Faculty of Environment and Technology
Academic Year:
16/17
Examination Period: January
Module Leader:
Module Code:
Module Title:
N Larsen
UFMFL8-15-2
Dynamics
Duration:
2 hours
Standard materials required for this examination:
Examination Answer Booklet
Yes
Multiple Choice Answer Sheet
No
Graph Paper
Type of paper e.g. G3, G14
N/A
Number of sheets per student
0
Additional materials required for this examination:
Details of additional material supplied by UWE:
None
To be collected with Answer Booklet (please delete as appropriate)
Details of approved material supplied by Student:
1 Side of A4 handwritten notes only
To be collected with Answer Booklet (please delete as appropriate)
Yes
University approved Calculator
Yes
Candidates permitted to keep Examination Question Paper
Yes
Candidates are NOT permitted to turn the page
over until the exam starts
UFMFL8-15-2
Page 1 of 4
Instructions to Candidates:
Candidates must answer any THREE questions.
Question 1
The deck of a car ferry, loaded with vehicles may be thought of as a lumped mass of
250Tonnes supported by springs of coefficient k=620 k N/m with damping C =78.75 kNs/m
Damping
coefficient C
Spring
coefficient k
M
Fig Q1a - car ferry deck
Fig Q1b – schematic of deck
a)
What are the damping ratio, undamped and damped natural frequencies of this
arrangement?
(6 marks)
b)
Under certain sea conditions, the sea waves have a wavelength of 20m. What
speed would the vessel have to attain in order to excite the system at its resonant
frequency?
(4 marks)
c)
The ship is actually sailing at 6.5 m/s. Assuming the excitation due to the waves to
be of the form F  F0 Cos(t   ) and to have a peak amplitude F0 of 30kN,
evaluate the resulting displacement of the deck, and the phase relationship of the
deck with the exciting force.
(15 marks)
UFMFL8-15-2
Page 2 of 4
Question 2
A schematic diagram of a two degree of freedom system is shown in Fig Q2.
k1  10k , k 2  k , m1  10m and m2  m .
10k
k1
F1
x1
10m
kk2
F2
x2
m
Fig Q2
a) Write the equations of motion in matrix form.
(8 marks)
b) Go on to find the undamped natural frequencies and mode shapes of the system described by
Fig Q2
(10 marks)
c) The diagram of Fig Q2 could be used to represent a vibration absorber. Giving one or more
example applications briefly describe why vibration absorbers are fitted and how they work.
(7 marks)
Question 3
A car of mass 800kg has an overall suspension stiffness of 100 kN/m; the damping is 30% of
critical.
a)
sketch a lumped parameter model of the system, and elaborate on any assumptions made
in such a model.
(4 marks)
b)
Assuming that, for vertical oscillations, the car can be modelled with lumped parameters,
find the overall damping coefficient c. Also find the undamped natural frequency f 0, the damped
𝑓
natural frequency f d and the ratio of the damped to the undamped frequencies, 𝑑⁄𝑓
0
(8 marks)
Continued overleaf……...
UFMFL8-15-2
Page 3 of 4
c)
The car is set into vertical oscillation with an initial amplitude of 20mm. Calculate the
number of cycles and the time for the amplitude of oscillation to fall below 2mm
(8 marks)
d)
Explain the effects on performance in detail if the dampers previously considered to be
viscous are frictional in their effect.
In particular, describe the effect on the rate of decay of oscillation amplitude, you may wish to
illustrate your answer with a sketch.
(5 marks)
Question 4
B
C
B
C
A
A
O
O
The suspension linkage on a mountain bike may be represented as a four bar linkage as shown in
the diagrams Fig Q4 above.
The dimensions are known:
r AO  0.4i m
r BA  0.16i  0.36 j m
r CB  0.12i  0.04 j m
a)
Evaluate the absolute positions r B and r C
(6 marks)
A bump in the road causes a rotation of link OA with velocity  OA = 2 rad/s clockwise. Using vector
notation:
Find the resulting linear velocity of B vB and hence the rotational velocity of link BC  BC
(15 marks)
c)
The link BC is extended to reach the shock absorber mount. Assuming the (perpendicular)
radial distance from C to the shock absorber mount to be 0.08m, what is the linear velocity of the
shock absorber top mount?
(4 marks)
END OF QUESTION PAPER
b)
UFMFL8-15-2
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