An Alternative Approach of Modeling Structures Using Dynamic Stiffness Matrices
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AN ALTERNATIVE APPROACH TO MODELING OF STRUCTURES USING DYNAMIC STIFFNESS MATRICES Kyung-Taek Yang Dept. of Mechatronic Engineering Daelin College of Technology Anyang KOREA ABSTRACT. A nwdeling method is described to provide a smaller structural dynamic nwdel which can be used to compare analytical nwdel of a structure with its experimental counter-part. A structural dynamic model ts assumed to be represented by dynamic stiffness matrix. To validnte a finite element it is often necessary to condense a large degrees of freedom (dofs) to a relatively small number of dofs. For these purpose, static reduction techniques are widely used. However, ermrs in these techniques are caused by neglecting frequency dependent terms in the functions relating slave dofs and master dofs. An alternative method is proposed in this paper in which the frequency dependent terms are considered by expressing the reduced dynamic stiffness matrix with ortlzogonal polynomials. The reduced nwdel ha_<; finally a minimum set of dofs, such as sensor and excitation points and it is under the same condition as the physical system. It is proposed that the reduced model can be derived from finite element nwdel and also can be identified from experimentally measured frequency responses. By comparing these nwdels, it is possible to check the differences between experimental and theoretical models in spatial coordinates. The procedure is applied to example structure and the results are discussed. Hak-soo Kim Structural Dynamics Lab. Honam University K wangjoo KOREA NOMENCLATURE [C] Damping matrix [I] Cnit matrix [K] Stiffness matrix [M] Mass matrix [U] Left singular vector [V] Right singular vector [ 6,] : Singular value c : Condensed matrix T -1 +1 s m Transpose of a matrix Inverse of a matrix Generalized inverse of a matrix Slave degrees of freedom Master degrees of freedom 1. INTRODUCTION Nowadays many finite element packages have been developed, and they are widely used for structural dynamic problems. However, quite often, the results of finite element analysis differ from those of actual tests. The discrepancy comes from the differences between actual structure and a corresponding finite element model. To validate a finite element model, various techniques have been proposed in which experimental data are integrated with a corresponding finite element model. When a structural system is complicated and includes many different joints, the analytical model is difficult to obtain by a theoretical method. To overcome the 674
