Paper , Order, or Assignment Requirements

Answer all questions showing all working out and stating any assumptions made.

Vibrations and Kinetics Questions

Instructions

Answer all questions showing all working out and stating any assumptions made.

Submissions can be handwritten or typed as long as the document is clear and legible.

If the document is submitted in electronic form, the submission has to be in a single

PDF or Word document. Other file types (such as images) or multiple files will not

be accepted.

Penalty for Late Submissions

Work submitted after the deadline will be marked, but the mark awarded will reduce

progressively for each day, or part thereof by which the work is late. The mark

awarded will reduce by 10% of the marks available, per day late (e.g. 71 would

reduce to 61, 55 would reduce to 45 etc.). Work submitted later than 5 days will be

awarded a mark of zero.

Question 1

An electric motor with a mass of 45 kg is attached to a platform that is supported by

four springs; each spring has a stiffness of 12 kN/m (Figure 1). A 5 kg disk (D) has

been mounted incorrectly onto the motor shaft such that the disk centre is 25 mm

from the centre of the shaft. Assume that the motor only vibrates in the vertical

direction and the mass of the platform is negligible.

Figure 1 Electric motor and eccentric disk

1. a) Determine the angular velocity ω at which resonance will occur.

[4 marks]

Dynamics MACE20442

Page 2 of 3

1. b) If the motor operates at 400 rpm, plot the steady state response of the system

over 0 to 0.5 s.

[14 marks]

1. c) As the eccentric disk cannot be remounted, the operators decide to add a

dashpot between the ground and the platform. This dashpot has a viscous

damping coefficient on 1.5 kN s/m. Calculate the damped natural frequency

and plot the steady state response of this new system over 0 to 0.5 s.

[17 marks]

1. d) Comment of the effect adding the dashpot has had on the steady state

behaviour of the system.

[3 marks]

1. e) Plot the modulus of the magnification factor for both the undamped and

damped system for motor frequencies of 0 to 60 rad/s and comment what this

comparison indicates.

[12 marks]

1. f) Assuming that the motor will operate at a single speed and that the disk cannot

be remounted, describe with the aid of a diagram how the vibration of the

motor can be eliminated.

[10 marks] [Total 60 marks]

Question 2

The rod assembly shown in Figure 2 is supported by journal bearings at A and B. The

shaft AB is rotating in the direction shown at 4 rad/s. Assume the mass of each rod is

1.2 kg/m.

Figure 2 Diagram of the rod assembly

Dynamics MACE20442

Page 3 of 3

1. a) Calculate the mass moment of inertia Iyy and the products of inertia Iyz and Ixy

for the rod assembly at the instance shown.

[9 marks]

1. b) For the same instance, determine the shaft’s angular acceleration and the

reactions at the bearings A and B.

[31 marks] [Total 40 marks]