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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 Rayleigh-Ritz 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 trial-and-error approaches are common to use
Structural dynamics modification using non-matching 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, non-matching nodes problem occurs naturally in the process of synthesizing substructures. Virtual reference node concept is used to enforce the interface compatibility constraint between non-matching 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.