A homogenization-based Chebyshev interval finite element method for periodical composite structural-acoustic systems with multi-scale interval parameters

2018 ◽  
Vol 233 (10) ◽  
pp. 3444-3458 ◽  
Author(s):  
Ning Chen ◽  
Jiaojiao Chen ◽  
Jian Liu ◽  
Dejie Yu ◽  
Hui Yin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Pressure ◽  
Acoustic System ◽  
Interval Parameters ◽  
Multi Scale ◽  
Small Uncertainty ◽  
Interval Finite Element Method ◽  
Scale Interval ◽  
Element Method

For the periodical composite structural-acoustic system with multi-scale interval uncertainties, a new interval analysis approach is presented in this study. In periodical composites structural-acoustic systems with multi-scale interval parameters, the variation ranges of the sound pressure response can be calculated using the homogenization-based interval finite element method. However, the homogenization-based interval finite element method that is based on Taylor series can only suit periodical composites structural-acoustic problems with small uncertainty degree. To consider larger uncertainty degree, by combining the Chebyshev polynomial series and the homogenization-based finite element, a homogenization-based Chebyshev interval finite element method is presented to predict the sound pressure responses of the structural-acoustic system involving periodical composite and multi-scale interval parameters. Compared with homogenization-based interval finite element method, homogenization-based Chebyshev interval finite element method can obtain higher accurate numerical solutions in the approximate process. Besides, homogenization-based Chebyshev interval finite element method can be implemented without conducting the complex derivation process. Numerical results verify the validity and practicability of the presented homogenization-based Chebyshev interval finite element method for the periodical composite structural-acoustic problem.

Modified Interval Perturbation Finite Element Method for a Structural-Acoustic System With Interval Parameters

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Baizhan Xia ◽  
Dejie Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Dynamic Equilibrium ◽  
Dynamic Stiffness ◽  
Response Analysis ◽  
Acoustic System ◽  
Dynamic Stiffness Matrix ◽  
Interval Parameters ◽  
Element Method

For the frequency response analysis of the structural-acoustic system with interval parameters, a modified interval perturbation finite element method (MIPFEM) is proposed. In the proposed method, the interval dynamic equilibrium equation of the uncertain structural-acoustic system is established. The interval structural-acoustic dynamic stiffness matrix and the interval force vector are expanded by using the first-order Taylor series; the inversion of the invertible interval structural-acoustic dynamic stiffness matrix is approximated by employing a modified approximate interval-value Sherman–Morrison–Woodbury formula. The proposed method is implemented at an element-by-element level in the finite element framework. Numerical results on a shell structural-acoustic system with interval parameters verify the accuracy and efficiency of the proposed method.

scholarly journals A posteriori error estimates for a multi-scale finite-element method

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Khallih Ahmed Blal ◽  
Brahim Allam ◽  
Zoubida Mghazli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
A Posteriori Error Estimates ◽  
Numerical Test ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
A Posteriori ◽  
Essential Information ◽  
Multi Scale ◽  
Element Method

AbstractWe are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an a posteriori analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.

Analysis for Vehicle Interior Noise Using Helmholtz Resonator

2005 ◽  
Author(s):  
Wakae Kozukue ◽  
Ichiro Hagiwara ◽  
Yasuhiro Mohri
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Resonance Frequency ◽  
Sound Pressure ◽  
Helmholtz Resonator ◽  
The Finite Element Method ◽  
Vehicle Interior ◽  
Vehicle Cabin ◽  
Set Up ◽  
Element Method

In this paper the reduction analysis of the so-called ‘booming noise’, which occurs due to the resonance of a vehicle cabin, is tried to carry out by using the finite element method. For the reduction method a Helmholtz resonator, which is well known in the field of acoustics, is attached to a vehicle cabin. The resonance frequency of a Helmholtz resonator can be varied by adjusting the length of its throat. The simply shaped Helmholtz resonator is set up to the back of the cabin according to the resonance frequency of the cabin and the frequency response of the sound pressure at a driver’s ear position is calculated by using the finite element method. It is confirmed that the acoustical characteristics of the cabin is changed largely by attaching the resonator and the sound quality is quite varied. The resonance frequency of the resonator can be considered to follow the acoustical characteristics of the cabin by using an Origami structure as a throat. So, in the future the analysis by using an Origami structure Helmholtz resonator should be performed.

scholarly journals A substructure-based interval finite element method for problems with uncertain but bounded parameters

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668407
Author(s):  
Yihuan Zhu ◽  
Guojian Shao ◽  
Jingbo Su ◽  
Ang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Evaluation System ◽  
Nonlinear Problems ◽  
Expansion Method ◽  
Constant Matrix ◽  
Approximation Solution ◽  
Interval Finite Element Method ◽  
Necessary Constraints ◽  
Element Method

In this article, the dependency between different elements in solid structures is considered and a substructure-based interval finite element method is used to model the interval properties. The penalty method is applied to impose the necessary constraints for compatibility. In order to obtain the interval stresses, an approximation solution based on the Taylor expansion method is presented. Then, the proposed interval substructure model is expanded to nonlinear problems. In consideration of the nonlinear property of the elasticity modulus, an interval elastoplastic substructure analysis method using constant matrix based on the incremental theory is proposed and the interval expression of the interval stress updated formation is derived. Finally, numerical examples are carried out to demonstrate the reasonability and feasibility of the proposed method and evaluation system.

Development of Multi-scale Plastic Analysis Code Based on Crystalline Homogenization Finite Element Method

2002 ◽  
Vol 2002.15 (0) ◽  
pp. 127-128
Author(s):  
Shinji IIHOSHI ◽  
Y. P. CHEN ◽  
Sei UEDA ◽  
Yasutomo UETSUJI ◽  
Eiji NAKAMACHI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Multi Scale ◽  
Plastic Analysis ◽  
Element Method
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