New procedure for dynamic structural reanalysis

Abstract

The methods of structural dynamic modification, especially those with their roots in finite element models, have often been described as reanalysis. The present paper deals with the problem of improving of dynamic characteristics some structures. New dynamic modification procedure is given as using distribution of potential and kinetic energy in every finite element is used for analysis. The main goal of dynamic modification is to increase natural frequencies and to increase the difference between them. Some information should be prepared, before setting up the FE model. The first pack of information includes referent pieces of information about the structure: size, material, and boundary conditions. It should be noticed that dynamic response is given primarily through corresponding eigenfrequencies and main oscillation forms as characteristic (typical) variables. Changing them by changing the design parameters of a structure it is possible to achieve (can bring about) requested structural dynamic response. Sensitivity analysis is an important point within the dynamical modification process. Sensitivity analysis represents a collection of mathematical methods for reanalyzing constructions which is, within dynamical modification, related to sensitivity of eigenvalues and eigenvectors. Therefore, the application of sensitivity analysis is limited to construction of segments for which necessary mathematical relations can be determined. If this is not possible, sensitivity analysis is only partially applicable. Dynamical analysis of complex structures can easily be conducted via finite elements modeling. Therefore, while finite element analysis method is highly adequate for modeling complex structures, one of its major drawbacks lies in the usage of large number of degrees of freedom in calculating the exact eigenpairs. This number can amount to few tens of thousands, or even more. To reduce the calculation time it is possible to divide the complex structure into connected substructures and analyze each one separately. The dynamical behavior of each substructure is represented only by a reduced set of eigenpairs of interest, which contributes to significant problem simplification. A more general problem of structural dynamic analysis has three important aspects. Firstly, the observed physical structure is represented by initial finite element model. Modeling is based on numerous idealizing approximations within an exaggerated elaboration of details, which in essence does not significantly improve the accuracy of output data, especially having available powerful computers and appropriate software packages. Optimal alternative is to have the possibility of verifying outputted data that were measured on a prototype or real structure. Secondly, the dynamic characteristics of construction under reanalysis are analyzed. What is basically observed are eigenvalues and main forms of oscillations as characteristic variables that can invoke inadequate actual dynamic behavior. Thirdly, on the basis of analysis of actual dynamic behavior, modification steps are proposed after which a modified model is obtained. Having in mind that mechanical structures are most often very complex, the most convenient modification steps are not easily obtained. Figure 1 shows a simplified triangle of fine reanalysis. Choosing the structural parts most suitable for reanalysis requires the analysis of sensitivity for separate segments to changes in construction. Most importantly, the best result should be obtained with minimal changes. This most frequently involves the icrease in frequency and distance between two neighboring frequencies.