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.

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.

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.

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.

scholarly journals Physical Modeling, Algorithms, and Sound Synthesis: The NESS Project

2020 ◽  
Vol 43 (2-3) ◽  
pp. 15-30 ◽  
Author(s):  
Stefan Bilbao ◽  
Charlotte Desvages ◽  
Michele Ducceschi ◽  
Brian Hamilton ◽  
Reginald Harrison-Harsley ◽  
...  
Keyword(s):  
Physical Modeling ◽  
Large Scale ◽  
Algorithm Design ◽  
Sound Synthesis ◽  
Synthesis Methods ◽  
String Instruments ◽  
Time Stepping ◽  
Modal Synthesis ◽  
Percussion Instruments ◽  
Simplifying Assumptions

Synthesis using physical modeling has a long history. As computational costs for physical modeling synthesis are often much greater than for conventional synthesis methods, most techniques currently rely on simplifying assumptions. These include digital waveguides, as well as modal synthesis methods. Although such methods are efficient, it can be difficult to approach some of the more detailed behavior of musical instruments in this way, including strongly nonlinear interactions. Mainstream time-stepping simulation methods, despite being computationally costly, allow for such detailed modeling. In this article, the results of a five-year research project, Next Generation Sound Synthesis, are presented, with regard to algorithm design for a variety of sound-producing systems, including brass and bowed-string instruments, guitars, and large-scale environments for physical modeling synthesis. In addition, 3-D wave-based modeling of large acoustic spaces is discussed, as well as the embedding of percussion instruments within such spaces for full spatialization. This article concludes with a discussion of some of the basics of such time-stepping methods, as well as their application in audio synthesis.

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 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.

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