Analysis of Medium-Frequency Vibrations in a Frequency Range

2003 ◽  
Vol 11 (02) ◽  
pp. 255-283 ◽  
Author(s):  
P. Ladevèze ◽  
P. Rouch ◽  
H. Riou ◽  
X. Bohineust
Keyword(s):  
Frequency Range ◽  
Variational Theory ◽  
Elastic Structures ◽  
Medium Frequency ◽  
New Approach ◽  
Numerical Examples ◽  
Vibrational Response ◽  
Complex Rays ◽  
Medium Frequency Range

A new approach called the ''Variational Theory of Complex Rays'' (VTCR) is being developed in order to calculate the vibrations of slightly damped elastic structures in the medium-frequency range. Here, the emphasis is put on the extension of this theory to analysis across a range of frequencies. Numerical examples show the capability of the VTCR to predict the vibrational response of a structure in a frequency range.

THE MULTISCALE VTCR APPROACH APPLIED TO ACOUSTICS PROBLEMS

2008 ◽  
Vol 16 (04) ◽  
pp. 487-505 ◽  
Author(s):  
HERVÉ RIOU ◽  
PIERRE LADEVEZE ◽  
BENJAMIN SOURCIS
Keyword(s):  
Variational Formulation ◽  
Computational Effort ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Frequency Range ◽  
Variational Theory ◽  
Structural Vibrations ◽  
Medium Frequency ◽  
Great Flexibility ◽  
Complex Rays

An approach, called the "Variational Theory of Complex Rays," was proposed recently for calculating the vibrations of slightly damped elastic structures in the medium-frequency range. One key feature of this approach is the use of a new variational formulation of the vibration problem which allows the shape functions to be discontinuous across element boundaries, thus giving this strategy great flexibility and robustness. This method was fully developed for structural vibrations. In this paper, we apply it to acoustics problems. Examples of two-dimensional Helmholtz problems show that this method is very robust and accurate yet requires much less computational effort than the finite element method, which enables one to use it up to much higher frequencies.

ANALYSIS OF STRUCTURES WITH STOCHASTIC INTERFACES IN THE MEDIUM-FREQUENCY RANGE

2005 ◽  
Vol 13 (04) ◽  
pp. 711-729 ◽  
Author(s):  
CLAUDE BLANZÉ ◽  
PHILIPPE ROUCH
Keyword(s):  
Complex Structures ◽  
Random Response ◽  
Shape Functions ◽  
Frequency Range ◽  
Variational Theory ◽  
Medium Frequency ◽  
Stochastic Parameters ◽  
Interface Parameters ◽  
Interface Equations ◽  
Complex Rays

This paper proposes efficient techniques to obtain effective quantities when dealing with complex structures (including stochastic parameters, such as interface parameters) in medium-frequency vibrations. The first ingredient is the use of a dedicated approach — the Variational Theory of Complex Rays (VTCR) — to solve the medium-frequency problem. The VTCR, which uses two-scale shape functions verifying the dynamic equation and the constitutive relation, can be viewed as a means of expressing the power balance at the different interfaces between substructures. The second ingredient is the use of the Polynomial Chaos Expansion (PCE) to calculate the random response. Since the only uncertain parameters are those which appear in the interface equations (which, in this application, are the complex connection stiffness parameters), this approach leads to very low computation costs.

Topographic Analysis of Steady-State Visual Evoked Potentials (SVEPs) in The Medium Frequency Range in Migraine With and Without Aura

Cephalalgia ◽  
1992 ◽  
Vol 12 (4) ◽  
pp. 244-249 ◽  
Author(s):  
Franco M Puca ◽  
Marina de Tommaso ◽  
Maria A Savarese ◽  
Sergio Genco ◽  
Addolorata Prudenzano
Keyword(s):  
Steady State ◽  
Frequency Range ◽  
Medium Frequency ◽  
Topographic Analysis ◽  
Absolute Power ◽  
Interhemispheric Coherence ◽  
The Mean ◽  
Student’S T ◽  
Medium Frequency Range ◽  
Student’S T Test

Topographic analysis of SVEPs in the medium frequencies range was performed in 30 migraineurs without aura, 20 migraineurs with aura and in 20 control subjects. The mean absolute power values of the fundamental component F1, the subharmonic F1/2 and the first harmonic F2, corrected by logarithmic transformation, were computed in each group and then compared using Student's t-test. The interhemispheric coherence of the F1 component was also evaluated. The 18, 21 and 27 Hz F1 components were increased in both migraineurs with and without aura, particularly in the temporo-parietal regions. The 24 Hz F1 component was augmented only in migraineurs without aura in the parieto-occipital regions in comparison with migraineurs with aura and controls. Migraine with aura patients had a reduced interhemispheric coherence mostly of 12 Hz and 15 Hz F1 components in frontal and temporo-parietal regions. Results of the study confirm abnormalities of SVEPs in migraineurs with and without aura. These consist of widespread increases of F1 components in the medium frequency range over the temporo-parietal regions.

Measurements of the Surface Elasticity in Medium Frequency Range Using the Oscillating Bubble Method

1998 ◽  
Vol 208 (1) ◽  
pp. 34-48 ◽  
Author(s):  
Klaus-Dieter Wantke ◽  
Horst Fruhner ◽  
Jiping Fang ◽  
Klaus Lunkenheimer
Keyword(s):  
Surface Elasticity ◽  
Frequency Range ◽  
Medium Frequency ◽  
Medium Frequency Range

scholarly journals AN ADAPTIVE NUMERICAL STRATEGY FOR THE MEDIUM-FREQUENCY ANALYSIS OF HELMHOLTZ'S PROBLEM

2012 ◽  
Vol 20 (01) ◽  
pp. 1250001 ◽  
Author(s):  
HERVÉ RIOU ◽  
PIERRE LADEVÈZE ◽  
BENJAMIN SOURCIS ◽  
BÉATRICE FAVERJON ◽  
LOUIS KOVALEVSKY
Keyword(s):  
Degrees Of Freedom ◽  
Acoustic Vibration ◽  
Accurate Solution ◽  
Variational Theory ◽  
Wave Shape ◽  
Medium Frequency ◽  
Governing Differential Equation ◽  
Vibration Problems ◽  
Complex Rays ◽  
Numerical Strategy

The variational theory of complex rays (VTCR) is a wave-based predictive numerical tool for medium-frequency problems. In order to describe the dynamic field variables within the substructures, this approach uses wave shape functions which are exact solutions of the governing differential equation. The discretized parameters are the number of substructures (h) and the number of wavebands (p) which describe the amplitude portraits. Its capability to produce an accurate solution with only a few degrees of freedom and the absence of pollution error make the VTCR a suitable numerical strategy for the analysis of vibration problems in the medium-frequency range. This approach has been developed for structural and acoustic vibration problems. In this paper, an error indicator which characterizes the accuracy of the solution is introduced and is used to define an adaptive version of the VTCR. Numerical illustrations are given.

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