Virtual mass

[izax1]

We are dealing with vibration in a ship propeller. This is a thruster. Consider a baseball with propeller wings in one end. The CofG is in the baseball centre. What would be the lowest natural frequency based on added mass influence? Along the long axis, or the short axis?

Thanks a lot!

 

[EnglishMuffin]

Since you mention a propellor, the lowest most significant frequencies are likely to be torsional (ie about the rotation axis). Whatever rotation axis you are interented in, howevever, the corresponding resonant frequencies will depend on moment of inertia and stiffness. So you probably need to clarify your problem a bit.

 

[izax1]

In this case I am not interested in the propeller shaft natural frequencies, but the housing natural frequency.

And, sorry. I mean a football (american football, not soccer) of course, not a baseball. The housing has something like a football shape with the propeller coming out at the "long end". The housing is suspended from the hull with a cylinder-shaped structure. I need to optimise the hull attachment area, but I am uncertain in which direction I will get my lowest natural frequency.

As I said, my stiffness in the propeller housing an suspension is symmetrical. What about my added mass from water? That will not be symmetrical, but which direction will have most added mass? Longitudinal or transverse?

 

[EnglishMuffin]

Well, I can't tell from your description what the mode shape of the lowest resonant frequency will be (which is basically what you are asking). It sounds like a job for FEA, but the fact that it is submerged complicates matters - I guess one would have to use computational fluid dynamics. If I could see a drawing of it, I could probably give you a good guess. But since you say the stiffness is "symmetrical", it may be hard to tell. The fact that the housing is football shaped (ie elliptical) suggests that the added mass effect of the water may be lowest in the direction of the "long axis", so all other things being exactly equal (questionable) the lowest frequency would be in the "short axis" direction, although there might not be much in it. Blevins, in "Formulas for Natural Frequency and Mode Shape" has a section on calculation of the added mass for various sections, including circular and elliptical, and some general comments, so this might be of some help. But the propellor will come into it too, and the major direction of vibration may be more influenced by excitation and turbulence/wake effects etc etc - all in all a very complicated problem.

 

[GregLocock]

I'll take a punt that the most important mode is the torsion of the cantilever between the hull and the pod.



Cheers

Greg Locock

 

[izax1]

Sorry for my poor way of explaining the problem, but what I am really after is which direction of a football shape will have most added mass.

Thanks EnglishMuffin for your input. I dont't have Blevins book available, but your suggestion would mean that my lowest natural frequency is perpendicular to the propeller thrust! Which is, of course, good news.

 

[EnglishMuffin]

bernt : Since I don't fully understand the problem, (and probably never will), I wouldn't assign very much significance to my answer if I were you. But if we restrict ourselves just to the question "which direction of a football shape will have most added mass", a definitive answer should be possible. On that I'll stick by my answer that, assuming we compare translation in the direction of the three princpal axes, the highest added mass will occur when vibration is in one of the transverse directions (short axis), and see if anyone cares to shoot it down. But I am rather skeptical that it has much relevance to the overall design issues with which you are faced.

 

[GregLocock]

To add mass to reduce a mode's frequency add it to the point of maximum amplitude.



Cheers

Greg Locock