From the results of vibration tests on several masonry buildings, we have found the facts that the horizontal amplitude of any point along the vertical axis of such buildings shows a linear modal line, and its magnitude is remarkably affected by the horizontal shifting of the foundation and the rotation of the structure due to the deformation of soil. (cf. Fig. 1 and Fig. 2)Taking these facts into consideration, we present an analytical theory which can explain vibrational features of masonry structure not only in elastic range but also in plastic. Considering the linearity of modal line, we assume in the theory that a masonry structure can be represented by a rigid model with horizontal and vertical springs at its bottom as shown in Fig. 3, where the actual deformability of the structure itself is considered to be amalgamated into the coefficient of the soil spring.From theoretical calculations of forced, coupled vibration, we can see the nodal point always exists at a nearly fixed position when the frequency approaches to the fundamental resonance and, accordingly, we can treat the model as a rotating vibration system with one degree of freedom having its rotating center at the nodal point.Using this simplification we can explain the behavours of large vibration whose resonance diagram shows a non-linear characteristic. (cf. Fig. 6).While, in the present paper, the authors submit a theory of vibration of masonry structures excited by a vibrator as shown in Fig. 3 and prove the coincidence of theoretical results with the experiment, they also give some consideration to the acceleration which will take place in such structures when shaked by ground motion.In the last part of this paper, there are listed some values of spring constants of soils or the coefficients of both subgrade reaction and subgrade shear reaction, which have been obtained from the test results on some actual masonry buildings.
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