Approximation of the Vibration Modes of a Plate and Shells Coupled With a Fluid

2006 ◽  
Vol 73 (6) ◽  
pp. 1005-1010 ◽  
Author(s):  
E. Hernández
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Compressible Fluid ◽  
Numerical Experiments ◽  
Vibration Modes ◽  
Solid Interface ◽  
Thin Structure ◽  
Fluid Equations ◽  
Element Method

We consider a method to compute the vibration modes of an elastic thin structure (shell or plate) in contact with a compressible fluid. For the structure, the classical Naghdi equations, based on the Reissner–Mindlin hypothesis, are considered and its approximation using the mixed interpolation of tensorial component 4 finite element method. The fluid equations are discretized by using Raviart–Thomas elements, and a non-conforming coupling is used on the fluid-solid interface. Numerical experiments are reported, assessing the efficiency of this coupled scheme.

scholarly journals A Least-Squares FEM for the Direct and Inverse Rectangular Cavity Scattering Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Enxi Zheng ◽  
Fuming Ma ◽  
Yujie Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Numerical Experiments ◽  
Bessel Functions ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Rectangular Cavity ◽  
Total Field ◽  
Element Method

This paper is concerned with the scattering problem of a rectangular cavity. We solve this problem by a least-squares nonpolynomial finite element method. In the method, we use Fourier-Bessel functions to capture the behaviors of the total field around corners. And the scattered field towards infinity is represented by a combination of half-space Green functions. Then we analyze the convergence and give an error estimate of the method. By coupling the least-squares nonpolynomial finite element method and the Newton method, we proposed an algorithm for the inverse scattering problem. Numerical experiments are presented to show the effectiveness of our method.

Numerical experiments in quantum physics: Finite‐element method

1988 ◽  
Vol 56 (5) ◽  
pp. 444-448 ◽  
Author(s):  
Debra J. Searles ◽  
Ellak I. von Nagy‐Felsobuki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Quantum Physics ◽  
Element Method

scholarly journals Determination of the frequencies and forms of free vibrations of pentagonal plates by the finite-element method

2020 ◽  
pp. 61-66
Author(s):  
A. Grigorenko ◽  
M. Borysenko ◽  
O. Boychuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibrations ◽  
Vibration Modes ◽  
The Finite Element Method ◽  
Rigid Attachment ◽  
Equivalent Mass ◽  
Practical Convergence ◽  
Element Method

Frequencies and modes of free vibrations of an isotropic thin pentagonal plate of regular shape with various configurations of rigid attachment at the edges are determined using the finite element method (FEM). The results obtained for some pentagonal plates are compared with the results obtained for square plates of an equivalent mass with corresponding boundary conditions. We present the vibration modes of the studied plates and the topology of the vibration modes for some of the considered plates corresponding to the square plates with free edges and rigidly fixed edges. The reliability of the obtained results is ensured by the use of a substantiated mathematical model, the correct formulation of the problem and the practical convergence of the calculated frequencies when using the FEM.

scholarly journals Application of control volume based finite element method for solving the black-oil fluid equations

2013 ◽  
Vol 10 (3) ◽  
pp. 361-372 ◽  
Author(s):  
S. A. Ghoreishian Amiri ◽  
S. A. Sadrnejad ◽  
H. Ghasemzadeh ◽  
G. H. Montazeri
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Control Volume ◽  
Black Oil ◽  
Fluid Equations ◽  
Element Method
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