Study On The Method For Calculating Earthquake Response Base On Flexibility Matrix Of Low Mode

Generally, the modal response spectrum analysis was used in evaluation of seismic response of complex structure. which is involved in how to select the number of modes combination. In recent years, many scholars have studied on how to select the reasonable modes number, which include two methods, the one takes effective modal mass as criterion, and the other uses static method to approximate estimate the influence of higher-order vibration modes. Based on previous studies, using lower-order modes flexibility matrix to approximate estimate the seismic response was put forword.On the other hand, in shaking table test, the error is large between the results of model experiment and theoretical analysis results, even in elastic stage, the error of dynamic response cannot get very good agreement. This needs to amend the model's mass matrix, stiffness matrix and modal matrix by test results. Among the correction methods, it is always needed to measure the complete modal matrix. However, the high-order mode was really hard to measure in actual experiment, so the suggestion of using low modes flexibility matrix to approximate estimate the seismic response could also be used in shaking table test to avoid testing of high order modes and improve the precision of the numerical simulation model.According to three different structure deformation forms, including the shear structure, flexible-shear structure and torsional structure, the approximate formulas to estimate the higher-order vibration modes influence were deduced respectively in this paper, and realized simulation analysis using existing commercial software such as Sap2000. Two models including 5-story and 20-story structural excited by earthquake wave and sine wave were calculated using the method put forword in this paper, the dynamic time history of displacement and acceleration and its peak value were compared. It indicated that the method proposed in the paper can achieved more accurate result of earthquake responses of structures.Because the calculation methods still exist a certain error. Several reasons caused the error were also analysed in the paper. The contribution of high-order modes to structure dynamic response and error of the method to approximate calculation method suggested in this paper were discussed. It shown that if the excitation wave's cycle close to the natural vibration period of high order, the high-order mode's contribution increased, and the error of approximate calculation method will significantly increased.