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Structural Dynamics 

Structural Dynamic Modification is a design technique that is required to acquire desired
design quality by stiffener addition/reduction or shape modification. The
following topics will be studied.
First, inverse design problem requires precise finite element model. The initial model
must be updated because the dynamic characteristics between ideal and real model
are different. The field of model updating has a long history and almost of the
theoretical background have been completely developed, but still there exist
some problems to be solved before applying to real large structure with complex
shape. Modeling of structure joint or welding spot is still one of the major
problems in model updating theory because the parameter identification is
important to update model quality.
Second, design of optimal experimental environment which can provide reliable
experimental data to identify dynamic characteristics of structures is needed.
Model updating procedure and design problem require modal testing because
experimental data must be provided. Sensor placement and selection of exciting
position have deep relation to the reliability of modal testing result. Although
commercial softwares have some function to select optimal sensor position, the
level of its algorithm is not up to date thus a more sophisticated algorithm
should be developed.
And lastly, sensitivity analysis should be studied for redesign. It is the kernel of
optimal design problem and various advanced mathematical theories have been
applied. Eigenvalue/eigenvector or frequency response function sensitivity
analysis are one of basic theories in vibration design

Component Mode Synthesis 
Dynamic analysis of complex flexible
structures is readily accomplished using discrete parameter models usually
formulated by the finite element method. Whereas the finite element method
lends itself to modeling very complex structures, it has the major disadvantage
that it often requires a very large number of degrees of freedom to obtain
accurate estimates of the vibration modes, where the number can reach into the
tens of thousands. Although many available computer programs have been
developed specifically to manipulate and solve large complex models, the
eigenvalue solution procedure still requires considerable computation time to
obtain desired results. In order to reduce the computational effort in the
solution of the associated eigenvalue problem, component mode synthesis method
has been developed. The mode synthesis method is a technique of matrix order
reduction for structural dynamic analysis and aims to determine the lower
vibration modes of the complex structures. It is based on the RayleighRitz
procedure and treats the structure as an assemblage of connected substructures,
each of which is analyzed separately. The dynamic behavior of each substructure
represented by a reduced set of substructure modes that accommodates the
structure eigenvalues and modes of interest. Depending on the method, the
substructure mode set consists of the free, fixed, or loaded interface modes of
the lower vibration modes of the substructure.

FE Model Updating 
Finite element model updating is a procedure to minimize the difference between
analytical and experimental results and is usually posed as an optimization
problem. In model updating process, one requires significance of updated
parameters. For this ppose, setting up of an objective function and selecting
updating parameters are crucial steps in model updating. These require
considerable physical insight and usually trialanderror approaches are common
to use

Structural dynamics modification using nonmatching substructure synthesis 
Substructure¡¯s position is considered as design parameter to obtain optimal
structural changes to raise its dynamic characteristics based on a measured
frequency response function (FRF). In conventional SDM (structural dynamics
modification) method, the layout of modifying substructure¡¯s position is first
fixed and at that condition the structural optimization is performed by using
the substructure¡¯s size and/or material property as design parameters. But in
this paper as a design variable substructure¡¯s global translational and
rotational position is treated. To get system equation substructure synthesis
concept is used. Since the modifying substructure should be synthesized to
another one continuously at any location, nonmatching nodes problem occurs
naturally in the process of synthesizing substructures. Virtual reference node
concept is used to enforce the interface compatibility constraint between
nonmatching nodes of substructures. Through this reference node the
substructure based SDM can be processed in positional optimization problem. For
effective structural modification the eigenvalue sensitivity with respect to
that design parameter is derived based on measured frequency response function.
The optimal structural modification is calculated by combining eigenvalue
sensitivities and eigenvalue reanalysis technique iteratively. Numerical
examples are presented to the case of beam stiffener optimization to raise the
natural frequency of plate.




