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:(adsbygoogle = window.adsbygoogle || []).push({});

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 cant 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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Unexpected result with bar fixed to spring with periodic loading

**Physics Forums | Science Articles, Homework Help, Discussion**