Strength of carbon silicon beam #1
11/23/03
Wieman

A 50 by 10 grid of measurements was done on the vision coordinate machine by Bob Connors with the beam supported at one end, free cantilever. The measurements were repeated for a second set with a 10 gm weight attached to the free end of the cantilever.

Content:

Display of measured surface

Deflection compared to calculated value

Fundamental vibration frequency

Deduced deflection of beam from gravity

Surface contour of beam without weight. Vertical units in mm, other scales in grid count. The grid in the narrow direction is in ~2mm steps and the grid in the long direction is in ~ 5mm steps.

Deflection of fixed beam with weight on the free end (Roark)

Young's modulus of composite

thickness of composite

The closed gull wing structure is approximated as a closed triangle beam

base width

triangle height

cantilever length

moment of inertial of triangle beam, solid

moment of inertia of solid triangle - inner solid

so, moment of inertia of triangle shell beam

Deflection formula from Roark

End load

Max angle, the angle at the weighted tip

Deflection at the weighted tip

Deflection as a function of x, the distance from the weighted end. x=L is at the fixed support.

vector of x values along the beam.

Measured beam deflection with a 10 gm weight on the end compared to Roark hollow triangle beam formula.

The beam is actually supported out a ways, so taking this into account and reducing stiffness to get a fit.

scale factor for Young's modulus x Moment of Inertia

glue support offset

Conclusion, the triangle beam formula comes our reasonably close. The silicon layer in place of the carbon only reduces the stiffness (Young's Modulus * Moment of Inertia) by 20%

Determine fundamental frequency of vibration

To get the fundamental frequency of the beam use a formula from

http://web.usna.navy.mil/~ratcliff/EM423/Continuous/Beams2.PDF

mass per length

Young's modulus

cantilever beam, fundamental frequency

mass of beam, measured

fundamental frequency of vibration

Conclusion, stiff, but not super stiff

Deflection under own weight

beam deflection under it's own weight, from or derived from Roark

Conclusion: more than allowed 4 mm, we will need calibration factors or we will need to couple the free end of the four ladders in the module to increase the moment of inertia.