Energy Flow Analysis of Bars and Beams: Theoretical Formulations

Lase, Yuskar; Ichchou, Mohamed; Jézéquel, L.

doi:10.1006/jsvi.1996.0188

Cited by 72 publications

(45 citation statements)

References 1 publication

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“…In 1996, Läse et al [131] introduced the general energy method (GEM). To develop this method, they considered both the total energy density (sum of kinetic and potential energy densities) and the Lagrangian energy density (difference between kinetic and potential energy densities).…”

Section: Local Energy Flow Analysismentioning

confidence: 99%

Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Pierre¹,

Castanier²

2002

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searchi AUTHOR(S)PROFESSOR CHRISTOPHER PIERRE Approved for public rsleas3 ; distribution unlinätsd, PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)8 ABSTRACT (Maximum 200 words)One of the last frontiers of structural dynamics is mid-frequency vibration analysis of complex structures. In the low-frequency range, finite element analysis (FEA) is well established as the standard method, However, as the frequency of vibration increases, the cost of FEA becomes prohibitive due to the necessary refinement of the finite element mesh to capture the shorter wavelength of vibration. Furthermore, the system response becomes sensitive to small parameter variations at higher frequencies, which means that a statistical analysis should be employed to make confident response predictions. In the high-frequency range, statistical energy analysis (SEA) is popular. However, SEA provides only averaged response predictions and cannot capture the resonant behavior in the response that becomes evident as frequency decreases. ABSTRACTOne of the last frontiers of structural dynamics is mid-frequency vibration analysis of complex structures. In the low-frequency range, finite element analysis (FEA) is well established as the standard method. However, as the frequency of vibration increases, the cost of FEA becomes prohibitive due to the necessary refinement of the finite element mesh to capture the shorter wavelength of vibration. Furthermore, the system response becomes sensitive to small parameter variations at higher frequencies, which means that a statistical analysis should be employed to make confident response predictions. In the high-frequency range, statistical energy analysis (SEA) is popular. However, SEA provides only averaged response predictions and cannot capture the resonant behavior in the response that becomes evident as frequency decreases. Thus, there exists a midfrequency range in which there is no established analysis technique analogous to FEA or SEA. The goal of this research is to produce a review paper on mid-frequency vibration analysis that will provide a survey of the relevant literature, identify the key technical challenges, formulate an assessment of the state of the art, and propose directions for future research. OBJECTIVESThe main objectives of this research are as follows: 1. Perform a comprehensive literature search on mid-frequency vibration analysis and related topics, and collect an extensive set of references 2. Review the relevant literature and summarize the mid-frequency approaches and techniques that have been developed to date 3. Assess the state of the art by determining the major research challenges in the field and drawing conclusions on research progress to date, including applications to realistic complex structures 4. Based on these findings, propose general directions and specific topics for future research 5. Write a review paper that p...

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Section: Local Energy Flow Analysismentioning

confidence: 99%

Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Pierre¹,

Castanier²

2002

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“…The near field contribution is assumed equal to zero, finally the spatial average operation allows obtaining a relation between the total energy density and the active power flow. Lase et al [23], Ichochou et al [24] developed the General Energy Method (GEM) for rods and beams. This method consists of expliciting the different terms of the harmonic complex energy flow balance.…”

Section: Introductionmentioning

confidence: 99%

Stochastic BEM for the Vibroacoustic Analysis of Three‐Dimensional Structures

D'Amico

Pratellesi

Pierini

et al. 2011

Advances in Acoustics and Vibration

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Nowadays, extending the NVH prediction reliability to the whole frequency range is an attractive goal of vibroacoustics. Deterministic methodologies are well established for the low-frequency range, but, decreasing the wavelength, energy-based methods are necessary. In such a range, a crucial role is played by small perturbations which highly influence the response sensitivity. Moreover, taking into account these variations allows to make the product design more robust and even quicker. Introducing geometrical uncertainties within the classic BEM formulation allows to obtain the so-called stochastic BEM. As a result, the solution shows deterministic behaviour at low frequencies; decreasing the wavelength, the effect of the uncertainties smooths the response. Consequently, it is possible to obtain an averaged trend over the whole frequency range which asymptotically tends to the deterministic one. In this paper, we deal with three-dimensional acoustic SBEM. First, the formulation and its basic assumptions are presented. Secondly, they are applied to academic cases to show its potentialities in predicting vibroacoustic behaviour over a wide frequency range.

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“…Basically, this way of thinking can be viewed as a local energy formalism whereas the SEA formalism is based on global energies of finite subsystems. This model has been improved in [5,6,7,8,9,10]. Among other contributors to this subject, let mention references [11,12,13,14] where interesting discussions are given.…”

Section: Introductionmentioning

confidence: 99%

“…Among other contributors to this subject, let mention references [11,12,13,14] where interesting discussions are given. In [8,9,10] energy models started with the so-called general energy method. The main goal of this method was to reformulate the classical displacement models using four energy variables: the total energy as well as the Lagrangian energy density, the active and the reactive energy flow.…”

Section: Introductionmentioning

confidence: 99%

“…References [9,10,15,16,17] give in depth the formulations used in the context of local energy approach applications. The MES has already been applied to various domains: beams [8,18], membranes and plates [19,20,11,8,15] and acoustical radiation [21,22,18]. In this paper, the main concern is the improvement of MES prediction for internal acoustics [23].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Coupled Bem and Energy Flow Method for Mid-High Frequency Internal Acoustic

2010

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To cite this version:Sébastien Besset, Mohamed Ichchou, Louis Jezequel. A coupled BEM and energy flow method for midhigh frequency internal acoustic. Abstract This paper deals with the behaviour of acoustic cavities in the mid-high frequency range. The method proposed here is based on an energy flow method named Simplified Energy Method (MES). MES method is quite efficient in the mid-high frequency range but the directivity of the boundary sources is not well estimated. We propose a hybrid method which couples MES and the Boundary Element Method (BEM). Thus, the BEM method is used to estimate the direct field, considering a "correct" directivity. As a complete calculation is not adapted to BEM in mid-high frequency range because of the calculation costs, we only apply BEM on the domains including boundary sources. Other parts of the system and the reverberated field are estimated by the mean of MES method. This hybrid method leads to a consistent prediction of injected power densities. Numerical comparisons prove the efficiency of the proposed reformulation.

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Energy Flow Analysis of Bars and Beams: Theoretical Formulations

Cited by 72 publications

References 1 publication

Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Stochastic BEM for the Vibroacoustic Analysis of Three‐Dimensional Structures

A Coupled Bem and Energy Flow Method for Mid-High Frequency Internal Acoustic

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