To analyze the dynamic responses of a structure, the dynamic equation of motion should be solved numerically or analytically. The analytic solution is more accurate than the numerical solution, but often it is very difficult or impossible to obtain analytic solution. Therefore, various step-by-step integration methods like Runge-Kutta Method, Central Difference Method, Houbolt Method, Newmark Method, Wilson (Method and etc. are developed and modified for the numerical solution. Among the various methods, we don't know which method gives more accurate responses than the others. So we need criteria for selecting a specific method among many other step-by-step integration methods under given integration time increment. This criteria depend on the stability and the accuracy of the each step-by-step integration method. The stability assures convergence of the numerical solution, and the accuracy assures that the relative error between the numerical solution and the exact solution is very small. The integration time increment is usually determined before selecting a specific method and is generally depends on sampling time interval of the forces. This integration time increment should be small enough to get sufficient accuracy and large enough to reduce the time for solving numerical solution. The compromise between these conflicting needs can also be achieved by analyzing the stability and the accuracy.
In this study, free vibration responses of a SDOF system using different step-by-step integration method for varying integration time increment will be compared in both the stability and the accuracy aspects. And by solving practical examples using different step-by-step integration method, the criteria for selecting more accurate step-by-step integration method will be given.
