A Ranking Method for the Selection of the Interior Modes of Reduced Order Resonant System Models

2014 ◽  
Author(s):  
Ilaria Palomba ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Normal Modes ◽  
Reduced Order Model ◽  
Ranking Method ◽  
Resonant System ◽  
Order Model ◽  
Reduced Order ◽  
Design And Optimization ◽  
Optimization Stage ◽  
Dimensional Models ◽  
Selection Of

Resonant system design and optimization is usually supported by finite element models. Large dimensional models are often needed to achieve the desired accuracy in the representation of the vibrational behaviour at the frequency of interest. Unfortunately, large dimensional models are frequently too cumbersome to be actually useful, mainly at the optimization stage. On the other hand, the choice of the most appropriate reduction strategy and dimension for a reduced-order model is generally left to designers’ experience. Having recognized the effectiveness and spreading of the Craig Bampton reduction technique, the aim of this paper is to propose a rigorous ranking method, called Interior Mode Ranking (IMR), for the selection of the interior normal modes of the full order model to be inherited by the reduced order one. The method is aimed at finding the set of interior modes of minimum dimensions which allows achieving a desired level of accuracy of the reduced order model at a frequency of interest. The method is here applied to a resonator widely employed in industry: an ultrasonic welding bar horn, which is usually designed to operate excited in resonance. The results achieved through the application of the IMR method are compared with those yielded by other ranking techniques available in literature in order to prove its effectiveness.

Vibration Control for Integrally Bladed Disks Using Friction Ring Dampers

2007 ◽  
Author(s):  
Denis Laxalde ◽  
Fabrice Thouverez ◽  
Jean-Pierre Lombard
Keyword(s):  
Frequency Domain ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Design And Optimization ◽  
Beam Elements ◽  
Parametric Studies ◽  
Frequency Domain Approach

A damping strategy for integrally bladed disks (blisks) is discussed in this paper; this involves the use of friction rings located underside the wheel of bladed disks. The forced response of the blisk with friction rings is derived in the frequency domain using a frequency domain approach known as Dynamic Lagrangian Frequency-Time method. The blisk is modeled using a reduced-order model and the rings are modeled using beam elements. The results of some numerical simulations and parametric studies are presented. The range of application of this damping device is discussed. Parametric studies are presented and allow to understand the dissipation phenomena. Finally some design and optimization guidelines are given.

Control of Asymmetric Systems Using Complex Modes

1991 ◽  
Author(s):  
G. W. Fan ◽  
H. D. Nelson
Keyword(s):  
Normal Modes ◽  
Original System ◽  
High Order ◽  
Reduced Order Model ◽  
Order System ◽  
Matrix Transformations ◽  
Linear Quadratic ◽  
Order Model ◽  
Reduced Order ◽  
Complex Modes

Abstract The complex modal approach is introduced for the optimal vibration control (Linear Quadratic Regulator) of high-order nonsymmetric discrete systems. An LQ regulator is designed based on a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex coordinates are derived. A 52 degree-of-freedom finite element based rotordynamic system is used for illustration. Simulation results show that an LQ regulator based on a reduced-order system obtained by using normal modes of a high-order system with asymmetric models can possibly destabilize the original system i.e., the spill-over problem (Ulsoy, 1984), however, this problem might be avoided by applying complex modes which provides a more accurate reduced-order model than obtained by normal modes. Comparison of the reduced-order models using normal modes and complex modes is presented. Frequency, time transient and steady state responses of the controlled and uncontrolled systems are also shown.

Reduced Order Model for the Geometric Nonlinear Response of Complex Structures

2012 ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Model Parameters ◽  
Complex Structures ◽  
Order Model ◽  
Plate Structures ◽  
Reduced Order ◽  
Nonlinear Static ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (> 50 say) that would be needed for complex structures, and (ii) extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a 9-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

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.

The Construction of Nonlinear Normal Modes for Systems With Internal Resonance: Application to Rotating Beams

2002 ◽  
Author(s):  
Dongying Jiang ◽  
Christophe Pierre ◽  
Steven W. Shaw
Keyword(s):  
Invariant Manifold ◽  
Internal Resonance ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Reduced Order Model ◽  
Degree Of Freedom ◽  
Beam Model ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Normal

A numerical method for constructing nonlinear normal modes for systems with internal resonances is presented based on the invariant manifold approach. In order to parameterize the nonlinear normal modes, multiple pairs of system state variables involved in the internal resonance are kept as ‘seeds’ for the construction of the multi-mode invariant manifold. All the remaining degrees of freedom are constrained to these ‘seed’ variables, resulting in a system of nonlinear partial differential equations governing the constraint relationships, which must be solved numerically. The solution procedure uses a combination of finite difference schemes and Galerkin-based expansion approaches. It is illustrated using two examples, both of which focus on the construction of two-mode models. The first example is based on the analysis of a simple three-degree-of-freedom example system, and is used to demonstrate the approach. An invariant manifold that captures two nonlinear normal modes is constructed, resulting in a reduced-order model that accurately captures the system dynamics. The methodology is then applied to a more large system, namely an 18-degree-of-freedom rotating beam model that features a three-to-one internal resonance between the first two flapping modes. The accuracy of the nonlinear two-mode reduced-order model is verified by time-domain simulations.

scholarly journals A Reduced-Order Model for the Vibration Analysis of Mistuned Blade–Disc–Shaft Assembly

2019 ◽  
Vol 9 (22) ◽  
pp. 4762
Author(s):  
Wang ◽  
Bi ◽  
Zheng
Keyword(s):  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Normal Modes ◽  
Order Reduction ◽  
Symmetry Analysis ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Reduced Order

An effective reduced-order model is presented in this paper for the vibration analysis of a mistuned blade–disc–shaft assembly considering the flexibility of the shaft and the rotordynamic effects. For the sake of accurate modeling and quantitative analysis, three-dimensional (3D) finite element models were employed in obtaining the governing equations of motion with the Coriolis force, centrifugal stiffening, and spin softening effects taken into account. Then, an efficient model order reduction technique based on the coordinate projection by normal modes of tuned assembly and cyclic symmetry analysis was developed for mistuned blade–disc–shaft assembly. The criterion of whether one matrix could be incorporated in cyclic symmetry analysis is presented. During the modeling, the mistuning in blade and disc was taken into account and dealt with independently. In mistuning projection, the blade and disc parts were both projected onto their tuned counterparts of the sector model, where the boundary conditions were set to be fixed and free, respectively. Finally, an example of a blade–disc–shaft assembly was employed to validate the effectiveness of the presented method in free and forced vibration analysis.

Component Mode Synthesis Using Nonlinear Normal Modes

2003 ◽  
Author(s):  
Polarit Apiwattanalunggarn ◽  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Reduced Order Model ◽  
Component Mode Synthesis ◽  
Structural Systems ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Structural ◽  
Fixed Interface ◽  
Nonlinear Normal

This paper describes a methodology for developing reduced-order dynamic models of nonlinear structural systems that are composed of an assembly of component structures. The approach is a nonlinear extension of the fixed-interface component mode synthesis technique developed for linear structures by Hurty and modified by Craig and Bampton. Specifically, the case of nonlinear substructures is handled by using fixed-interface nonlinear normal modes. These normal modes are constructed for the various substructures using an invariant manifold approach, and are then coupled through the traditional linear constraint modes (i.e., the static deformation shapes produced by unit interface motions). A simple system is used to demonstrate the proof of concept and show the effectiveness of the proposed procedure. Simulations are performed to show that the reduced-order model obtained from the proposed procedure outperforms the reduced-order model obtained from the classical fixed-interface linear component mode synthesis approach. Moreover, the proposed method is readily applicable to large-scale nonlinear structural systems.

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