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CE 335
Programming Assignment 4
Differential Equations: Seismic response of buildings
Horizontal acceleration of the ground during an earthquake causes shear stress on building members as
the building tries to keep up with the ground motion. If the acceleration is too large, the building can
fail and collapse.
The response of the frames of multistory buildings to seismic forces can be roughly modeled as a
system of differential equations describing coupled linear oscillators, one for each floor. For a building
with
n
floors, this is a system of
n
secondorder differential equations (which, as we learned, can be
written as a system of 2
n
firstorder differential equations) in the n unknown displacements
x
(
t
)
Mx'
' +
Cx'
+
Kx
=
m
a
(1)
where
x
is the
n
x 1 vector of the horizontal displacement of each floor,
M
is an
n
x
n
matrix with
diagonal elements equal to the mass of each floor (and
m
is the corresponding
n
x 1 vector of the
diagonal elements),
C
is an
n
x
n
matrix with elements representing the damping rate of vibrations in
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 Spring '11
 Lybas

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