CE 573 – Structural Dynamics
Homework #11
due 29 November 2010, Monday, 1:30pm
1)
For the 2story building with fixed foundation conditions as shown below:
a.
Determine the natural vibration frequencies and modes; express the frequencies in terms of
m
,
E I
, and
h
.
b.
Verify that the modeshapes satisfy the orthogonality properties.
c.
Normalize each mode so that the roof displacement is unity. Sketch the modeshapes and identify the
associated natural frequencies.
d.
Normalize each mode so that the modal mass matrix is a unity (identity) matrix, i.e. find the mass
normalized modeshapes.
e.
Consider the following two cases:
i.
a constant force F
o
is applied at first floor level quasistatically to give an initial displaced shape,
and the force is removed to start freevibration response;
ii.
a constant force F
o
is applied at second floor level quasistatically to give an initial displaced
shape, and the force is removed to start freevibration response.
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 Spring '11
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 Frequency, Fundamental frequency

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