Case Study: Force Vibration Analysis of Building Consider the selection of dampers to attenuate building vibration which is subjected to based excitation (e.g. earthquake), as shown in the figure. -x(t) 2 FA m y(t) = Y cos wt Figure 1: A simple model of a single story building frame subjected to ground excitation of amplitude Y and frequency A single story building frame is modeled by rigid floor of mass m and columns having equivalent stiffness of k. Suppose, a damper denoted with c is to be selected to absorb vibration due to any base excitation, for example during earthquake. The differential equation of motion associated with building subjected to base excitation is mx+cx + kx = cy + ky. k2 X(s) Y(s) and F,(s) Y(s) (1) (a) By taking Laplace transform of (1) obtain the transfer functions X(s) and Y(s) are the Laplace transform of building vibration amplitude x(t) and base displacement input y(t). where The Laplace transformation of the transmitted force fr(t)=-k(x-y)-c(x - y) from the base excitation (earthquake) to the floor mass m is denoted by F, (s). Assume all the initial conditions to be zero for Laplace transform: x(0)= x(0)= y(0) = y(0)=0