Dynamic Substructuring Based on a Double Modal Analysis

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
S. Besset ◽  
L. Jézéquel
Keyword(s):  
Finite Element Method ◽  
Forthcoming Paper ◽  
Synthesis Methods ◽  
Generalized Coordinates ◽  
Multimodal Analysis ◽  
Modal Synthesis ◽  
Dynamic Substructuring ◽  
Primal And Dual ◽  
Modal Truncation ◽  
Continuous Formulation

Modal synthesis methods have long been studied because the use of generalized coordinates makes it possible to reduce calculation costs. Our approach uses modes to describe each part of the assembly of several substructures. This method, called “Double Modal Synthesis,” is presented through primal and dual formulations. As modal truncation usually introduces a lack of precision, we will use an ω2 development if necessary. These formulations will first be explained using a continuous formulation. A finite element method will then be proposed. Another aim of the paper is to introduce formulations needed to understand the multimodal analysis methods that will be presented in a forthcoming paper.

Vibroacoustical Analysis Based on a Multimodal Strategy: Triple Modal Synthesis

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Sébastien Besset ◽  
Louis Jézéquel
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Coupled System ◽  
High Order ◽  
Synthesis Methods ◽  
Fluid Structure ◽  
Generalized Coordinates ◽  
Multimodal Strategy ◽  
Modal Synthesis ◽  
Modal Truncation

Modal synthesis methods have long been studied because the use of generalized coordinates makes it possible to reduce calculation costs. Our approach uses modes to describe each part of the assembly of several substructures, coupled with a fluid cavity. In a previous paper, we explained that ω2 developments could be used to minimize modal truncation. In the present paper, we consider a fluid-structure coupled system using a method called “triple modal synthesis.” High order developments will be made to describe the fluid part. First, two kinds of formulation will be explained: in displacement and in force. Second, calculation using finite element methods will be processed.

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.

Response Prediction and Dynamic Substructuring for Coupled Structures in the Frequency Domain

2020 ◽  
Vol 36 (6) ◽  
pp. 867-879
Author(s):  
X. H. Liao ◽  
W. F. Wu ◽  
H. D. Meng ◽  
J. B. Zhao
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Dynamic Properties ◽  
Main Idea ◽  
Prediction Method ◽  
Response Prediction ◽  
Synthesis Methods ◽  
Dynamic Substructuring ◽  
Coupled Structures

ABSTRACTTo evaluate the dynamic properties of a coupled structure based on the dynamic properties of its substructures, this paper investigates the dynamic substructuring issue from the perspective of response prediction. The main idea is that the connecting forces at the interface of substructures can be expressed by the unknown coupled structural responses, and the responses can be solved rather easily. Not only rigidly coupled structures but also resiliently coupled structures are investigated. In order to further comprehend and visualize the nature of coupling problems, the Neumann series expansion for a matrix describing the relation between the coupled and uncoupled substructures is also introduced in this paper. Compared with existing response prediction methods, the proposed method does not have to measure any forces, which makes it easier to apply than the others. Clearly, the frequency response function matrix of coupled structures can be derived directly based on the response prediction method. Compared with existing frequency response function synthesis methods, it is more straightforward and comprehensible. Through demonstration of two examples, it is concluded that the proposed method can deal with structural coupling problems very well.

A Survey of Modal Synthesis Methods

1971 ◽  
Author(s):  
Gary C. Hart ◽  
Walter C. Hurty ◽  
Jon D. Collins
Keyword(s):  
Synthesis Methods ◽  
Modal Synthesis

Study on the Stress-Stiffening Effect and Modal Synthesis Methods for the Dynamics of a Spatial Curved Beam

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Jianshu Zhang ◽  
Xiaoting Rui ◽  
Bo Li ◽  
Gangli Chen
Keyword(s):  
Small Deformation ◽  
Dynamics Simulation ◽  
Variation Principle ◽  
Synthesis Methods ◽  
Curved Beam ◽  
The Finite Element Method ◽  
High Rotational Speed ◽  
Modal Synthesis ◽  
Geometric Stiffening ◽  
Stiffening Effect

In this paper, based on the nonlinear strain–deformation relationship, the dynamics equation of a spatial curved beam undergoing large displacement and small deformation is deduced using the finite-element method of floating frame of reference (FEMFFR) and Hamiltonian variation principle. The stress-stiffening effect, which is also called geometric stiffening effect, is accounted for in the dynamics equation, which makes it possible for the dynamics simulation of the spatial curved beam with high rotational speed. A numerical example is carried out by using the deduced dynamics equation to analyze the stress-stiffening effect of the curved beam and then verified by abaqus software. Then, the modal synthesis methods, which result in much fewer numbers of coordinates, are employed to improve the computational efficiency.

scholarly journals Flow ratio design of primal and dual network models of distribution

2004 ◽  
Vol 45 (4) ◽  
pp. 573-583 ◽  
Author(s):  
G. A. Mohr
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Saddle Point ◽  
Network Models ◽  
Work Flow ◽  
Flow Ratio ◽  
The Finite Element Method ◽  
Point Solution ◽  
Primal And Dual ◽  
Distribution Problems

AbstractThe finite element method can be used to provide network models of distribution problems. In the present work ‘flow ratio design’ is applied to such models to obtain approximate minima and maxima for both the primal and dual FEM models. The resulting primal MIN and dual MAX solutions are equal to or close to the exact solutions but, intriguingly, the primal MAX and dual MIN solutions are approximately equal to an intermediate saddle point solution.

Dynamics of Robotic Manipulators With Flexible Links

1991 ◽  
Vol 113 (1) ◽  
pp. 54-59 ◽  
Author(s):  
Liang-Wey Chang ◽  
J. F. Hamilton
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Model ◽  
Nonlinear Equations ◽  
Robotic Manipulators ◽  
The Finite Element Method ◽  
Small Motion ◽  
Flexible Links ◽  
Generalized Coordinates ◽  
Large Motion

This paper presents a dynamic model for the robotic manipulators with flexible links by means of the Finite Element Method and Lagrange’s formulation. By the concept of the Equivalent Rigid Link System (ERLS), the generalized coordinates are selected to represent the total motion as a large motion and a small motion. Two sets of coupled nonlinear equations are obtained where the equations representing small motions are linear with respect to the small motion variables. An example is presented to illustrate the importance of the flexibility effects.

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