Computation of normal modes based on a coupled finite/infinite element formulation

2021 ◽  
Vol 149 (4) ◽  
pp. A67-A67
Author(s):  
Felix Kronowetter ◽  
Eser Martin ◽  
Suhaib K. Baydoun
Keyword(s):  
Normal Modes ◽  
Element Formulation ◽  
Infinite Element

A Combined Perfectly Matching Layer and Infinite Element Formulation for Unbounded Wave Problems in the Frequency Domain

2014 ◽  
Author(s):  
Joseph S. Pettigrew ◽  
Anthony J. Mulholland ◽  
Jeffrey L. Cipolla ◽  
John Mould ◽  
Robert Banks
Keyword(s):  
Frequency Domain ◽  
Marked Improvement ◽  
Test Problem ◽  
Near Field ◽  
Element Formulation ◽  
Infinite Element ◽  
Matching Layer ◽  
Modal Response ◽  
New Type ◽  
Wave Problems

In this paper, Berenger’s Perfectly Matching Layer (PML) and Bettess’ Infinite Element (IE) scheme are combined to create a new type of element for unbounded acoustic wave problems. An assessment of this new element formulation is made through its use in the calculation of the acoustic modal response of a spherical radiator in the frequency domain. The performance of the PML+IE approach is contrasted with the IE only methodology by comparing them to the exact solution of this test problem in terms of the surface inertia and resistance in the near field. The results are encouraging and the PML+IE approach shows a marked improvement in performance, particularly at lower frequencies.

scholarly journals Spectral Stochastic Infinite Element Method in Vibroacoustics

2020 ◽  
Vol 28 (02) ◽  
pp. 2050009
Author(s):  
Felix Kronowetter ◽  
Lennart Moheit ◽  
Martin Eser ◽  
Kian K. Sepahvand ◽  
Steffen Marburg
Keyword(s):  
Input Data ◽  
Solution Technique ◽  
Element Formulation ◽  
Random Input ◽  
Infinite Element ◽  
Time Harmonic ◽  
Generalized Polynomial ◽  
Infinite Element Method ◽  
Random Input Data ◽  
Element Method

A novel method to solve exterior Helmholtz problems in the case of multipole excitation and random input data is developed. The infinite element method is applied to compute the sound pressure field in the exterior fluid domain. The consideration of random input data leads to a stochastic infinite element formulation. The generalized polynomial chaos expansion of the random data results in the spectral stochastic infinite element method. As a solution technique, the non-intrusive collocation method is chosen. The performance of the spectral stochastic infinite element method is demonstrated for a time-harmonic problem and an eigenfrequency study.

scholarly journals Geometrically nonlinear autonomous reduced order model for rotating structures

2018 ◽  
Author(s):  
Mikel Balmaseda ◽  
Georges Jacquet-Richardet ◽  
Antoine Placzek ◽  
Duc-Minh Tran
Keyword(s):  
Normal Modes ◽  
Harmonic Balance Method ◽  
Reduced Order Model ◽  
Static Equilibrium ◽  
Evaluation Procedure ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Reduced Basis ◽  
Order Model ◽  
Reduced Order

In the present work, as an extension to [2], an autonomous geometrically nonlinear reduced order model for the study of dynamic solutions of complex rotating structures is developed. In opposition to the classical finite element formulation for geometrically nonlinear rotating structures that considers small linear vibrations around the static equilibrium, nonlinear vibrations around the pre-stressed equilibrium are now considered. For that purpose, the linear normal modes are used as a reduced basis for the construction of the reduced order model. The stiffness evaluation procedure method (STEP) [4] is applied to compute the nonlinear forces induced by the displacements around the static equilibrium. This approach enhances the classical linearised small perturbations hypothesis to the cases of large displacements around the static pre-stressed equilibrium. Furthermore, a comparison between the steady solution given by HHT-α [1] and the Harmonic Balance Method (HBM) [3] is carried out. The proposed reduced order models are evaluated for a rotating beam case study.

scholarly journals Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

2021 ◽  
pp. 108128652110408
Author(s):  
Joseph S. Pettigrew ◽  
Anthony J. Mulholland ◽  
Katherine M. M. Tant
Keyword(s):  
Finite Element ◽  
Elastic Wave ◽  
Three Dimensions ◽  
Element Formulation ◽  
Infinite Element ◽  
Matching Layer ◽  
Plane Wave Incident ◽  
The Time Domain ◽  
Wave Problems ◽  
Stress Free Boundary

This paper presents a framework for implementing a novel perfectly matching layer and infinite element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain. To achieve this, traditional hexahedral finite elements are used to model wave propagation in the inner domain and IE test functions are implemented in the exterior domain. Two alternative implementations of the PML formulation are studied: the case with constant stretching in all three dimensions and the case with spatially dependent stretching along a single direction. The absorbing ability of the PML+IE formulation is demonstrated by the favourable comparison with the reflection coefficient for a plane wave incident on the boundary achieved using a finite-element-only approach where stress free boundary conditions are implemented at the domain edge. Values for the PML stretching function parameters are selected based on the minimisation of the reflected wave amplitude and it is shown that the same reduction in reflection amplitude can be achieved using the PML+IE approach with approximately half of the number of elements required in the finite-element-only approach.

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