Faculty of Environment and
Technology
Academic year: 2018/19
Assessment Period 1/2/3
Module leader:
Module code:
Module title:
Examination duration
(hours):
N Larsen
UFMFL8-15-2
Dynamics
2 hours
Standard materials required, to be collected
Examination Answer Booklet
Multiple Choice Answer Sheet
Type of graph paper
Number of graph paper sheets per student
Yes
No
None
Additional materials required for this examination
Please list any additional material supplied by UWE Bristol and whether or
not they need to be collected.
NONE

Please list any additional material supplied by the student and specify if
they need to be collected.
1 Side of A4 handwritten notes only, to be collected
University approved calculator (not programmable)
Yes
Candidates permitted to keep this examination paper
Yes
Candidates are not permitted to turn this page over
until the examination starts
UFMFL8-15-2
Page 1 of 5
Instructions to Candidates:
Candidates must answer any THREE questions. Marks will be scaled to a
percentage.
Show your workings in any calculations you do for all questions.
Question 1
A mobile phone manufacturer wishes to install a device such that the
phone will vibrate when called.
The mechanism is made up of a small electric motor with an eccentric
weight on the spindle as shown:
The motor has a total mass of 2.5g, and the eccentric mass has an
unbalance u of 0.6 g-mm.
The motor is firmly soldered to a printed circuit board mounted in the
phone’s case. The circuit board may be modelled as having a spring
coefficient k of 1000 N/m and damping coefficient c of 2.2 Ns/m
a) Evaluate the amplitude and frequency of the (vertical component of)
force acting due to the unbalanced rotation at 8,400 rpm motor
speed
[3 marks]
b) Sketch a lumped parameter model that describes the system,
showing all relevant variables and components
[3 marks]
c) Show the force balance equation for the system, and sketch a
phasor diagram showing all relevant (force-like) quantities and
thereby find the displacement amplitude of the mass.
[10 marks]
d) Find the amplitude of the force transmitted to the case of the phone.
[6 marks]
e) Will the force be sufficient to make the phone “jump” up from the
surface on which it’s lying? (The phone’s total mass is 150g) State
any assumptions you may wish to make.
[3 marks]
UFMFL8-15-2
Page 2 of 5
Question 2
An inner city high rise building is designed
to withstand earth tremors by permitting a
sideways swaying motion in the structure –
fig Q2.
The building may be represented as a
lumped mass of 200*106 kg.
The steel structure of the building has an
effective spring constant of 1.260*109 N/m
Fig Q2
a)
Find the undamped natural frequency ωn of the system.
[4 marks]
b)
Following an earth tremor, the initial displacement amplitude of the
oscillation of the building is 2.3 m
The oscillation amplitude has diminished to 0.1m after 5 cycles. Evaluate:
i.
the logarithmic decrement λ
[2 marks]
ii.
the damping ratio ζ
[4 marks]
iii.
the actual (damped) circular frequency of oscillation
iv.
the damping present in the system
[2 marks]
[4 marks]
c)
The building’s owners are worried about movement arising from forced
oscillation that may be brought about in future events. Sketch and fully label
a graph showing the effect of frequency on the displacement amplitude if a
forcing function of fixed amplitude is applied.
[4 marks]
d)
The architects decide to change the behaviour of the building by
introducing a vibration absorber. Describe how such a device might work,
including any useful quantitative information, and sketch a possible resulting
(new) response of displacement amplitude to frequency of the building
[5 marks]
UFMFL8-15-2
Page 3 of 5
Question 3
Shown in Fig Q3a below is a two degree of freedom system in free
(torsional) oscillation. It consists of two inertias with moment of inertia j and 2j
Nms2/radian respectively as shown on the diagram.
The inertias are connected with torsion springs of coefficient k or 5k
Nm/radian as shown
θ2
θ1
k(torsional)
k(torsional)
5k(torsional)
k
j
2j2j
Fig Q3a
a)
Find the equations of motion of the system in matrix form
[6 marks]
and hence the natural frequencies of oscillation.
[6 marks]
Go on to find the mode shapes for the system
[4 marks]
(b) The system shown in Fig Q3b is semi-definite, “floating” or degenerate 2
degrees of freedom system.
k
m
x1
m
x2
Fig Q3b
(i) Find the natural frequency.
[3 marks]
(ii) Find the mode shape.
[3 marks]
(iii) Explain your reasoning in (b) (i) and (ii).
[3 marks]
UFMFL8-15-2
Page 4 of 5
Question 4
A motor car “double wishbone” suspension may be represented as a four bar
linkage with dimensions as shown in the diagram Fig Q4 below:
D
j
θCD
C
k
θBA
θCB
A
B
Given the geometric information, taken from the car:
AB= 400mm, BC = 250mm, CD = 300mm
θBA = -12°, θCD = -6°, θCB=90°
a) The car travels over a bump in the road which produces an angular
velocity of 2rad/s anticlockwise in the link AB.
Find the resultant angular velocity of the upright BC (ωBC)
[15 marks]
b) The crank-slider mechanism, as implemented in the typical internal
combustion engine crankshaft and piston assembly produces a nonsinusoidal motion of the piston when the crankshaft is rotated at a
constant angular velocity.
Discuss the effect of this on the nature of the vibratory forces produced
by such a mechanism. Further discuss means for minimising the
effects of such forces in both single and multi-cylinder arrangements.
[10 marks]
END OF QUESTION PAPER
UFMFL8-15-2
Page 5 of 5
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