Finite Element Solution and Dispersion Analysis for the Transient Structural Acoustics Problem

1990 ◽  
Vol 43 (5S) ◽  
pp. S381-S388 ◽  
Author(s):  
N. N. Abboud ◽  
P. M. Pinsky
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Dispersion Analysis ◽  
Time Dependent ◽  
Element Approximation ◽  
Element Formulation ◽  
Structural Acoustics ◽  
Boundary Operators

In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. The variational statement of the governing equations is developed from a Hamiltonian approach that is modified for nonconservative systems. The dispersive properties of finite element semidiscretizations of the three dimensional wave equation are examined. This analysis throws light on the performance of the finite element approximation over the entire range of wavenumbers and the effects of the order of interpolation, mass lumping, and direction of wave propagation are considered.

Transient Finite Element Analysis of the Exterior Structural Acoustics Problem

1990 ◽  
Vol 112 (2) ◽  
pp. 245-256 ◽  
Author(s):  
P. M. Pinsky ◽  
N. N. Abboud
Keyword(s):  
Finite Element ◽  
Single Layer ◽  
Mirror Image ◽  
Time Dependent ◽  
Element Approximation ◽  
Element Formulation ◽  
Structural Acoustics ◽  
Element Analysis ◽  
Displacement Potential ◽  
Variational Formalism

Considerable progress has been made in the development of numerical methods for the time-harmonic exterior structural acoustics problem involving solution of the coupled Helmholtz equation. In contrast, numerical solution procedures for the transient case have not been studied so extensively. In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. In the fluid domain, a mixed two-field finite element approximation, based on a specialization of the Hu-Washizu principle for elasticity, is proposed and employs pressure and displacement potential as independent fields. Since radiation dissipation renders the coupled system nonconservative, a variational formalism based on the Morse and Feshbach concept of a “mirror-image” adjoint system is used. The variational formalism also accommodates viscoelastic dissipation in the structure (or its coatings) and this is considered in the paper. Very accurate results for model problems involving a single layer of fluid elements have been obtained and are discussed in detail.

Well‐posedness and finite element approximation of time dependent generalized bioconvective flow

2019 ◽  
Vol 36 (4) ◽  
pp. 709-733
Author(s):  
Yanzhao Cao ◽  
Song Chen ◽  
Hans‐Werner Wyk
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Time Dependent ◽  
Element Approximation ◽  
Well Posedness ◽  
Bioconvective Flow

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

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