Dynamic Characteristics Analysis Of Primary-secondary Structure Based On Components Mode Synthesis

Modal synthesis method is an effective way to solve dynamic characteristic problems of the large complex structures. It is based on the finite element method, and first divides the large and complex structure into several sub-structures, then conducts modal synthesis based on the sub-structure dynamic analysis, finally gets the characteristics of the overall structure.By summing up the development and conditions of modal synthesis method, the theoretical derivation of fixed interface mode synthesis method is systemic introduced.Because failing to reduce the interface degrees of freedom, the fixed interface modal synthesis method cannot get a high computational efficiency when conducting modal analysis of some large and complex structures. Therefore, this paper presents a dynamic characteristics analysis method of primary-secondary structure based on components mode synthesis. By using this method,we can get the computing matrix which does not depend on the number of interface degrees of freedom but the retention modes of the primary-secondary structure. Thus the order of the equation has been effectively reduced,the computational efficiency is improved. Then noting that this method ignores the impact on the primary structure caused by secondary structure,so the accuracy is not very high. Then this paper proposes a correction method which considers the impact of secondary structure on the primary structure by adding the condensation stiffness and mass matrices of secondary structure to the corresponding ones of primary structure through model reduction techniques. And this revised method is verified by some examples.This paper also proposes the implementation method of modal synthesis in finite element analysis software Sap2000 and numerical software MATLAB,and details the method of extracting the stiffness and mass matrix from Sap2000. Finally, this paper analyzes a ten-story frame model containing stairs by taking the body frame structure as the main structure and the staircase secondary structure,and contrasts the results, which are computed by retaining different modes of primary and secondary structure, with the results of the finite element method. The results show that the frequencies and mode shapes of composite structures computed by the proposed method are very close to the results of the finite element method. And furthermore,with taking more and more numbers of reservation modes of the primary and secondary structure,the accuracy of the results can be further improved. And the methods herein can efficiently compute the modal information within a specific frequency range of composite structure. Since only the frequencies within the target range modal are integrated, the computational efficiency is greatly improved.