This paper discusses the novel method to enhance transient statistical energy analysis (SEA) for nonlinear vibrating structures. We will use the concept of statistical entropy from statistical mechanics, the relationship of entropy and temperature in classical thermodynamics, and the Clausius Law of thermodynamics to derive the fundamental governing equations of SEA for nonlinear systems.&nbsp;The most fundamental equation in SEA is the power flow or power proportionality equation. The power flow equation is exactly derived for a 2-DOF&nbsp;coupled&nbsp;linear system. Using several restrictive ad hoc assumptions, one can extend the power proportionality equation to complex linear structures. To the best of our knowledge, there are&nbsp;only few&nbsp;articles&nbsp;devoted to nonlinear SEA.&nbsp;This approach allows us to derive the fundamental equations of SEA, using a thermodynamic analogy without the restrictive assumptions of linearity.&nbsp;Although the thermodynamic analogy has been known for a long time, this framework using both statistical and classical definitions of entropy for deriving the power flow equation is novel.&nbsp;The purpose of this research is to expand the applicability and accuracy of transient statistical energy analysis.&nbsp;&nbsp;&nbsp;&nbsp;This paper will review the background and motivation behind this research along with a literature review of its predecessors from&nbsp;the&nbsp;late&nbsp;1960’s to 2021. A general overview of the statistical energy analysis will provide the reader with the fundamentals necessary to&nbsp;comprehend and&nbsp;apply this theory such as power flow or power proportionality. The assumptions and limitations of this method will be stated for transparency and completeness. A thermodynamic perspective will be applied to classical SEA using&nbsp;statistical&nbsp;entropy. The Clausius Law will be used to define a vibrational temperature which is&nbsp;equivalent to the subsystems vibroacoustic definition of temperature or the average modal energy density.&nbsp;This will require both a classical and statistical entropy definition.&nbsp;Khinchin’s&nbsp;Entropy will be introduced as our statistical entropy definition&nbsp;which is based on prior research as the best suited for this application.&nbsp;This will allow us to show improved accuracy when compared to published results as this research&nbsp;does not assume linearity.&nbsp;All results will be provided in the time domain as this is preferred for transient response analysis as well as&nbsp;more intuitively&nbsp;understanding the flow of energy between&nbsp;coupled&nbsp;subsystems.&nbsp;We will verify our proposed method using&nbsp;numerical analysis and&nbsp;Monte Carlo Simulation.&nbsp;&nbsp;&nbsp;Keywords:&nbsp;Statistical Energy Analysis (SEA),&nbsp;Nonlinearity,&nbsp;Entropy, Thermodynamics, Clausius Law, Power Flow, Power Proportionality, Transient Coupling Loss Factor (CLF), Modal Energy, Vibrating Energy, Weakly Coupled Systems, Vibrating Temperature,&nbsp;Time-Domain,&nbsp;Numerical Analysis,&nbsp;Monte Carlo Simulation.&nbsp;&nbsp;We presented our preliminary research on this topic as a technical presentation at IMECE 2020 (#57553). This proposed paper will document our progress, complete results, and conclusions.&nbsp;

Statistical Energy Analysis of Vibrating Structures With Energy and Entropy

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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