scholarly journals Numerical comparison of reduced order models for non-linear vibrations of damped plates

2012 ◽  
Author(s):  
F. Boumediene ◽  
L. Duigou ◽  
A. Miloudi ◽  
J.M. Cadou
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Computational Time ◽  
Numerical Comparison ◽  
Processing Unit ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Central Processing ◽  
Non Linear ◽  
Linear Vibrations

This work deals with the computation of the non-linear solutions of the vibration of damped plates by coupling a harmonic balance method and the asymptotic numerical method. These computations can lead to lengthy central processing unit (CPU) times if the solution sought contains an important number of harmonics. In this study, we propose two reduced order models which can be applied to solve this type of problem. Both reduced methods are based on a first computation carried out with a small number of harmonics (here two). Numerical examples of plate vibration show that these algorithms help save a great deal of computational time and can be applied to problems involving numerous harmonics.

Dynamic Analysis of Structures With Nonlinear Bolted Joints by Using an Adaptive Harmonic Balance Method

2009 ◽  
Author(s):  
Vincent Jaumouille´ ◽  
Jean-Jacques Sinou
Keyword(s):  
Harmonic Balance ◽  
Strain Energy ◽  
Harmonic Balance Method ◽  
Bolted Joints ◽  
Balance Method ◽  
Continuation Methods ◽  
Computational Time ◽  
Bolted Joint ◽  
Non Linear ◽  
Linear Effects

Aeronautical structures are commonly assembled with bolted joints in which friction phenomena provide damping on the dynamic behaviour. Some models, mostly non linear, have consequently been developed and the harmonic balance method (HBM) is adapted to compute non linear response functions in the frequency domain. The basic idea is to develop the response as a Fourier series and to solve equations linking Fourier coefficients. One specific HBM feature is that response accuracy improves as the number of harmonics increases, at the expense of larger computational time. Thus the aim of this study is to develop an adaptive HBM which appreciates numerically the contribution of each harmonic on the dynamic response. For a given precision, the number of retained harmonics is adapted by an algorithm which integrates a numerical criterion based on an approximate strain energy. The application case is an asymmetrical two cantilever beam system linked by a bolted joint represented by a nonlinear LuGre model. Condensation and continuation methods are used to accelerate calculation. Adaptive HBM shows that, for a given value of the criterion, the number of harmonics may increase on resonances indicating that non linear effects are predominant.

The Study of Aeroelastic Reduced-Order Model Based on CFD/CSD Method and its Application

2014 ◽  
Vol 978 ◽  
pp. 131-134
Author(s):  
Rui Li ◽  
Chang Hong Tang
Keyword(s):  
Harmonic Balance ◽  
Unsteady Aerodynamics ◽  
Harmonic Balance Method ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Advantages And Disadvantages ◽  
Aeroelastic Analysis ◽  
Proper Orthogonal

Unsteady aerodynamics research is the foundation of aeroelastic analysis. How to effectively improve the aeroelastic computational efficiency,it is the key of current research on aeroelasticity now.Reduced order models are proposed as a powerful tool to solve this problem. Analyzed the three reduced-order models for Volterra ,Proper Orthogonal Decomposition and Harmonic Balance method ,their advantages and disadvantages were pointed out. The direction of the reduced order model in the future was Proposed and some suggest was given out for its application.

A Scalable Time-Parallel Solution of Periodic Rotor Dynamics in X3D

2021 ◽  
Author(s):  
Mrinalgouda Patil ◽  
Anubhav Datta
Keyword(s):  
Harmonic Balance ◽  
Large Scale ◽  
Structural Model ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Flight Test ◽  
Solution Procedure ◽  
Balance Method ◽  
Computational Time ◽  
Near Resonance

A time-parallel algorithm is developed for large-scale three-dimensional rotor dynamic analysis. A modified harmonic balance method with a scalable skyline solver forms the kernel of this algorithm. The algorithm is equipped with a solution procedure suitable for large-scale structures that have lightly damped modes near resonance. The algorithm is integrated in X3D, implemented on a hybrid shared and distributed memory architecture, and demonstrated on a three-dimensional structural model of a UH-60A-like fully articulated rotor. Flight-test data from UH-60A Airloads Program transition flight C8513 are used for validation. The key conclusion is that the new solver converges to the time marching solution more than 50 times faster and achieves a performance greater than 1 teraFLOPS. The significance of this conclusion is that the principal barrier of computational time for trim solution using high-fidelity three-dimensional structures can be overcome with the scalable harmonic balance method demonstrated in this paper.

Simulations of Unsteady Blade Row Interactions Using Linear and Non-Linear Frequency Domain Methods

2015 ◽  
Author(s):  
Christian Frey ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Measurement Data ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Frequency Domain Methods ◽  
Blade Row ◽  
Non Linear ◽  
Rotor Stator Interaction ◽  
Unsteady Simulation

This paper compares various approaches to simulate unsteady blade row interactions in turbomachinery. Unsteady simulations of turbomachinery flows have gained importance over the last years since increasing computing power allows the user to consider 3D unsteady flows for industrially relevant configurations. Furthermore, for turbomachinery flows, the last two decades have seen considerable efforts in developing adequate CFD methods which exploit the rotational symmetries of blade rows and are therefore up to several orders of magnitude more efficient than the standard unsteady approach for full wheel configurations. This paper focusses on the harmonic balance method which has been developed recently by the authors. The system of equations as well as the iterative solver are formulated in the frequency domain. The aim of this paper is to compare the harmonic balance method with the time-linearized as well as the non-linear unsteady approach. For the latter the unsteady flow fields in a fan stage are compared to reference results obtained with a highly resolved unsteady simulation. Moreover the amplitudes of the acoustic modes which are due to the rotor stator interaction are compared to measurement data available for this fan stage. The harmonic balance results for different sets of harmonics in the blade rows are used to explain the minor discrepancies between the time-linearized and unsteady results published by the authors in previous publications. The results show that the differences are primarily due to the neglection of the two-way coupling in the time-linearized simulations.

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