USE MATLAB Engineers and scientists use mass-spring models to gain insights into

Question

USE MATLAB

Engineers and scientists use mass-spring models to gain insights into the dynamics of structures under the influence of disturbances such as earthquakes. The figure shows such as representation for a three-story building. For this case, the analysis is limited to horizontal motion of the structure. Using Newton s second law, the governing of motion can be developed for this system as where x is the displacement. Using Ode45. write a MATLAB script to simulate the dynamics of this structure from t = 0 to 20 seconds, given the initial condition that the velocity of the ground floor is dx t / dt = 1 m/s. and all other initial values of displacements and velocities arc zero. Present your results as two time-series plots (a) displacements vs. time and (b) velocities vs. time.

Explanation / Answer

First we have to write this as a system of 1st order ODEs

take

w1 = x1

w2 = x2

w3 = x3

w4 = x1'

w5 = x2'

w6 = x3'

then the system of ODE is :

w1' = w4

w2' = w5

w3' = w6

w4' = -(k1/m1)w1 + (k2/m1)(w2-w1)

w5' = -(k2/m2)(w2-w1) + (k3/m2)(w3-w2)

w6' = -(k3/m3)(w3-w2)

Initial conditions being

w1(0) = 0

w2(0) = 0

w3(0) = 0

w4(0) = 1

w5(0) = 0

w6(0) = 0

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.