Introducing Entropy for the Statistical Energy Analysis of an Artificially Damped Oscillator

2015 ◽  
Author(s):  
Dante A. Tufano ◽  
Zahra Sotoudeh
Keyword(s):  
Energy Analysis ◽  
Lagrangian Method ◽  
Statistical Energy Analysis ◽  
Artificial Damping ◽  
Energy Behavior ◽  
Resonator System ◽  
The Individual ◽  
Entropy Formulation ◽  
Damped Oscillator

The purpose of this paper is to introduce the concept of entropy for a main resonator attached to a “fuzzy structure”. This structure is described explicitly using the Lagrangian method, and is treated as a layer of discrete resonators. A generic entropy formulation is then developed for the layer of resonators, which is used to determine the individual oscillator entropies. The combined entropy of the linear resonator system is then determined and compared numerically to the sum of the individual oscillator entropies. The entropy behavior of the system is then related to the energy behavior of the system and explained in regards to the the “artificial damping” of the main resonator.

scholarly journals Entropy and Mixing Entropy for Weakly Nonlinear Mechanical Vibrating Systems

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 536 ◽  
Author(s):  
Zahra Sotoudeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Systems ◽  
Power Flow ◽  
Energy Analysis ◽  
Vibrational Temperature ◽  
Statistical Energy Analysis ◽  
Phase Volume ◽  
Weakly Nonlinear ◽  
Mixing Entropy ◽  
Energy Behavior

In this paper, we examine Khinchin’s entropy for two weakly nonlinear systems of oscillators. We study a system of coupled Duffing oscillators and a set of Henon–Heiles oscillators. It is shown that the general method of deriving the Khinchin’s entropy for linear systems can be modified to account for weak nonlinearities. Nonlinearities are modeled as nonlinear springs. To calculate the Khinchin’s entropy, one needs to obtain an analytical expression of the system’s phase volume. We use a perturbation method to do so, and verify the results against the numerical calculation of the phase volume. It is shown that such an approach is valid for weakly nonlinear systems. In an extension of the author’s previous work for linear systems, a mixing entropy is defined for these two oscillators. The mixing entropy is the result of the generation of entropy when two systems are combined to create a complex system. It is illustrated that mixing entropy is always non-negative. The mixing entropy provides insight into the energy behavior of each system. The limitation of statistical energy analysis motivates this study. Using the thermodynamic relationship of temperature and entropy, and Khinchin’s entropy, one can define a vibrational temperature. Vibrational temperature can be used to derive the power flow proportionality, which is the backbone of the statistical energy analysis. Although this paper is motivated by statistical energy analysis application, it is not devoted to the statistical energy analysis of nonlinear systems.

scholarly journals Modelling Bending Wave Transmission across Coupled Plate Systems Comprising Periodic Ribbed Plates in the Low-, Mid-, and High-Frequency Ranges Using Forms of Statistical Energy Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-19
Author(s):  
Jianfei Yin ◽  
Carl Hopkins
Keyword(s):  
Frequency Band ◽  
High Frequency ◽  
Energy Analysis ◽  
Wide Frequency Range ◽  
Wave Transmission ◽  
Statistical Energy Analysis ◽  
Frequency Range ◽  
The Individual ◽  
Coupled Plates ◽  
Bending Wave

Prediction of bending wave transmission across systems of coupled plates which incorporate periodic ribbed plates is considered using Statistical Energy Analysis (SEA) in the low- and mid-frequency ranges and Advanced SEA (ASEA) in the high-frequency range. This paper investigates the crossover from prediction with SEA to ASEA through comparison with Finite Element Methods. Results from L-junctions confirm that this crossover occurs near the frequency band containing the fundamental bending mode of the individual bays on the ribbed plate when ribs are parallel to the junction line. Below this frequency band, SEA models treating each periodic ribbed plate as a single subsystem were shown to be appropriate. Above this frequency band, large reductions occur in the vibration level when propagation takes place across successive bays on ribbed plates when the ribs are parallel to the junction. This is due to spatial filtering; hence it is necessary to use ASEA which can incorporate indirect coupling associated with this transmission mechanism. A system of three coupled plates was also modelled which introduced flanking transmission. The results show that a wide frequency range can be covered by using both SEA and ASEA for systems of coupled plates where some or all of the plates are periodic ribbed plates.

Experimental and Statistical Energy Analysis of the Structure-borne Noise in a Helicopter Cabin

2017 ◽  
Vol 10 (6) ◽  
pp. 323
Author(s):  
Raffaella Di Sante ◽  
Marcello Vanali ◽  
Elisabetta Manconi ◽  
Alessandro Perazzolo
Keyword(s):  
Energy Analysis ◽  
Statistical Energy Analysis

Power Flow and Energy Sharing between an Oscillator and a Continuous Receiver Structure

2011 ◽  
Vol 189-193 ◽  
pp. 1914-1917
Author(s):  
Lin Ji
Keyword(s):  
High Frequency ◽  
Power Flow ◽  
Energy Analysis ◽  
Statistical Energy Analysis ◽  
Coupled Subsystems ◽  
Modal Density ◽  
Vibration Problems ◽  
Energy Sharing ◽  
High Modal Density ◽  
Vibration Modeling

A key assumption of conventional Statistical Energy Analysis (SEA) theory is that, for two coupled subsystems, the transmitted power from one to another is proportional to the energy differences between the mode pairs of the two subsystems. Previous research has shown that such an assumption remains valid if each individual subsystem is of high modal density. This thus limits the successful applications of SEA theory mostly to the regime of high frequency vibration modeling. This paper argues that, under certain coupling conditions, conventional SEA can be extended to solve the mid-frequency vibration problems where systems may consist of both mode-dense and mode-spare subsystems, e.g. ribbed-plates.

scholarly journals Ergodic billiard and statistical energy analysis

Wave Motion ◽  
2019 ◽  
Vol 87 ◽  
pp. 166-178 ◽  
Author(s):  
H. Li ◽  
N. Totaro ◽  
L. Maxit ◽  
A. Le Bot
Keyword(s):  
Energy Analysis ◽  
Statistical Energy Analysis
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