Based On The Multibody System Transfer Matrix Method Of Structural Seismic Response Analysis

At present, improving the calculation efficiency is an important research direction in the seismic research field. Many researchers devote to shorten the computing time and seek some more effective structural modeling and calculating methods. As the transfer matrix method for multibody system dynamics does not need to establish the equation of multibody system dynamics and the calculate progress is concise, the scholars both home and abroad pay attention to this method and accept it. Unfortunately, compared with the use in other fields the transfer matrix method for multibody system dynamics is still at the exploration stage in the field of civil engineering.In this paper, based on transfer matrix method for multibody system dynamics, the linear transfer matrix and discrete time transfer matrix of the relevant components in civil engineering are developed for the first time. And also, the vibration equation is established and the analysis is carried out in the environment of MATLAB software. The seismic analysis consists of two kinds of structures, the single-layer frame structure with the roof of saddle-shaped plate and the three-layer frame structure of three spans. The main results are as the following:1.The natural periods of structures are calculated both with the transfer matrix method for multibody system dynamics and the method of finite element (ANSYS). For the single-layer frame structure with the roof of saddle-shaped plates, the error valve of the basic period is5.71%in these two methods. The transfer matrix method for multibody system dynamics takes about5seconds in the calculating progress, while the ANSYS takes about40seconds. For the three-layer frame structure of three spans, the error valve of the basic period is13.52%.The transfer matrix method for multibody system dynamics takes about20seconds in the calculating progress, while the ANSYS takes about45seconds.2. The seismic response of the structures subjected to frequently occurring earthquake are carried out both using the transfer matrix method for multibody system dynamics and the finite element method (ANSYS). For the single-layer frame structure with the roof of saddle-shaped plates, the error valve got by these two methods is as following:the error valve for the maximum average displacement of the top is4.17%; the error valve for the maximum average shear force at the bottom of the column A is5.09%; the error valve for the maximum average shear force at the bottom of the column B is1.75%.The transfer matrix method for multibody system dynamics takes less than60seconds but the ANSYS software takes approximately1800seconds. For the three-layer frame structure of three spans, the error valve got by these two methods is as following:the error valve for the maximum average displacement of the top is4.24%; the error valve for the maximum average displacement of the second layer is3.45%; the error valve for the maximum average displacement of the first layer is8.57%; the error valve for the maximum average shear force at the bottom of the column A is3.53%; the error valve for the maximum average shear force at the bottom of the column B is1.69%.The transfer matrix method for multibody system dynamics takes about120seconds but the ANSYS software takes approximately2100seconds.3. The seismic response of the structures subjected to rarely occurring earthquake are carried out both using the transfer matrix method for multibody system dynamics and the finite element method (ANSYS). For the single-layer frame structure with the roof of saddle-shaped plates, the error valve got by these two methods is as following:the error valve for the maximum average displacement of the top is5.66%; the error valve for the maximum average shear force at the bottom of the column A is9.5%; the error valve for the maximum average shear force at the bottom of the column B is7.06%.The transfer matrix method for multibody system dynamics takes less than100seconds but the ANSYS software takes approximately1800seconds. For the three-layer frame structure of three spans, the error valve got by these two methods is as following:the error valve for the maximum average displacement of the top is8.54%; the error valve for the maximum average displacement of the second layer is22.64%; the error valve for the maximum average displacement of the first layer is20.76%; the error valve for the maximum average shear force at the bottom of the column A is2.57%; the error valve for the maximum average shear force at the bottom of the column B is7.04%.The transfer matrix method for multibody system dynamics takes about300seconds but the ANSYS software takes approximately2100seconds.