scholarly journals A Combination of Modal Synthesis and Subspace Iteration for an Efficient Algorithm for Modal Analysis within a FE-Code

2003 ◽  
Vol 10 (1) ◽  
pp. 27-35 ◽  
Author(s):  
M.W. Zehn
Keyword(s):  
Eigenvalue Problem ◽  
Modal Analysis ◽  
Efficient Algorithm ◽  
Degrees Of Freedom ◽  
Synthesis Method ◽  
Problem Solver ◽  
Synthesis Methods ◽  
Combined Method ◽  
Subspace Iteration ◽  
Modal Synthesis

Various well-known modal synthesis methods exist in the literature, which are all based upon certain assumptions for the relation of generalised modal co-ordinates with internal modal co-ordinates. If employed in a dynamical FE substructure/superelement technique the generalised modal co-ordinates are represented by the master degrees of freedom (DOF) of the master nodes of the substructure. To conduct FE modal analysis the modal synthesis method can be integrated to reduce the number of necessary master nodes or to ease the process of defining additional master points within the structure. The paper presents such a combined method, which can be integrated very efficiently and seamless into a special subspace eigenvalue problem solver with no need to alter the FE system matrices within the FE code. Accordingly, the merits of using the new algorithm are the easy implementation into a FE code, the less effort to carry out modal synthesis, and the versatility in dealing with superelements. The paper presents examples to illustrate the proper work of the algorithm proposed.

Component Modal Synthesis Methods Based on Hybrid Models, Part I: Theory of Hybrid Models and Modal Truncation Methods

1994 ◽  
Vol 61 (1) ◽  
pp. 100-108 ◽  
Author(s):  
L. Jezequel ◽  
H. D. Seito
Keyword(s):  
Synthesis Method ◽  
Integral Operators ◽  
Hybrid Models ◽  
Force Distribution ◽  
Synthesis Methods ◽  
Displacement Distribution ◽  
New Methods ◽  
Modal Synthesis ◽  
Intermediate Problem ◽  
Modal Truncation

The assembly of structures along continuous boundaries poses great difficulties for expressing generalized boundary coordinates in modal synthesis, especially in the context of experiments. In order to solve such problems, a hybrid modal synthesis method is proposed in this study. This approach is based on the intermediate problem theory of Weinstein and brings out the duality between the formulation in displacement and the formulation in force. Generalized boundary coordinates are defined by introducing static deformations resulting from force distribution or displacement distribution along the boundaries depending on which formulation is to be used. By introducing integral operators associated with intermediate problems, two new methods of modal truncation can be proposed.

PARALLEL SUBSPACE ITERATION METHOD FOR THE SPARSE SYMMETRIC EIGENVALUE PROBLEM

2006 ◽  
Vol 05 (04) ◽  
pp. 801-818 ◽  
Author(s):  
RICHARD LOMBARDINI ◽  
BILL POIRIER
Keyword(s):  
Eigenvalue Problem ◽  
Iteration Method ◽  
Degrees Of Freedom ◽  
Sparse Matrices ◽  
Model Systems ◽  
Symmetric Matrices ◽  
Six Degrees Of Freedom ◽  
Subspace Iteration ◽  
The Matrix ◽  
Parallel Iterative

A new parallel iterative algorithm for the diagonalization of real sparse symmetric matrices is introduced, which uses a modified subspace iteration method. A novel feature is the preprocessing of the matrix prior to iteration, which allows for a natural parallelization resulting in a great speedup and scalability of the method with respect to the number of compute nodes. The method is applied to Hamiltonian matrices of model systems up to six degrees of freedom, represented in a truncated Weyl–Heisenberg wavelet (or "weylet") basis developed by one of the authors (Poirier). It is shown to accurately determine many thousands of eigenvalues for sparse matrices of the order N ≈ 106, though much larger matrices may also be considered.

Component Modal Synthesis Methods Based on Hybrid Models, Part II: Numerical Tests and Experimental Identification of Hybrid Models

1994 ◽  
Vol 61 (1) ◽  
pp. 109-116 ◽  
Author(s):  
L. Jezequel ◽  
H. D. Setio
Keyword(s):  
Synthesis Method ◽  
Hybrid Models ◽  
Synthesis Methods ◽  
Mass Loading ◽  
Frequency Range ◽  
Compatibility Conditions ◽  
Experimental Identification ◽  
Numerical Tests ◽  
Modal Synthesis ◽  
Vibration Tests

A double modal synthesis method in which compatibility conditions at substructure interfaces are ensured by the introduction of loaded modes is presented in this study. These loaded modes, which are obtained by introducing mass loading or stiffness loading along the boundaries, are used to define generalized boundary coordinates. Thus the hybrid models presented in the first part of this study are developed so that they can be derived from test data as results of independent modal identifications. Unlike in classical modal synthesis methods, in this double modal synthesis method, it is not necessary to clamp the interfaces, which is always difficult to carry out during vibration tests. By introducing loaded modes, generalized boundary coordinates which represent boundary deformability in the frequency range under study can be defined.

The Application of Modal Synthesis Method in the Processing Center Dynamics Analysis

2012 ◽  
Vol 163 ◽  
pp. 207-210
Author(s):  
Peng Liu ◽  
Chun Jie Wang ◽  
Ru Sun
Keyword(s):  
Computational Efficiency ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Vibration Mode ◽  
Synthesis Method ◽  
Component Mode Synthesis ◽  
Dynamics Analysis ◽  
Full Model ◽  
Modal Synthesis ◽  
Five Axis

Modal synthesis method is a method which can reduce structural degrees of freedom, it is applicable for analysis and calculations of Machining centers and other large-scale structure. In this paper, the dynamical performance of Five-axis boring and milling processing center was studied with component mode synthesis technology . Compared with full model FEM, component mode synthesis technology could meet the accuracy requirements and have higher computational efficiency. Modal characteristics of processing center in different positions was studied, the result showed that each frequency of processing center in different position was different while the vibration mode remained unchanged.

Torsional Vibration Analysis of Complicated Multi-Branched Shafting Systems by Modal Synthesis Method

2003 ◽  
Vol 125 (3) ◽  
pp. 317-323 ◽  
Author(s):  
Chun-Ping Zou ◽  
Duan-Shi Chen ◽  
Hong-Xing Hua
Keyword(s):  
Torsional Vibration ◽  
Vibration Analysis ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Elastic Coupling ◽  
Improved Method ◽  
Modal Synthesis ◽  
Rigid Connection ◽  
Flexible Connections ◽  
Fixed Interface

The torsional vibration calculations of the complicated multi-branched system with rigid connection and flexible connections made up of elastic-coupling parts are very difficult to perform using conventional methods. In this paper, a modal synthesis method of torsional vibration analysis for the system is proposed. This approach is an improved method of Hurty’s fixed-interface and Hou’s free-interface modal synthesis methods. Because of the introduction of flexible substructure, the improved modal synthesis method can effectively treat the complicated system in which there exists a rigid connection and a flexible connection that is formed by an elastic-coupling part. When the calculation is performed, the complicated multi-branched system is divided into several substructures that are analyzed by FEM (finite element method) except the special elastic-coupling part that is defined as flexible substructure and treated individually. The efficiency of modal synthesis is improved by choosing suitable number of lower-frequency modes in modal synthesis. As an example of an application of this method, the analysis of torsional vibration of a cam-type engine shafting system is carried out both numerically and experimentally. The results show that the above kind of multi-branched shafting system can be analyzed effectively by the proposed method.

Structural Dynamics Optimization Based on a Hybrid Inverse Synthesis Method Using a Quadratic Approximation

2004 ◽  
Vol 126 (2) ◽  
pp. 253-259 ◽  
Author(s):  
Alain Schorderet ◽  
Thomas Gmu¨r
Keyword(s):  
Structural Dynamics ◽  
Shape Factor ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
The Novel ◽  
Synthesis Algorithm ◽  
Numerical Examples ◽  
Dynamic Constraints ◽  
Modal Synthesis ◽  
Synthesis Approach

This paper lies within the framework of the so-called redesign problem of structures subjected to dynamic constraints. A hybrid synthesis algorithm is developed, combining the truncated modal basis of the initial system and the spatial or material co-ordinates of an added component, which is modelled with shell-type finite elements parameterized with respect to a shape factor. Based upon a quadratic inverse formulation, the proposed technique shows several advantages in comparison to other synthesis methods, such as a refined sensitivity strategy, a powerful modal synthesis approach and a simplified optimization phase. Numerical examples are provided illustrating the capabilities of the novel procedure.

Modal Synthesis with the Isogeometric Kirchhoff–Love Shell Elements

2017 ◽  
Vol 09 (02) ◽  
pp. 1750017 ◽  
Author(s):  
Zhen Lei ◽  
Frederic Gillot ◽  
Louis Jezequel
Keyword(s):  
Modal Analysis ◽  
Isogeometric Analysis ◽  
Synthesis Method ◽  
Response Analysis ◽  
Analysis Framework ◽  
Shell Elements ◽  
Harmonic Response ◽  
Large Structures ◽  
Modal Synthesis ◽  
Harmonic Response Analysis

The modal synthesis method is frequently used for the analysis of large structures composed of multiple parts concerning dynamic aspects. In this paper, we extended the modal synthesis method under the isogeometric analysis framework. The isogeometric Kirchhoff–Love shell elements are used for the analysis of the substructures, the Craig–Bampton method is used for the modal synthesis and the bending-strip method is used for the substructures coupling. We give examples on the modal analysis and the harmonic response analysis. The results show the effectiveness of the method.

Optimization of the dynamic behavior of vehicle structures by means of passive interface controls

2016 ◽  
Vol 24 (3) ◽  
pp. 466-491 ◽  
Author(s):  
Xingrong Huang ◽  
Louis Jézéquel ◽  
Sébastien Besset ◽  
Lin Li
Keyword(s):  
Dynamic Behavior ◽  
Degrees Of Freedom ◽  
Passive Control ◽  
Dynamic Performance ◽  
Synthesis Method ◽  
Optimal Solution ◽  
Kriging Interpolation ◽  
Objective Functions ◽  
Modal Synthesis ◽  
Acoustic Comfort

As a form of passive control, padding rubber layers onto the most heavily deformed zones of a system can improve the dynamic behavior and the acoustic comfort of a vehicle system. This paper proposes an extensive hybrid modal synthesis method in order to study coupled fluid-structure systems, in retaining a few degrees of freedom. Modal criteria, corresponding to noise transmission paths between substructures in the system, have been derived to characterize the dynamic phenomenon from a modal view. These criteria were then substituted by Kriging interpolation models to avoid prohibitive simulation steps during optimization of the complex system. Once the mathematical models of the investigated modal criteria were established and the multi-objective functions for rubber characteristics defined, an approximate optimal solution leading to superior dynamic performance could be obtained based on a genetic algorithm. The analytical results and numerical experiments conducted have also justified the efficiency of our proposed strategy.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Interrelations of Synthesis Method, Polyethylene Glycol Coating, Physico-Chemical Characteristics, and Antimicrobial Activity of Silver Nanoparticles

Nanomaterials ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 2475
Author(s):  
Amirah Shafilla Mohamad Kasim ◽  
Arbakariya Bin Ariff ◽  
Rosfarizan Mohamad ◽  
Fadzlie Wong Faizal Wong
Keyword(s):  
Antimicrobial Activity ◽  
Silver Nanoparticles ◽  
Polyethylene Glycol ◽  
Pathogenic Bacteria ◽  
Synthesis Method ◽  
Chemical Characteristics ◽  
Synthesis Methods ◽  
Uniform Size ◽  
Transmission Electron Microscopy Analysis ◽  
Physico Chemical

Silver nanoparticles (AgNPs) have been found to have extensive biomedical and biological applications. They can be synthesised using chemical and biological methods, and coated by polymer to enhance their stability. Hence, the changes in the physico-chemical characteristics of AgNPs must be scrutinised due to their importance for biological activity. The UV-Visible absorption spectra of polyethylene glycol (PEG) -coated AgNPs displayed a distinctive narrow peak compared to uncoated AgNPs. In addition, High-Resolution Transmission Electron Microscopy analysis revealed that the shapes of all AgNPs, were predominantly spherical, triangular, and rod-shaped. Fourier-Transform Infrared Spectroscopy analysis further confirmed the role of PEG molecules in the reduction and stabilisation of the AgNPs. Moreover, dynamic light scattering analysis also revealed that the polydispersity index values of PEG-coated AgNPs were lower than the uncoated AgNPs, implying a more uniform size distribution. Furthermore, the uncoated and PEG-coated biologically synthesised AgNPs demonstrated antagonisms activities towards tested pathogenic bacteria, whereas no antagonism activity was detected for the chemically synthesised AgNPs. Overall, generalisation on the interrelations of synthesis methods, PEG coating, characteristics, and antimicrobial activity of AgNPs were established in this study.

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