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I need to transfer vibration to 10 meters. I can do this with solid metal rod, but its making mechanical design complex. So, I am thinking to do it hydraulically (tubes can easily be bend). But, I am not confident with hydraulics for vibration transfer.

Vibration is an exclusive attribute of solids. Can pressurized liquid in hydraulic device hold and transfer vibration?

What would happen if I apply vibration to one end of hydraulic pump? I want to see it at molecular level, too. Mathematical model is encouraged.

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Any fluid has a bulk modulus, which is a pressure volume relationship. Elastic waves can propagate through it, but I would be more concerned about damping and losses. –  ja72 Jul 6 '12 at 0:09
@ja72 In hydraulics, volume is kept constant. That's why I want to see it at molecular level as well as with mathematical model. –  Sachin Shekhar Jul 6 '12 at 3:40
that is not true .. read here engineeringtoolbox.com/bulk-modulus-elasticity-d_585.html –  ja72 Jul 6 '12 at 12:55
The speed of sound (and hence vibration transfer) is $c=\sqrt{\frac{K}{\rho}}$ with $K$ the bulk modulus, and $\rho$ the density. For SAE oil this is about $c=1390\; \rm m/s$. –  ja72 Jul 6 '12 at 13:11
@ja72 Why are you displaying this? I am specially talking about hydraulics which keeps fluid under fully compressed states (if it is compressible). Plus, I would like to move piston of hydraulic pump in S.H.M... I don't just want to use it as medium of sound type vibration. –  Sachin Shekhar Jul 6 '12 at 13:55

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