51
25. The response of a system excited at its base by
y
(
t
) =
Y
sin
!t
is given by
x
(
t
) =
X
sin(
!
b
t
)
;
with
X
Y
=
1 + (2
±!
b
=!
n
)
2
(1
!
2
b
=!
2
n
)
2
+ (2
±!
b
=!
n
)
2
±
1
=
2
:
Use Figure 3.29 for displacement transmissibility in answering the following questions, but do
not solve any equations.
(a) Assume that the maximum amplitude of the base load is
Y
= 1
cm. A design for a rotating
machine with the above base load and with natural frequency
!
n
= 3
rad/s is required such
that
X
±
2
cm across all frequencies
!
b
. Which
±
value should be chosen?
(b) Suppose that instead of the criteria in (a), we require
X
±
1
cm and
± <
1
:
0
. The machine
operates at
!
b
= 9
rad/s. What are the options for satisfying this criterion?
(c) What is the equation for the maximum force transmitted to the base in terms of
±;
(
!
b
=!
n
)
;k;
and
Y
? For
±
= 1
:
0
, what is the force transmissibility
(
F
T
=kY
)
when the machine is running
at
!
b
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 Fall '11
 Benaroya

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