Unexpected result with bar fixed to spring with periodic loading

[ENgez]

Hi, I solved a steady state problem involving a bar fixed to string in the left side and pulled periodically on the right side $f(x,t)=P_0sin(wt)$. 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) = $\frac{P_0sin(wt)}{k}$

which is hookes law.

but the expression i received was:

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

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:
$(AEu)''+f(x,t)=ρ\stackrel{..}{u}$

 

[AlephZero]

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.

 

[ENgez]

Thank you, I see it know.