構造物の彈性振動に関する一問題

抄録

As an example of earthquake-proof structures, we studied on the free vibration of the simple structure which has pillars of different width and thickness. If both pillars have square sections and we fix the size of one pillar constant and vary that of another one, it will be supposed that the period of the free vibration increases with the decrease of the size, of the later pillar. According to our theoretical results, however, it should not increase monotonously but it reaches a maximum value once, and then decreases gradually to a minimum one and again increases as shown in Fig. (3). Thus between these maximum and minimum. values there are three combinations of pillars of a same period of free vibration. And in these three combinations, periods are equal but displacements, bending moments and shearing stres_??_ are different among each other.
For example as shown in this paper, we can show that weak parts exist in the pillar with smaller section of one structure of the three one_??_. with _??_ _??__??_me periods, becaus_??_ the amplitude of its d_??__??_placement become_??_ much _??_reater th_??_ those _??_n the two other structures. But shearing st_??_e_??_ and bending moment do not differ so much that it will not happen that the smaller pillar breaks earlier than the other by backling or _??_hearing.
In the case of rectanglar pillars, corresponding to the sectional size one pillar, maximum and minimum periods do not appear, but there exists a region with a nearly constant period. So we can say that, in this case again, structures have a similar nature as in the square sections.