Engineers and scientists use mass-spring models to gain insight into the dynamics of structures under the influence of d

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Engineers And Scientists Use Mass Spring Models To Gain Insight Into The Dynamics Of Structures Under The Influence Of D 1 (131.01 KiB) Viewed 19 times

Engineers and scientists use mass-spring models to gain insight into the dynamics of structures under the influence of disturbances such as earthquakes. Figure 1 shows such a representation for a three-story building. ,- 8,000 kg m kx = 1800 kN/m m = 10,000 kg m- , 2400 kN/m 7,12,000 kg k = 3000 kN/m Figure 1 For this case, the analysis is limited to the horizontal motion of the structure. Using Newton's second law, force balances can be developed for this system as: dr dx dr k. k = ---+---x2 - 1) MI M ky = (x1 - x) + (x3 - 2) M2 dr? = (x2 - x3) 3 where x1, x2 and x3 are the horizontal displacements of each floor. Simulate the dynamics of this structure from t = 0 to 20s using a second-order numerical solver, given the initial condition that the velocity of the ground floor is dxs/dt = 1m/s, and all other initial values of displacements and velocities are zero. Present your results as time-series plots of horizontal: 1. displacements, 2. velocities, 3. accelerations and 4. forces of each floor.