scholarly journals A Multidomain Spectral Method for Analysis of Interior Vibroacoustic Systems with Segmented Boundaries

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Zhenguo Zhang ◽  
Haiting Yu ◽  
Ningyuan Duan ◽  
Hongxing Hua
Keyword(s):  
Finite Element ◽  
Elastic Solid ◽  
Acoustic Medium ◽  
Generalized Variational Principle ◽  
Structural Acoustics ◽  
High Frequencies ◽  
Single Plate ◽  
Structure Assembly ◽  
High Computational Efficiency ◽  
Discretization Procedure

Spectral methods have previously been applied to analyze a multitude of vibration and acoustic problems due to their high computational efficiency. However, their application to interior structural acoustics systems has been limited to the analysis of a single plate coupled to a fluid-filled cavity. In this work, a general multidomain spectral approach is proposed for the eigenvalue and steady-state vibroacoustic analyses of interior structural-acoustic problems with discontinuous boundaries. The unified formulation is derived by means of a generalized variational principle in conjunction with the spectral discretization procedure. The established framework enables one to easily accommodate complex systems consisting of both a structure assembly and a built-up cavity with moderate geometric complexities and to effectively analyze vibroacoustic behaviors with sufficient accuracy at relatively high frequencies. Two practical examples are chosen to demonstrate the flexibility and efficiency of the proposed formulation: a built-up cavity backed by an assembly of multiple connected plates with arbitrary orientations and a thick irregular elastic solid coupled with a heavy acoustic medium. Comparison to finite element simulations and convergence studies for these two examples illustrate the considerable computational advantage of the method as compared to finite element procedures.

Non-Reflecting Finite Element Schemes for Three-Dimensional Acoustic Waves

1997 ◽  
Vol 05 (01) ◽  
pp. 95-115 ◽  
Author(s):  
Igor Patlashenko ◽  
Dan Givoli
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Infinite Medium ◽  
Wave Guide ◽  
Acoustic Medium ◽  
Structural Acoustics ◽  
Artificial Boundary ◽  
Finite Element Schemes

The finite element solution of problems involving three-dimensional acoustic waves in an infinite wave guide, and in the infinite medium around a structure is considered. Such problems are typical in structural acoustics, and this paper concentrates on the efficient numerical treatment of the infinite acoustic medium away from the structure. The unbounded domain is truncated by means of an artificial boundary ℬ. On ℬ, non-reflecting boundary conditions are used; these are either nonlocal Dirichlet-to-Neumann conditions, or their localized counterparts. For the high-order localized conditions, special three-dimensional finite elements are constructed for use in the layer adjacent to ℬ. The performance of the nonlocal and localized boundary conditions is compared via numerical experiments involving a three-dimensional wave guide.

Design of an Induction Glass Melting Furnace by Means of Mathematical Modelling Using the Finite Element Method

2007 ◽  
Vol 553 ◽  
pp. 124-129 ◽  
Author(s):  
Isaac Arellano ◽  
Gabriel Plascencia ◽  
Elías Carrillo ◽  
Miguel A. Barrón ◽  
Adolfo Sánchez ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Glass Melting ◽  
Melting Furnace ◽  
The Finite Element Method ◽  
Glass Melting Furnace ◽  
High Frequencies ◽  
Harmful Emissions ◽  
The Mathematical Model ◽  
Element Method

In this paper we propose the design of a novel induction furnace for glass melting. The design is based on a mathematical analysis and performed numerically by means of the Finite Element Method. Several induction coils configurations were tested. The results from the mathematical model show that it is possible to melt glass in a furnace whose hearth is no larger than half a metre by using axial induction coils and high frequencies. This furnace configuration may result in increased glass melting rates along with the elimination of harmful emissions.

A Multi-Field Space-Time Finite Element Method for Structural Acoustics

1995 ◽  
Author(s):  
Lonny L. Thompson
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Acoustic Waves ◽  
Space Time ◽  
High Order ◽  
Elastic Structure ◽  
Structural Acoustics ◽  
Field Representation ◽  
Element Discretization ◽  
Acoustic Fluid

Abstract A Computational Structural Acoustics (CSA) capability for solving scattering, radiation, and other problems related to the acoustics of submerged structures has been developed by employing some of the recent algorithmic trends in Computational Fluid Dynamics (CFD), namely time-discontinuous Galerkin Least-Squares finite element methods. Traditional computational methods toward simulation of acoustic radiation and scattering from submerged elastic bodies have been primarily based on frequency domain formulations. These classical time-harmonic approaches (including boundary element, finite element, and finite difference methods) have been successful for problems involving a limited range of frequencies (narrow band response) and scales (wavelengths) that are large compared to the characteristic dimensions of the elastic structure. Attempts at solving large-scale structural acoustic systems with dimensions that are much larger than the operating wavelengths and which are complex, consisting of many different components with different scales and broadband frequencies, has revealed limitations of many of the classical methods. As a result, there has been renewed interest in new innovative approaches, including time-domain approaches. This paper describes recent advances in the development of a new class of high-order accurate and unconditionally stable space-time methods for structural acoustics which employ finite element discretization of the time domain as well as the usual discretization of the spatial domain. The formulation is based on a space-time variational equation for both the acoustic fluid and elastic structure together with their interaction. Topics to be discussed include the development and implementation of higher-order accurate non-reflecting boundary conditions based on the exact impedance relation through the. Dirichlet-to-Neumann (DtN) map, and a multi-field representation for the acoustic fluid based on independent pressure and velocity potential variables. Numerical examples involving radiation and scattering of acoustic waves are presented to illustrate the high-order accuracy achieved by the new methodology for CSA.

New Finite Element Modeling Strategy for Large-Scale Industrial Problems in Structural Acoustics

2000 ◽  
Author(s):  
Saikat Dey ◽  
Luise S. Couchman
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Large Scale ◽  
Structural Acoustics ◽  
Simple Scheme ◽  
Numerical Examples ◽  
High Wave ◽  
Wave Numbers ◽  
Complex Structural ◽  
Modeling Strategy

Abstract A simple scheme to model and mesh stiffened shell-like structures is presented. Combined with a high-order finite/infinite element based infrastructure, it enables the solution of complex structural acoustics problems at high wave numbers. Numerical examples are presented to show the applicability of the method at high wave-numbers.

Implementing Stretch-Based Strain Energy Functions in Large Coupled Axial and Torsional Deformations of Functionally Graded Cylinder

2019 ◽  
Vol 11 (04) ◽  
pp. 1950039 ◽  
Author(s):  
Arash Valiollahi ◽  
Mohammad Shojaeifard ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Hoop Stress ◽  
Constitutive Models ◽  
Elastic Solid ◽  
Functionally Graded ◽  
Deformation Tensor ◽  
Element Analysis ◽  
Hyperelastic Materials ◽  
Ogden Model ◽  
Exponential Power

In this paper, coupled axial and torsional large deformation of an incompressible isotropic functionally graded nonlinearly elastic solid cylinder is investigated. Utilizing stretch-based constitutive models, where the deformation tensor is non-diagonal is complex. Hence, an analytical approach is presented for combined extension and torsion of functionally graded hyperelastic cylinder. Also, finite element analysis is carried out to verify the proposed analytical solutions. The Ogden model is employed to predict the mechanical behavior of hyperelastic materials whose material parameters are function of radius in an exponential fashion. Both finite element and analytical results are in good agreement and reveal that for positive values of exponential power in material variation function, stress decreases and the rate of stress variation intensifies near the outer surface. A transition point for the hoop stress is identified, where the distribution plots regardless of the value of stretch or twist, intersect and the hoop stress alters from compressive to tensile. For the Ogden model, the torsion induced force is always compressive which means the total axial force starts from being tensile and then eventually becomes compressive i.e., the cylinder always tends to elongate on twisting.

scholarly journals Analysis of Very Fast Transients Using Black Box Macromodels in ATP-EMTP

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 698
Author(s):  
Jonathan James ◽  
Maurizio Albano ◽  
David Clark ◽  
Dongsheng Guo ◽  
Abderrahmane (Manu) Haddad
Keyword(s):  
Finite Element ◽  
Electromagnetic Transients ◽  
Element Analysis ◽  
Simple Method ◽  
Model Order ◽  
High Frequencies ◽  
Transient Simulations ◽  
Improved Stability ◽  
Fast Transients ◽  
Gas Insulated Substation

Modelling for very fast transients (VFTs) requires good knowledge of the behaviour of gas insulated substation (GIS) components when subjected to high frequencies. Modelling usually takes the form of circuit-based insulation coordination type studies, in an effort to determine the maximum overvoltages and waveshapes present around the system. At very high frequencies, standard transmission line modelling assumptions may not be valid. Therefore, the approach to modelling of these transients must be re-evaluated. In this work, the high frequency finite element analysis (FEA) was used to enhance circuit-based models, allowing direct computation of parameters from geometric and material characteristics. Equivalent models that replicate a finite element model’s frequency response for bus-spacer and 90° elbow components were incorporated in alternative transients program-electromagnetic transients program (ATP-EMTP) using a pole-residue equivalent circuit derived following rational fitting using the well-established and robust method of vector fitting (VF). A large model order is often required to represent this frequency dependent behaviour through admittance matrices, leading to increased computational burden. Moreover, while highly accurate models can be derived, the data extracted from finite element solutions can be non-passive, leading to instability when included in time domain simulations. A simple method of improved stability for FEA derived responses along with a method for identification of a minimum required model order for stability of transient simulations is proposed.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

THE EQUATION OF MOTION OF A GEOPHONE ON THE SURFACE OF AN ELASTIC EARTH

Geophysics ◽  
1944 ◽  
Vol 9 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Alfred Wolf
Keyword(s):  
Wave Length ◽  
Elastic Solid ◽  
Damping Force ◽  
High Frequencies ◽  
Elastic Earth ◽  
Linear Dimensions ◽  
The Earth ◽  
Restoring Forces ◽  
System Equations

The motion of a geophone case placed on the surface of an elastic earth does not follow faithfully the motion of the earth at high frequencies. In effect, a weight placed on the surface of an elastic solid constitutes a damped oscillating system. The elastic restoring forces are determined by the area of contact between the weight and the surface of the solid and by the elastic moduli of the solid. The damping force is due to emission of elastic waves by the oscillating weight. The motion of the solid also contributes to the inertia of the system. Equations are developed for these forces on the assumption that the wave length is long compared to the linear dimensions of the area of contact between the weight and the elastic solid. This leads to a determination of the frequency of oscillation and of the decrement of such a system.

Separable K-Canonical Formulation of Rectangular Element and Symplectic Integration Method for Analysis of Laminated Plates

2011 ◽  
Vol 194-196 ◽  
pp. 1496-1505
Author(s):  
Guang Hui Qing ◽  
Liang Wang ◽  
Li Zhong Shi
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Canonical System ◽  
Laminated Plates ◽  
Linear Elastic ◽  
Canonical Formulation ◽  
Single Plate ◽  
Static Responses ◽  
Rectangular Element ◽  
Symplectic Schemes

In the state space framework, a separable K-canonical formulation of rectangular element and explicit symplectic schemes for the static responses analysis of three-dimensional (3D) laminated plates are proposed in this paper. Firstly, the modified Hellinger-Reissner (H-R) variational principle for linear elastic solid is simply mentioned. Secondly, the separable J-canonical system with Hamiltonian H and the separable K-canonical formulation of rectangular element are constructed. Thirdly, on the basis of the symplectic difference schemes, the explicit symplectic schemes are employed to solve the separable K-canonical governing equation for a single plate. Then, to obtain the high accurate numerical results, a multi-scale iterative technique is also presented. Finally, based on the interlaminar compatibility condition (displacements and stresses), the excellent performance of the method presented in this paper is demonstrated by several numerical experiments of the static responses of laminated plates.

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