Solutions to Assignment No. 2
Solution 2.2
(a)
Physically, w n is the natural frequency o f the system, and f is the phase ( lead )
angle of the response.
&
x = Aw n cos(w n t + f )
or
&
x = Aw n sin(w n t + f +
&
Velocity x
p
)
2
Displacement x
p
2
w nt
MECH 364: MECHANICAL VIBRATIONS
Solution Guidelines for the Mid-Term Examination, March 2010
Problem 1
(a)
(i)
Undamped Natural Frequency ( n)
This is the frequency at which the system will oscillate in response to an initial condition
excitation in a giv
VIBRATION ENGINEERING
Solution 1.1
Mechanical vibration deals with the oscillatory response of mechanical systems to some
form of an excitation (initial-condition or forcing excitation). Since the performance of an
engineering system can greatly depend on
MECH 364 Mechanical Vibrations
SOLUTION GUIDELINES TO MID -TERM EXAMINATION
November 06, 2008
Problem 1
(a) Since the springs are uniform and one end of them is assumed fixed, the distributed
spring mass can be lumped at the other (free) end at one-third
MECHANICAL VIBRATIONS
Solutions to the Final Examination 2
Problem 1.
(a)
Natural vibrations are oscillatory responses. Hence, both displacement and velocity
of the mass elements of the system will undergo cyclic variations in natural
vibration. That mean
Mechanical Vibrations
Solution to Final Examination 1
Problem 1:
a) (i) Modal analysis decouples a coupled, complex, dynamic system. The uncoupled
equations are easier to analyze, and standard procedures and results are available.
(ii) The dynamic perform
MECHANICAL VIBRATIONS
SOLUTIONS TO FINAL EXAM 3
Problem 1
(a)
(i)
Piezoelectric Accelerometer:
Produces an electric charge that is proportional to the inertia force in the
mass element of the accelerometer. This charge measures the acceleration
of the mas
MECHANICAL VIBRATIONS:
SOLUTIONS TO MID-TERM EXAM 1
Problem 1:
F
48EI
=
ym
l3
(i)
ke =
(ii)
For the beam,
l
1m
2
KE =
[ ym q(t )] sin 2 px dx
2l
l
0
l
But sin 2
0
px
l
dx =
l
2
Hence,
1m
KE =
[ ym q(t )]2
22
where, [ y m q(t )] is the velocity at mid span
Mechanical Vibrations
SOLUTIONS TO MID -TERM EXAMINATION 3
Problem 1
(a)
Assume a suitable velocity profile (typically linear) and, through
integration, determine the kinetic energy of the distributedparameter system in terms of the velocity at the coordi
MECHANICAL VIBRATIONS
Solutions to the Mid-Term Examination 2
Problem 1
i)
Figure 1.
Shapes of the test responses
(a) Hammer test, (b) Shaker test.
-1-
Note that the response from the Hammer test is oscillatory and decaying. This is the
behavior of an und