Research On The Keeping Structure Decoupling Method Based On Similarity Transformation

Second-order systems can be represented by second-order differential equations,and systems in many engineering fields tend to be generalized to second-order systems such as structural dynamics systems.When analyzing the characteristics of second-order systems,it often involves the decoupling of second-order systems.Mathematically,it involves the simultaneous diagonalization of the three matrices and is almost impossible to achieve.The SPIF method establishes a same spectral information system flow by preserving the Lancaster structure,and iteratively updates it with the decoupling of the same spectral information system.However,there is decoupling failure when applying this algorithm to solve practical problems.In this paper,the structure-based flow algorithm based on similarity transformation is studied.The reasons for the failure of the algorithm are analyzed.The objective functions,Keep the spectrum information unchanged and the matrix symmetry are respectively analyzed.Previous studies have found that the proposed structure-based flow method based on similarity transformation is still valid for the failure of the SPIF method.However,after a large number of numerical experiments are performed on the guaranteed structure flow based on the similarity transformation,it is found that the proposed solution still exists Example of a failed coupling.Therefore,this paper conducts in-depth research,analyzes and researches the data of decoupling failures by the similar flow method,and adjusts the iteration of the algorithm through the modification of the objective function.After modifying the objective function,a series of numerical simulation experiments based on improved similarity flow algorithm were carried out by using the program written in MATLAB language.The results verify the effectiveness and superiority of the improved method.In the numerical experiment,when the initial two matrices are asymmetric matrices,the structure-based flow method based on the similarity transformation gradually becomes a symmetric matrix in the process of iteration and finally makes the matrices diagonalize at the same time.In this process Second order system is always keep the spectral information unchanged.However,when using the SPIF method,if the original second-order system is asymmetric,it can not be symmetrical in the iterative process.In view of the abovephenomenon found,this paper analyzes and compares the differences between them based on two algorithms and analyzes the reason of symmetry.In this paper,based on the similar transformation of structure-preserving decoupling method found some problems,the problems were analyzed,and an effective improvement.The structure-preserving decoupling method based on similarity transformation has obtained the ideal result in decoupling the system,and has important value for further research.