Abstract：With the complex Cotes integral method improving the precise integration method，a new efficient precise integration method: C-PTSIM is developed. Based on finite element theory, the application of the method is discussed in random vibration dynamic response of linear structures under arbitrary random excitations. The complex Cotes integration method is used to calculate the integral term of the general solution of state equation of structural dynamic response, and the explicit expression of structural dynamic response is deduced, and then the mean and variance of structural response are calculated with the first moment and second moment operation laws. The C-PTSIM method avoided the problem to solve the coefficient matrix inversion in the process of precise integration, and efficiently reduced the errors by assuming linear loads within the time step. With the time step keeping unchanged, the high number complex Cotes integration can obtain the same precision of the results as integration of finer time step, showing weak sensitivity to the time step, and large amounts of time can be saved. The example of the random vibration response of structures is analyzed based on C-PTSIM, and the high efficiency and precision of this method are illustrated compared with other methods.
宋向华;安伟光;蒋运华. 任意随机激励下结构随机振动分析的一种数值方法[J]. , 2013, 32(13): 147-152.
SONG Xiang-hua;AN Wei-guang;JIANG Yun-hua. A Numerical Method for the Random Vibration Analysis of Structures Under Arbitrary Random Excitations. , 2013, 32(13): 147-152.
2013, Vol. 32 
