16.20 Handed Out: Lecture 20
Due: Lecture 30
DESIGN PROBLEM #3
Your company has contracted with Moontowers International to provide
engineering consulting services for the preliminary design of a transmission
tower at the new Lunar Base III that is under construction. Previous
transmission towers have met with difficulty due to the temperature swings
various points of the moon undergo during the moon’s revolution around the
earth. Maximum temperatures up to 100°C have been recorded on such
structures while the structure is in full sunlight and minimum temperatures as
low as -75°C have been recorded when the structure faces away from the sun.
The rotation and revolution of the moon are slow enough that the temperature
conditions are basically "constant" (hourly change is very small) and thus
thermal gradients do not need to be considered in these transmission tower
structures.
The previous transmission towers have been unable to meet the design
requirements that the transmission dish stay within 10 mm of the design point at
all times. This is due to the large thermal differential that occurs and the
difficulties in designing and manufacturing a structure with those specifications
and tolerances. This has caused the previous stations to be out of contact with
other stations and Earthbase during a significant fraction of the month (i.e. the
lunar cycle) and has thus resulted in auxiliary transmission towers being erected
to overcome this difficulty, but at substantial cost.
Moontowers International has decided to consider the new piezoelectric
technology as a solution to this problem. They have contracted your group to
provide them the expertise and the suggestions. Other specialists are also
working on the design, so you are not responsible for the overall design but only
for some specific items as noted below.
The tower structure can be considered to be a constant cross-sectional
shape 30 meters in height. The transmission/reception dish is mounted 29
meters above the lunar surface. Tension lines are utilized to stabilize the tower.
This configuration (without tension lines) is shown in Figure 1. It should be
noted that this configuration is initially assembled at an ambient temperature of
approximately 0°C. Strength and buckling considerations are the concern of
another set of consultants. For your work, Moontowers indicates that you can
consider the tower to have a cross-section of base material, piezoelectric material,
and base material in a symmetric and solid configuration as shown in Figure 2.
The voltage is applied across the thickness of the piezoelectric material.
Various base materials, with different costs and different basic properties,
are under consideration. Different piezoelectric materials are also being
considered. The properties, costs, and other pertinent facts are listed in the
accompanying table. These properties are "room temperature (on earth)
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