By James Marshall Kelly PhD, BSc, MSc (auth.)

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The horizontal displacements of the center of mass are denoted by u" and u,,' where x and yare the principal directions. The rotation of the rigid deck about a vertical axis through the center of mass is denoted by 0 and a rotational coordinate with the dimensions of the displacement, U6 = rO, where r is the radius of gyration of the deck, will be used. , k! respectively, and these are usually the same. The overall stiffnesses of the isolation system in the x and y directions are N K" =L 1=1 N k!

U" - (JYI and the restoring forces are u! 27) The frequencies are given by the solution of det where A. 1 - A. -~ 0 -ey r I-A. +-r 0 ex r I-A. 28) £0 = - . 36) e" We note that for this choice, I«I»n I = 1, n = 1, 2, 3. , the damping matrix, C, is related to the stiffness matrix, K, through C = 2ocK.

References [1] Applied Technology Council. Tentative provisions for the development of seismic regulations for buildings. ATC Publication ATC-3-06, 1978. [2] Kawashima K, Aizawa K. Modification of earthquake response spectra with respect to damping ratio. S. National Conference on Earthquake Engineering, pp. 1107-1116, South Carolina, 1986. Chapter 4 Extension of Theory to Buildings The two-degree-of-freedom analysis of the simple linear model developed in the previous chapter can be applied to the case of a building with several stories.

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