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基础频率响应的离散时间有理近似是构建基础振动分析的时域递归算法的起点,离散时间有理近似的稳定性和精度决定时域递归算法的稳定性和精度。该文采用双线性变换法从基础频响的连续时间有理近似获得离散时间有理近似,避免离散和连续时间频率相等情况下由于离散时间有理近似的周期性而产生的高频尾部丢失和混叠现象,保证离散和连续时间有理近似的稳定性和精度一致。基于部分分式展开,获得的离散时间有理近似分别实现为直接型和并联型时域递归公式。通过分析几个典型基础振动问题并与Wu-Lee集中参数模型结果进行对比验证了双线性变换的有效性。
The discrete-time rational approximation of the fundamental frequency response is the starting point for constructing the time-domain recursive algorithm for fundamental vibration analysis. The stability and accuracy of discrete-time rational approximations determine the stability and accuracy of the time-domain recursive algorithm. In this paper, bilinear transform method is used to obtain the rational approximation of discrete time from the rational approximation of continuous time of basic frequency response, to avoid the loss and aliasing of high-frequency tail due to the rational approximation periodicity of discrete time and continuous time and frequency Phenomenon, to ensure that discrete and continuous approximation of similar stability and accuracy. Based on the partial fractional expansion, the obtained discrete-time rational approximations are respectively realized as direct-type and parallel-type time-domain recursion formulas. The effectiveness of bilinear transformation is verified by analyzing several typical fundamental vibration problems and comparing them with the Wu-Lee lumped parameter model results.