• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.1
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• pp.174-194
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• 2015

In this paper, an Energy Flow Analysis (EFA) for coplanar coupled Mindlin plates was performed to estimate their dynamic responses at high frequencies. Mindlin plate theory can consider the effects of shear distortion and rotatory inertia, which are very important at high frequencies. For EFA for coplanar coupled Mindlin plates, the wave transmission and reflection relationship for progressing out-of-plane waves (out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave) in coplanar coupled Mindlin plates was newly derived. To verify the validity of the EFA results, numerical analyses were performed for various cases where coplanar coupled Mindlin plates are excited by a harmonic point force, and the energy flow solutions for coplanar coupled Mindlin plates were compared with the classical solutions in the various conditions.

• Journal of Ocean Engineering and Technology
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• v.34 no.6
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• pp.428-435
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• 2020

Energy flow analysis (EFA) has been used to predict the frequency-averaged vibrational responses of built-up structures at high frequencies. In this study, the frequency-averaged exact energetics of the in-plane motions of the plate were derived for the first time by solving coupled partial differential equations. To verify the EFA for the in-plane waves of the plate, numerical analyses were performed on various coupled plate structures. The prediction results of the EFA for coupled plate structures were shown to be accurate approximations of the frequency-averaged exact energetics, which were obtained from classical displacement solutions. The accuracy of the results predicted via the EFA increased with an increase in the modal density, regardless of various structural parameters. Therefore, EFA is an effective technique for predicting the frequency-averaged vibrational responses of built-up structures in the high frequency range.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.11
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• pp.1097-1102
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• 2010

In this paper, the energy flow analysis(EFA) of the body-in-white door of a real automotive was performed using the energy flow finite element method(EFFEM) to effectively predict the vibrational responses of built-up structures in the medium to high frequency range. To increase the validity of EFA results, the structural hysteresis damping loss factor was measured by the experiment using the concept of statistical energy analysis(SEA). As the excitation frequency increases, the predicted results simulated with EFFEM generally agree with the experimental results.

• Journal of the Society of Naval Architects of Korea
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• v.53 no.4
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• pp.307-314
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• 2016

Energy flow analysis(EFA) is a representative method that can predict the statistical energetics of structures at high frequencies. Generally, as the frequency increases, the shear distortion and rotatory inertia effects in the out-of-plane motion of beams or plates become important. Therefore, to predict the out-of-plane energetics of coupled structures in the high frequency range, the energy flow analyses of Timoshenko beam and Mindlin plate are required. Unlike the energy flow model of Kirchhoff plate, the energy flow model of Mindlin plate is composed of three kinds of energy governing equations(out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave). This paper performed the energy flow finite element analysis(EFFEA) of coplanar coupled Mindlin plates. For EFFEA of coplanar coupled Mindlin plates, the energy flow finite element formulation of out-of-plane energetics in the Mindlin plate was performed. The general EFFEA program was implemented by MATLAB® language. For the verification of EFFEA of Mindlin plate, the various numerical applications were done successfully.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.10
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• pp.1082-1090
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• 2008

In this paper, a general solution for the vibrational energy and intensity distribution through a compliant and dissipative joint between plate structures is derived on the basis of energy flow analysis (EFA). The joints are modeled by four sets of springs and dashpots to show their compliancy and dissipation in all four degrees of freedom. First, for the EFA, the power transmission and reflection coefficients for the joint on coupled plate structures connected at arbitrary angles were derived by the wave transmission approach. In numerical applications, EFA is performed using the derived coefficients for coupled plate structures under various joint properties, excitation frequencies, coupling angles, and internal loss factors. Numerical results of the vibrational energy distribution showed that the developed compliant and dissipative joint model successfully predicted the joint characteristics of practical structures vibrating in the medium-to-high frequency ranges. Moreover, the intensity distribution of a compliant and dissipative joint is described.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.435-447
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• 2019

Energy Flow Finite Element Analysis (EFFEA) is a promising tool for predicting dynamic energetics of complicated structures at high frequencies. In this paper, the Energy Flow Finite Element (EFFE) formulation of complicated Mindlin plates was newly developed to improve the accuracy of prediction of the dynamic characteristics in the high frequency. Wave transmission analysis was performed for all waves in complicated Mindlin plates. Advanced Energy Flow Analysis System (AEFAS), an exclusive EFFEA software, was implemented using $MATLAB^{(R)}$. To verify the general power transfer relationship derived, wave transmission analysis of coupled semi-infinite Mindlin plates was performed. For numerical verification of EFFE formulation derived and EFFEA software developed, numerical analyses were performed for various cases where coupled Mindlin plates were excited by a harmonic point force. Energy flow finite element solutions for coupled Mindlin plates were compared with the energy flow solutions in the various conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.6
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• pp.574-580
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• 2013

At high frequencies, the statistical approach such as statistical energy analysis(SEA) and energy flow analysis(EFA) has been applied for estimation of vibroacoustic responses of various built-up structures. The energy coupling relationship between finite coupled structures is required to estimate vibrational energetics of built-up structures. Mindlin plate theory includes the rotatory inertia and shear deformation effects which are dominant as frequency increases. In this paper, the wave transmission analysis is successfully performed for EFA of co-planar coupled Mindlin plates.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.12
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• pp.999-1006
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• 2014

Mindlin plate theory includes the shear deformation and rotatory inertia effects which cannot be negligible as exciting frequency increases. The statistical methods such as energy flow analysis(EFA) and statistical energy analysis(SEA) are very useful for estimation of structure-borne sound of various built-up structures. For the reliable vibrational analysis of built-up structures at high frequencies, the energy transfer relationship between out-of-plane waves and in-plane waves exist in Mindlin plates coupled at arbitrary angles must be derived. In this paper, the new wave transmission analysis is successfully performed for various energy analyses of Mindlin plates coupled at arbitrary angles.

• International Journal of Naval Architecture and Ocean Engineering
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• v.5 no.3
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• pp.392-403
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• 2013

For the analysis of radiating noise problems in medium-to-high frequency ranges, the Energy Flow Boundary Element Method (EFBEM) was developed. EFBEM is the analysis technique that applies the Boundary Element Method (BEM) to Energy Flow Analysis (EFA). The fundamental solutions representing spherical wave property for radiating noise problems in open field and considering the free surface effect in underwater are developed. Also the directivity factor is developed to express wave's directivity patterns in medium-to-high frequency ranges. Indirect EFBEM by using fundamental solutions and fictitious source was applied to open field and underwater noise problems successfully. Through numerical applications, the acoustic energy density distributions due to vibration of a simple plate model and a sphere model were compared with those of commercial code, and the comparison showed good agreement in the level and pattern of the energy density distributions.

• Journal of the Society of Naval Architects of Korea
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• v.60 no.1
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• pp.20-30
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• 2023

In this paper, the Energy Flow Finite Element Analysis (EFFEA) was performed to predict the acoustic and vibrational responses of complicated plate structures considering improved Fluid-Structure Interaction (FSI). For this, a new power transfer relationship was derived at the area junction where two different fluids are in contact on both sides of the plate. In order to increase the reliability of EFFEA of complicated plate structures immersed in a high-density fluid, the corrected flexural wavenumber and group velocity considering fluid-loading effect were derived. As the specific acoustic impedance of the fluid in contact with the plate increases, the flexural wavenumber of the plate increases. As a result, the flexural group velocity is reduced, and the spatial damping effect of the flexural energy density is increased. Additionally, for the EFFEA of arbitary-shaped built-up structures, the energy flow finite element formulation for the acoustic tetrahedral element was newly performed. Finally, for validation of the derived theory and developed software, numerical applications of complicated plate structures submerged in seawater or air were successfully performed.