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.

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 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.

scholarly journals Hybrid Finite Element Method and Variational Theory of Complex Rays for Helmholtz Problems

2016 ◽  
Vol 24 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Hao Li ◽  
Pierre Ladevèze ◽  
Hervé Riou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Variational Theory ◽  
Numerical Examples ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Vibration Problems ◽  
Complex Rays ◽  
Element Method

In this paper, we consider the Weak Trefftz Discontinuous Galerkin (WTDG) method, which enables one to use at the same time the Finite Element Method (FEM) or Variational Theory of Complex Rays (VTCR) discretizations (polynoms and waves), for vibration problems. It has already been developed such that the FEM and the VTCR can be used in different adjacent subdomains in the same problem. Here, it is revisited and extended in order to allow one to use the two discretizations in the same subdomain, at the same time. Numerical examples illustrate the performances of such an approach.

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