Advanced structural systems - mechanical engineering

Problem Set 4 – KB6005 – Vibration analysis using MATLAB

1. Consider the system in question 1 of problem set 3; write the equations of motion in

first-order form.

2. Consider the system in question 4 of problem set 3; write the equations of motion in

first-order form.

3. Using MATLAB, obtain the natural frequencies and mode shapes of

(a) System (a) in question 5 of problem set 3, assuming k = 400 N/m and m = 2 kg.

(b) System (b) in question 5 of problem set 3, assuming k1 = 100 N/m, k2 = 200 N/m,

k3 = 300 N/m, m1 = m2 = m3 = 5 kg.

4. For the system shown below:

(a) Derive the equations of motion and write them in matrix form.

(b) Obtain the undamped natural frequencies using MATLAB assuming m1= m2=1 kg,

k1 = k3 = 100 N/m, and k2 = 400 N/m.

(c) Write the equations of motion as a set of first-order equations.

(d) Solve the equations of motion using MATLAB in the time range of [0 20] seconds.

Use m1= m2=1 kg, k1 = k3 = 100 N/m, k2 = 400 N/m, and c1 = c2 = c3 = 1 N-s/m.

Assume F1 = 0 and F2 = 10cos(ω1t), where ω1 is the smaller natural frequency of

the system. Plot x1 and x2 as a function of time. The system is initially at rest.

(e) Repeat (d) assuming F2 = 10cos(0.9ω1t).

(f) Compare vibration amplitudes of (d) and (e).

F1

F2