Unexpected result with bar fixed to spring with periodic loading

  • #1
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Hi, I solved a steady state problem involving a bar fixed to string in the left side and pulled periodically on the right side [itex]f(x,t)=P_0sin(wt)[/itex]. To check the solution i made E (young's modulus) go to infinity, essentially making the bar rigid. the expression i expected to receive is:

u(x,t) = [itex]\frac{P_0sin(wt)}{k}[/itex]

which is hookes law.

but the expression i received was:

u(x,t) = [itex]\frac{P_0sin(wt)}{k-ρ_{1D}Lw^{2}}[/itex]

the density is one dimensional and L is the bar length.
this expression has an extra term that depends on the frequency which subtracts from the spring constant.
i checked the units and my calculations and they seem to add up. i can't visualize the effect of frequency on the displacement field for a rigid bar. Does this term really "exist" or is this some kind of error?

BTW, the model i used for the bar is the longitudinal displacement equation for bars:
[itex](AEu)''+f(x,t)=ρ\stackrel{..}{u}[/itex]
 
  • #2
The "extra" term looks like the rotary inertia of the beam, and a term something like that should be there.

Look up the theory of single-degree-of-freedom (SDOF) vibrating systems.
 
  • #3
Thank you, I see it know.
 

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