With the complex Cotes integral method the precise integration method was improved,a new efficient precise integration method C-PTSIM was developed.Based on the finite element theory,the application of the method was discussed in random vibration response analysis of linear structures under arbitrary random excitations.The complex Cotes integration method was used to calculate the integral term of the general solution of a state equation of structural dynamic response,and the explicit expression of structural dynamic response was deduced,and then the mean and variance of structural response were calculated with the first moment and the 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 coming from assuming linear loads within the time step.It was shown that with the time step keeping unchanged,the higher order complex Cotes integration can have the same precision of the results as that of precise integration with finer time steps,the weak sensitivity of the new method to the time step is revealed,and large amounts of time can be saved.An example for random vibration response of a structure was analyzed with C-PTSIM,and the higher efficiency and precision of this method were illustrated compared with other methods.%应用复化Cotes数值积分方法改进精细积分方法,建立一种新的高效的精细积分方法:C-PTSIM,并基于有限元理论讨论了此方法在任意随机激励下线性结构随机动力响应的应用.采用复化Cotes积分方法计算结构动力响应状态方程一般解的积分项,推导出随机激励下结构动力响应的显式表达式,利用一阶矩和二阶矩运算规律计算结构响应的均值和方差.C-PTSIM方法避免了精细积分过程中系数矩阵求逆问题,有效改善了精细积分在时间步长内载荷线性化假设带来的误差,在不改变时间步长时采用高次数复化积分时获得与更精细步长时同样精度的结果,表明该方法对时间步长的弱敏感性,并能节省大量的计算时间.基于此方法给出结构随机振动响应分析算例,并与其他方法对比,说明了该方法的高效率和高精度.
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