A discontinuous enrichment method for the efficient solution of plate vibration problems in the medium-frequency regime

2010 ◽  
pp. n/a-n/a
Author(s):  
Paolo Massimi ◽  
Radek Tezaur ◽  
Charbel Farhat
Keyword(s):  
Efficient Solution ◽  
Plate Vibration ◽  
Medium Frequency ◽  
Enrichment Method ◽  
Discontinuous Enrichment ◽  
Frequency Regime ◽  
Vibration Problems

Recent Developments in High-Performance Computational Vibro-Acoustics in the Medium Frequency Regime

2012 ◽  
Author(s):  
Charbel Farhat ◽  
Radek Tezaur ◽  
Ulrich Hetmaniuk
Keyword(s):  
High Performance ◽  
Computational Cost ◽  
Medium Frequency ◽  
Time Frequency ◽  
Additional Information ◽  
Reduction Techniques ◽  
Discontinuous Enrichment ◽  
Recent Developments ◽  
Frequency Regime ◽  
Frequency Sweeps

Structural acoustics applications in the medium frequency regime are computationally challenging. One avenue of research pursues higher-order discretization methods that can deliver both accuracy and computational efficiency at smaller mesh resolutions. The Discontinuous Enrichment Method (DEM) is one example which distinguishes itself from competing approaches in the additional information it incorporates in the approximation method. It has shown a significant promise for acoustic and structural acoustic applications and therefore is reviewed here, together with new applications to shell problems. Frequency sweeps, which are almost inevitable in many vibro-acoustic engineering problems, present an additional challenge as they significantly increase the already high computational cost. Therefore, interpolatory model reduction techniques that successfully address this challenge and enable real-time frequency sweep analyses are also discussed in this paper.

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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