To improve the reliability and accuracy of dynamic machine in design process, high precision and efficiency of numerical computation is essential means to identify dynamic characteristics of mechanical system. In this paper, a new computation approach is introduced to improve accuracy and efficiency of computation for coupling vibrating system. The proposed method is a combination of piecewise constant method and Laplace transformation, which is simply called as Piecewise-Laplace method. In the solving process of the proposed method, the dynamic system is first sliced by a series of continuous segments to reserve physical attribute of the original system; Laplace transformation is employed to separate coupling variables in segment system, and solutions of system in complex domain can be determined; then, considering reverse Laplace transformation and residues theorem, solution in time domain can be obtained; finally, semi-analytical solution of system is given based on continuity condition. Through comparison of numerical computation, it can be found that precision and efficiency of numerical results with the Piecewise-Laplace method is better than Runge-Kutta method within same time step. If a high-accuracy solution is required, the Piecewise-Laplace method is more suitable than Runge-Kutta method.

为了提高动态机械设计过程中的可靠性和准确性，高精度、高效率的数值计算是识别机械系统动态特性的重要手段。本文提出了一种新的计算方法来提高耦合振动系统的计算精度和效率。该方法是分段常数法和拉普拉斯变换的结合，简称为分段拉普拉斯法。该方法求解过程中，首先将动态系统划分为一系列连续的线段，以保留原系统的物理属性；利用拉普拉斯变换分离分段系统中的耦合变量，可确定系统在复数域的解；然后，考虑逆拉普拉斯变换和留数定理，可以得到时域解；最后基于连续性条件给出系统的半解析解。通过数值计算比较可以发现，在相同的时间步长内，Piecewise-Laplace方法的数值结果精度和效率均优于Runge-Kutta方法。如果需要高精度的解，分段拉普拉斯法比龙格库塔法更合适。