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I am trying to determine some general cantilever equations.

I have an aluminum beam extending out 235 mm (L) from an aluminum

block. The beam is 25 mm wide (W) and 3 mm thick (H). A force is

applied at a point approx. 200 mm from the block and I am interested

at a point 25 mm away from the block. I know the exact measurement of

vertical deflection at a point 100 mm from the block.

I am assuming the modulus of elasticity E is 10*10^6 psi.

In general, I have the following diagram:

http://www.brentless.com/Images/station2.jpg

In the diagram

A: a driving rod that moves up and down from a loudspeaker setup not

shown, this guides the cantilever on this end

B: a measuring caliper to measure the vertical displacement at point

alpha measured from the aluminum block

C: a mounted strain gauge, the point of interest, centered at delta

from the aluminum block

D: an aluminum block mounted the cantilever on one end

Z1: a known, measurable displacement at alpha distance

Z2: a displacement not known, at the end of the beam

alpha: the measurement from the block to the measuring caliper

beta: the measurement from the caliper to the end of the beam

gamma: the measurement from the caliper to the driving rod

delta: the measurement from the block to the strain gauge

My problems to this point, most formulas I have found assume that the

measurement of deflection is actually taken at the end of the beam.

So how can I use the measurement at the 100 mm point above. I don't

specifically know the value of the force being applied (my cantilever

is being driven up and down by a loudspeaker, so if possible I would

like to leave out the force value and determine an equation based on

the measurement of deflection. Thoughts?

I am trying to determine a general equation of which I can relate to

stress and strain the values and measurements I have stated above for

a testing model. I am not a mechanical engineer, so I don't really

understand this stuff, so I appreciate any advice or help anyone can

give me.

I have an aluminum beam extending out 235 mm (L) from an aluminum

block. The beam is 25 mm wide (W) and 3 mm thick (H). A force is

applied at a point approx. 200 mm from the block and I am interested

at a point 25 mm away from the block. I know the exact measurement of

vertical deflection at a point 100 mm from the block.

I am assuming the modulus of elasticity E is 10*10^6 psi.

In general, I have the following diagram:

http://www.brentless.com/Images/station2.jpg

In the diagram

A: a driving rod that moves up and down from a loudspeaker setup not

shown, this guides the cantilever on this end

B: a measuring caliper to measure the vertical displacement at point

alpha measured from the aluminum block

C: a mounted strain gauge, the point of interest, centered at delta

from the aluminum block

D: an aluminum block mounted the cantilever on one end

Z1: a known, measurable displacement at alpha distance

Z2: a displacement not known, at the end of the beam

alpha: the measurement from the block to the measuring caliper

beta: the measurement from the caliper to the end of the beam

gamma: the measurement from the caliper to the driving rod

delta: the measurement from the block to the strain gauge

My problems to this point, most formulas I have found assume that the

measurement of deflection is actually taken at the end of the beam.

So how can I use the measurement at the 100 mm point above. I don't

specifically know the value of the force being applied (my cantilever

is being driven up and down by a loudspeaker, so if possible I would

like to leave out the force value and determine an equation based on

the measurement of deflection. Thoughts?

I am trying to determine a general equation of which I can relate to

stress and strain the values and measurements I have stated above for

a testing model. I am not a mechanical engineer, so I don't really

understand this stuff, so I appreciate any advice or help anyone can

give me.

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