Nonlinear Dynamic Analysis Of A Steel Frame Based On Nonlinear Modal Analysis

The nonlinear modal analysis method, which is based on the force analogy method, modal superposition method and state space method, is a new dynamic analysis algorithm, equations of motion,which are coupled for material nonlinear, can be decoupled by replacement of the elastic force in structure in the force analogy method, then the solution to equations of motion is different from the direct integral method. In this study, the modal superposition method used in dynamic analysis of linear structural system is extended to the nonlinear structural system based on nonlinear modal analysis.Based on related basic theory as well as research results, the research work is carried out in the following aspects:(1) Based on the basic theory and research results of the force analogy method, the general computational procedure of the nonlinear modal analysis is summarized and demonstrated in the paper.(2) A six-story steel frame is selected as an example, and a numerical algorithm code is developed to obtain the dynamic response of the steel frame on MATLAB platform. The influence on dynamic response of the steel frame due to corrosion occurred in different floors is mainly discussed, and conclusions are as follows:the response of the example,such as displacement, plastic displacement and so on, increases when the corrosion is occurred in a floor, and the story drift increases in the floor and the above one of it.The influence on PHL of column is bigger than beam when the corrosion occurred in different floors.(3) Further, dynamic nonlinear analysis of the steel frame are performed based on software SAP2000, and the results are compared with the results obtained from MATLAB analysis to demonstrate the accuracy and efficiency of the nonlinear modal analysis.