The study reported herein was conducted as part of the Research Project on the Development of the Pseudo Dynamic Test Application to Multi Degrees of Freedom Systems. The Project is within the scope of the U.S.-Japan Cooperative Research Program Utilizing Large Scale Testing Facilities.

Selection of the integration time interval is difficult when a system with many degrees of freedom is to be analyzed by the pseudo dynamic (PSD) test technique. This statement holds because, as an explicit integration method is employed for the direct integration of PSD test, the solution can only be numerically stable if the selected integration time interval does not exceed the critical value that is proportional to the highest natural period of the analyzed system. This report presents investigations on new direct integration techniques with which restriction in the integration time interval selection is released, and, accordingly, PSD test of systems with many degrees of freedom can be facilitated.

Three new techniques are proposed in this report. They are 1) modal reduction with the use of the substructure modal reduction concept, 2) integration with a combined central difference method (CDM)and Newmark method, designated the CDM-Newmark method, and 3) integration with a cornbined predictor-corrector method (PCM) and Newmark method, designated the PCM-Newmark method. In all techniques, the analyzed system is divided into two parts: the part to which the real PSD test is applied and the part operated numerically within a computer.

In the modal reduction technique, the numerically operated part is condensed in its degrees of freedom according to the substructure modal reduction procedure, whereas the PSD tested part remains unchanged. In the CDM-Newmark method, the PSD tested part is integrated by the conventional CDM, but the numerically operated part by the unconditionally stable Newmark method as in the CDM-Newmark method. the PSD tested part is integrated by PCM, while the numerical part by the uncondtionally stable Newmark method as in the CDM-Newmark method.

In all of those techniques, the integration time interval that can be selected in PSD test is enlarged significantly as compared to the integration time interval allowable in the conventional PSD test. This effectiveness in the integration time interval selection is proven by mathematical formulations and also demonstrated through numerical experimentations.

^*1 Research Engineer, Building Research Institute, Ministry of Construction,
^*2 Research Engineer, Hazama-Gumi Co. Ltd., Formerly, Visiting Research Engineer, Building Research Institute