It is a well known fact that, in the direct integration of equations of motion, the integration time interval governs both the stability and accuracy characteristics of the numerical solution.Because of this, the integration time interval should be carefully selected for good implementation of the pseudo dynamic (PSD) test since the PSD test is one variation of the direct integration. Theoretically,it is better to use as small a time interval as possible, but, in real PSD test environment, the largest time interval that yet ensures the accurate results must be the best choice.
The global purpose of this study is to provide information for good implementation of the PSD test. The specific objectives are 1) to investigate in detail the stability and accuracy characteristics of the central difference method which is used for the direct integration in the PSD test, 2) to supply guidelines for the selection of the time interval in the integration of the PSD test, and 3) to examine the possibility of employing a new integration method more effective in implementation of the PSD test in terms of the interaction between the time interval and solution accuracy. Study on the last objective 3) is encouraged in that an integration method having a larger stability limit than the central difference method is extremely attractive to the PSD test of multi degrees of freedom systems.
A general procedure to evaluate the stability characteristics of the central difference method was reviewed, and, for both undamped and damped systems, the numerical solution was found to be stable as long as the product of the circular natural frequency of the analyzed system and the time interval does not exceed 2. The general analytic solution which represents the numerical solution was also derived. Based upon the analytic solution, it was found out that the error of the numerical solution relative to the exact solution can be specified as a combination of the apparent period contraction, viscous damping ratio distortion, phase lag, and amplitude change. The quantities of those error parameters are expressed in visual forms. Those figures can provide guidelines for the selection of the integration time interval for any PSD test. Through mathematical formulation, it has been proven that there is no explicit method which fits into the PSD test and has a larger stability limit than the central difference method. In addition,from the accuracy view point, the central difference method was found to be no worse than any explicit methods covered in this study.
^{*1} Research Engineer, Production Department
