We propose a paradigm-shifting and 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. This approach allows us to derive the fundamental equations of SEA, using a thermodynamic analogy without the restrictive assumptions of linearity.

In the 1960’s Richard Lyons used the SEA to predict the vibrational response of launch vehicles and rocket noise. Since then, other researchers turned to SEA to study vibro-acoustics and vibrating strucutres. SEA applies statistical physics to the study of randomly vibrating mechanical and acoustical systems at medium to high frequencies. This is particularly benefitial as the finite element method (FEM) and modal analysis are not accurate and/or are numerically expensive in certain situations, such as high-freqeuncy excitation, high modal overlap or whenever a very large number of degrees of frredom (DOF) are required.

Traditionally, SEA is based on the conservation of energy or applying the first law of thermodynamics to subsystems of a larger system. The most fundamental equation in SEA is the power flow or power flow proportionality equation. The power flow equation is exactly derived for a 2-DOF 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 not many papers devoted to nonlinear SEA. It has been accepted that SEA is used for linear systems.

The power proportionality equation is a consequence of the first law of thermodynamics. We will use the classical definition of entropy to relate entropy to temperature. Using a statistical definition of entropy for a vibrating system, we will define a vibrational temperature as a function of energy. Therefore, we will derive the SEA power flow equations without any ad hoc assumptions. Using this method, we can expand SEA to nonlinear systems.

In this paper, we will illustrate this method using a linear and a nonlinear spring-mass system with two degrees-of-freedom. For each example, we will define and calculate vibrational temperature and entropy. Using our proposed approach, we will illustrate the power flow equation for each system. We will verify our proposed method using Monte Carlo Simulation.

Key Words: Statistical Energy Analysis (SEA), Nonlinearity, Entropy, Thermodynamics, Clausius Law, Power Flow, Power Proportionality, Coupling Loss Factor (CLF), Modal Energy, Vibrating Energy, Weakly Coupled Systems, Vibrating Temperature, Monte Carlo Simulation

 

 


Statistical Energy Analysis Using Entropy Concept

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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