Vibration and Signal Processing MECH3404
Tutorial 3
Q1.
Determine the natural frequencies and mode shapes for axial vibration of the system shown
in Fig. Q1.
Figure Q1
ANS.
1 =
k /m ; A1/A2 = 1.0 and 2 = 1.91 k /m ; A1/A2 = -3.0)
_
Q2.
Determine the natur
Mechanical & Chemical Engineering
SEMESTER 1, 2014 EXAMINATIONS
UNIT CODE (MECH4426)
UNIT NAME (Dynamics, Vibration and Sound)
FAMILY NAME: _ GIVEN NAMES: _
STUDENT ID:
SIGNATURE: _ : _
This Paper Contains: 6 pages (including title page)
Time allowed: 3 h
Past Exam Questions 2015
Dynamics (25%)
Q1.(12.5%) An Australian football is modelled as an oval as shown in Figure 1. If the
initial position and velocity of the ovals centre of mass are:
x(0) 0
y (0) 0
x(0) 5m/s
y (0) 5m/s
and the ovals angular velo
Solution of the MECH4426 Exam Paper (2015)
Dynamics (25%)
Q1.(12.5%) An Australian football is modelled as an oval as shown in Figure 1. If the
initial position and velocity of the ovals centre of mass are:
x(0) 0
y (0) 0
x(0) 5m/s
y (0) 5m/s
and the
Vibration and Signal Processing MECH3404
Tutorial 3 Solutions
Q1. Determine the natural frequencies and mode shapes for axial vibration of the system shown
Equations of motion
.
m x1 = kx1 2k(x1 x 2 ) . (1)
.
3m x2 = 2k(x1 x 2 ) 3kx2 . (2)
Assume sinusoid
PAST EXAM QUESTIONS 2013
Dynamics (20%)
Q1. A solid cylinder is capable of rotating on the surface of a stationary wedge without
slipping. The cylinders mass and mass moment of inertia (around the centre) are M
1
and
Mr 2 respectively, where r is the radi
Vibration and Signal Processing MECH3404
Tutorial 2
Q1.
For the system shown below, determine:
(a)
The damping ratio,
(b)
The damped natural frequency,
(c)
The log decrement,
(d)
If the system is given an initial velocity of 10
mm/s, determine the respons
Vibration and Signal Processing MECH3404
Tutorial 1 Solutions
Q1.
A simple mass-spring system with a natural frequency of 30 Hz is given the initial
conditions, x(0) = 0.2 m and x (0) = 10 m/s.
(a)
Determine the response x(t).
(b)
What is the maximum velo
Vibration and Signal Processing MECH3404
Tutorial 4 solutions
Q1.
Since no initial velocities
x1(t) = a11 cos1t + a12 cos 2t
x 2 (t) = a 21 cos1t + a 22 cos 2t
The mode shape information gives
. (1)
. (2)
a 11
a
= 1 and 12 = 3
a 21
a 22
When t = 0 from (1
Vibration and Signal Processing MECH3404
Tutorial 1
Q1.
A simple mass-spring system with a natural frequency of 30 Hz is given the initial conditions,
x(0) = 0.2 m and x (0) = 10 m/s.
(a)
Determine the response x(t).
(b)
What is the maximum velocity attai
Vibration and Signal Processing MECH3404
Tutorial 4
Q1.
Figure Q1
The system shown in Fig. Q1 of Tutorial 3 (and reproduced above) is initially displaced so
that,
x1 = + 0.01m and x2 = + 0.02m
and then released from rest. Given that the natural frequencie
Vibration and Signal Processing MECH3404
Tutorial 2
Q1.
For the system shown below, determine:
(a)
The damping ratio,
(b)
The damped natural frequency,
(c)
The log decrement,
(d)
If the system is given an initial velocity of
10 mm/s, determine the respons