Pole-residue method for numerical dynamic analysis
Date of Original Version
Systems of second-order linear ordinary differential equations (ODEs) to arbitrary input functions appear in many fields of physics and engineering. Numerical methods for solving these kinds of problems have been mainly performed in the time and frequency domains. In contrast, this paper develops an efficient, seminumerical pole-residue method implemented in the Laplace domain. In this article, a key concept and development is on how to compute the poles and residues of the output from those of the input and system transfer functions. Once the poles and residues of the output are known, the corresponding time history of the output is readily obtained. Even though the correctness of the new method has been verified by using a step-by-step time-domain solution, the accuracy of the new method in theory is higher than that of any time-domain approach, partially because the output obtained from the new method is a continuous function of time.
Journal of Engineering Mechanics
Hu, Sau-Lon J., Fushun Liu, Bin Gao, and Huajun Li. "Pole-residue method for numerical dynamic analysis." Journal of Engineering Mechanics 142, 8 (2016): 1-10. doi:10.1061/(ASCE)EM.1943-7889.0001089.