I imagine this is one of those cases where a picture is worth 10000 words. Are you trying to find the bending modes of the assembly, with oil in it? or what?

Cheers

Greg Locock


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I'd guess the rod/piston mass bouncing up and down on the oil column stiffness would be the one of interest. But that isn't related to model analysis of solid cylinders and barrels.

I was thinking like Brian in my deleted post that the scenario might be "compressible fluid trapped in a cylinder on each side of the piston and you're looking for the natural frequency of the piston oscillating axially"

of course we need op to clarify wtf he meant.

=====================================
(2B)+(2B)' ?

When an 18 year old knucklehead presses the emergency stop button (again) when riding in a nice new hydraulic elevator in Flint Michigan the vertical oscillation is so impressive his knucklehead buddies/fellow passengers holler at him to cut it out.

The knuckleheads used to pop the e-stop button to make the controls skip/avoid low floors when riding the elevator in my college dormitory. Until they borked the controller and ended up stuck between floors for several hours until the fire dept. got there. I used the stairs after a week of riding with knuckleheads.

I too thought the hydraulic column mode would be the one of interest, but I suppose a bending mode might be of interest too, for something like an aircraft landing gear exposed to a lateral shock load when it first contacts the ground...

I guess what I am trying to do is first calculate the natural frequency of the cylinder itself which is a solid (yes, bending modes and the frequency basically for each corresponding modes) and afterwards find the vibration modes and corresponding frequnecy of the double acting hydraulic cylinder. I need to know this because it'll be set in an intricately designed carriage, So basically I am trying to avoid the resonance. For that I want to figure out the nat. freq. of the actuator so I can design a damper if needed.

Isn't the cylinder a tube (not solid)? Modeling as a solid would miss any modes where the tube walls were vibrating.

Yes, hand-model it as a beam with a varying I along its length. Obviously the length and stiffness will vary as you move the piston. The stiffness of the lip seal and the piston seals will be significant, or quite possibly dominant.

Cheers

Greg Locock


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@BrianE22 , yes tube (rod) is a solid cylinder. And why would it miss any vibrating modes?

@GregLocock , yes with varying extensions of the rod, it will have different frequencies as a consequence of varying length and stiffness. But does anyone know nat. freq. formula for just a cylinder rod/column and a thick hollow cylinder?

Thanks,
Anne

Anne -

I think you are looking for the transverse vibrations of the cylinder, correct? If so, then the vibration of the tube wall is probably not important to you. However, for transverse vibration analysis of the assembly a tube is probably a better (more realistic) choice than a solid hunk of metal.

Are you worried about the oil column natural frequency? It would produce vibration in the axial direction of the cylinder.

I doubt there is a general formula for a pair of dissimilar beams linked by a rotational spring, which is what your system boils down to. If there is it'll be in Blevins, which I don't have to hand. The usual way of solving that by hand is Rayleigh-Ritz, discussed with excessive and unhelpful rigor at https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Rit..., although the last example does appear to have been written by an engineer.

Roughly speaking, define a mode shape as a function of time and some amplitude parameters, say .5, 1.5,2.5 wavelengths of a sin wave for bending. Then work out the potential+elastic energy at maximum deflection, and the KE at zero deflection. These are equal, with velocity= w.x, now differentiate w with respect to the amplitudes of the sin waves, and aim for minimising w. It takes a bit of practice, but is very powerful for simple but non uniform systems.

Cheers

Greg Locock


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