Equation of motion coursework

  • Thread starter KateyLou
  • Start date
  • #1
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Homework Statement



I have coursework on rhe convolution integral, however i am struggling to find the equation of motion to start the whole thing off with.

I will attach a picture of the problem, is is simply a cantilevered bar with a concentrated mass on the end and a damper.

Homework Equations



I am assuming you find the deflection at the end of the beam as a result of the force P(t), which i think is
P(t)L^3/3EI

However i am not sure where to go from here


The Attempt at a Solution



Thinking it may possibly be
m[tex]\ddot{x}[/tex]+c[tex]\dot{x}[/tex]=P(t)L^3/3EI
however i think i may need to add in stiffness somewhere else..
 

Attachments

  • cantelivered beam.png
    cantelivered beam.png
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Answers and Replies

  • #2
2,411
710
Your simple model for the cantilever, looks OK, and it gives you the stiffness if you look at it properly. You have a deflection relation that is usually written as
defl = P*L^3/(3*E*I)
Now re-arrange that to read
P = (3*E*I)/(L^3) * defl
and from there you can see that the stiffness of this system is
K = 3EI/L^3
Now back to your equation of motion, which will look like
m*xddot + c*xdot + K*x = F(t)
where F(t) is whatever applied forcing function acts on the mass.

See if that will get you going!
 

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