Statistical energy analysis by finite elements for middle frequency vibration

Yan, Harold; Parrett, Alan; Nack, Wayne V.

doi:10.1016/s0168-874x(99)00071-2

Cited by 17 publications

(7 citation statements)

References 2 publications

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“…e feasibility of this method was veri ed by comparison. Totaro et al [29][30][31][32] used mode data and FEM to evaluate CLF of an uncoupled subsystem. Simmons [31] estimated CLF of SEA subsystem mode parameters.…”

Section: Expression Of Coupling Loss Factor (Clf)mentioning

confidence: 99%

Research Progress on High‐Intermediate Frequency Extension Methods of SEA

Zheng

Deng

et al. 2019

Shock and Vibration

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Statistical energy analysis (SEA) can accurately describe the average vibration characteristics through system energy flow and transmission feedback. It is a powerful tool to solve the problem of high-frequency acoustics-vibration. SEA is widely used in vehicles, ships, aviation, and other transportation engineering fields. However, the expansion of SEA, based on the assumption of modal equipartition and weak coupling, is limited to the intermediate frequency. Although the SEA basic theory can be extended by relaxing the hypothesis conditions or the analysis of the medium-frequency acoustics-vibration can be carried out using the finite element method (FEM) and SEA mixing method, there are still many challenges associated with these options. To improve the basic theory of SEA and knowledge of intermediate frequency extension methods, as well as attract the attention of domestic scholars, this paper describes classical SEA and intermediate frequency extension methods. First, coupling loss factor (CLF) error propagation and parameter acquisition in classical SEA are introduced, and the three relative error calculation methods of CLF are compared. Then, the method of obtaining parameters is described from three aspects of energy transfer, input load, and modal density. Second, SEA intermediate frequency extension technology (experimental statistical energy analysis (ESEA), finite element statistical energy analysis (FE-SEA), statistical modal energy distribution analysis (SMEDA), and waveguide analysis (WGA)) are introduced. Neutron structure assembly and modeling, interval and mixed interval analysis, interval variable and mixed interval variable response are also described, so as to justify the development of a hybrid, large-scale interval algorithm. Finally, the engineering application of the above method is introduced, the limitations and shortcomings of SEA and intermediate frequency extension methods are reviewed, and unsolved problems are further discussed.

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Section: Expression Of Coupling Loss Factor (Clf)mentioning

confidence: 99%

Research Progress on High‐Intermediate Frequency Extension Methods of SEA

Zheng

Deng

et al. 2019

Shock and Vibration

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“…Yan et al [99] implemented this type of combined FEA/SEA approach in commercial software. They used NASTRAN to calculate impedance matrices at every driving frequency, and post-processed them to obtain coupling loss factors.…”

Section: Power Flow and Uncertainty 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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“…25 In a different approach from the traditional solutions of mechanical vibrations, the statistical method uses the energy of each subsystem as the basic parameters to solve the vibration problem. 26 Besides SEA, there are also other methods which utilize the energy contributions of vibration modes to make more accurate approximations to vibrations 27 such as the detection of dominant modes of shell structures under external excitations like wind or ground motion 28,29 and using dominating energy distribution to characterize the vibration signals. 30 In this paper, we focus on the high frequency vibration analysis of the quartz crystal resonator and target locating the pure thickness-shear mode from the coupled vibrations with energy formulation at each frequency with multiple vibration modes or degree-offreedoms (DOFs).…”

Section: Introductionmentioning

confidence: 99%

Identification of Vibration Modes of Quartz Crystal Plates with Proportion of Strain and Kinetic Energies

Huang¹,

Wu²,

Wang³

et al. 2020

The International Journal of Acoustics and Vibration

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For the design of quartz crystal resonators, finding and determining the vibration modes have always been very important and cumbersome. Vibration modes are usually identified through plotting displacement patterns of each coupled modes and making comparisons. Over the years, there is not much improvement in the identification procedure while tremendous efforts have been made in refining the equations of the Mindlin plate theory to obtain more accurate results, such as the adoption of the Finite Element Method (FEM) by implementing the high-order Mindlin plate equations for efficient analysis. However, due to the old fashioned mode identification method, the FEM application is still inadequate and cannot be fully automated for this purpose. To have this situation improved, a method using the proportions of strain and kinetic energies to characterize the energy level of each vibration mode is proposed. With solutions of displacements, the energy distribution of each vibration mode is calculated and the mode with the highest energy concentration at a specific frequency is designated as the dominant mode. The results have been validated with the traditional approach by plotting mode shapes at each frequency. Clearly, this energy approach will be advantageous with the FEM analysis for vibration mode identification automatically.

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Statistical energy analysis by finite elements for middle frequency vibration

Cited by 17 publications

References 2 publications

Research Progress on High‐Intermediate Frequency Extension Methods of SEA

Research Progress on High‐Intermediate Frequency Extension Methods of SEA

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

Identification of Vibration Modes of Quartz Crystal Plates with Proportion of Strain and Kinetic Energies

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