CEE 502 Problem Set 3 Winter 2008
(Due 5:00 PM, Friday, Feb 1, in 233 More)
Reading: Chopra Sections 3.1-3.5.
1. Solve Chopra Problem 2.14.
2. Solve Chopra Problem 2.15.
3. Solve Chopra Problem 2.20.
4. Machinery with rotating parts imparts a sinusoidal force, F(t), with intensity Fmax, to
the tower shown below. The tower will be modeled as a single-degree-of-freedom system
with mass, m, stiffness, k and negligible damping. The sinusoidal force has a period Tb.
a) Assuming that the tower is initially at rest, determine the total displacement response
history for Tb equal to:
i) Tn /2, where Tn is the natural period of the tower
ii) 0.95 Tn
iii) 2Tn
b) For each of the three values of Tb, plot the normalized
displacement history, u(t)/ustatic, versus t/Tn, where ustatic
= Fmax/k. Plot the response for t=0 to t=5Tn. Plot the
histories on a single plot with a spreadsheet or plotting
program.
c) For each of the three values of Tb, plot the normalized acceleration history,
max
(
)
/
u
t
Fm
&& ,
versus t/Tn. Plot the response for t=0 to t=5Tn. Plot the histories with a spreadsheet or
plotting program.
5. For a value of Tb = 0.95 Tn only, repeat Problem 4 for a damping ratio of 5%.
F(t)
