是作出根本性的贡献，一个新的和数学上严格的热力学解释的统计能量分析，是不受限制的假设的线性，因此潜在的可扩展的非线性系统。它将通过基于统计熵、经典熵和克劳修斯定律而不是基于能量守恒的传统类比来发展相应的理论来实现这一结果。该项目将使用物理实验和数值模拟，包括高保真有限元分析与蒙特卡罗技术相结合，以表征统计能量分析捕获离散结构以及耦合杆-杆和板-板系统中能量传递的线性和非线性效应的程度，从而还提供了一系列可用于测试相关理论的基准示例和验证度量。参数研究将被用来确定理论的有效性的上限，在强度的非线性。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

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.