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.

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.

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.

scholarly journals The variational theory of complex rays for the calculation of medium‐frequency vibrations

2001 ◽  
Vol 18 (1/2) ◽  
pp. 193-214 ◽  
Author(s):  
P. Ladevèze ◽  
L. Arnaud ◽  
P. Rouch ◽  
C. Blanzé
Keyword(s):  
Variational Theory ◽  
Medium Frequency ◽  
Complex Rays

scholarly journals A method for updating joint parameters in medium-frequency vibrations

2008 ◽  
pp. 713-723
Author(s):  
Olivier Dorival ◽  
Philippe Rouch ◽  
Olivier Allix
Keyword(s):  
Model Updating ◽  
Element Model ◽  
Numerical Approach ◽  
Complex Structures ◽  
Variational Theory ◽  
Joint Models ◽  
Medium Frequency ◽  
New Formulation ◽  
Stiffness And Damping ◽  
Complex Rays

Joints between substructures play a significant role in the vibrational behavior of complex structures because they govern energy flow and most of the dissipative phenomena. In order to identify joint models, this paper proposes a robust updating method which was initially based on studies of the error in constitutive relation in relation to finite element model updating. Here, it is redesigned in order to focus on joint models in medium-frequency problems. In order to do that, we use an alternative numerical approach called the Variational Theory of Complex Rays (VTCR). After introducing the new formulation, the paper analyzes the effectiveness of the approach in identifying a joint’s stiffness and damping.

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