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

Cal Poly Pomona Foundation, Inc., Pomona CA

Investigators

Abstract

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.