ENgez
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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 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}
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}