mode interaction 1

[mech2926]

Hi,
I have a question on mode interaction. There is a several thousand pound vertical vessel attached to a skid which is secured to the floor. Attached to the vessel are several piping assemblies. The piping assemblies weigh quite a bit less than the vessel. The first few modes of the system (as viewed from NASTRAN results) consist of the piping moving quite a bit and the vessel moving slightly. The first mode that involves mainly the vessel is considerably higher.

So, to get to the question: if I have a small, relatively stiff object (relief valve) mounted to the top of the tank, do I need to worry that it will interact much with the other modes of the system? Or can I just assume that since it weighs so little (~10 lb) and is so stiff (when considered by itself) that it doesn't lower the modes of the overall system?

 

[electricpete]

There is certainly a set of frequencies where the relief valve will have a big effect on the system. Those are the frequencies near where the relief valve studied in isolation (as if mounted to a fixed point) becomes resonant. The point of attachment of the larger structure becomes a node for this modeshape/natural frequency. This is the principle of a "dynamic absorber" or "tuned mass damper", where a small structure can be used to reduce motion of a larger structure usually at a single frequency of interest.

I believe at most frequencies far removed from the ones discussed above, the relief valve will have little effect.

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(2B)+(2B)' ?

 

[hacksaw]

first you estimate the relief valve thrust components, then sort out the excitation of the various modes. Usually the static thrust transmitted to the vessel is the biggest concern and design for that. If the valve is not properly sized and it chatters then it is concievable that you might excite some of the shell modes but you have to sort that all out with the other your design disciplines

 

[electricpete]

I understood the question to be: how will addition of a relief valve to the system change the modes of the system (compared to system analysed without relief valve). That is a completely different question than what modes will be excited. Modes are a characteristic of the system, not the excitation. Maybe op can clarify.

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(2B)+(2B)' ?

 

[mech2926]

Sorry for the delay; thank you all for your replies. I'll try to clarify:

Yes, I was asking whether adding the relief valve will change the system modes. The main excitation frequencies of concern are from earthquake, and the ZPA is around 30 Hz. So the valve would be fine by itself because its mode is an order of magnitude higher. The issue I have is, the overall system is very close to the earthquake ZPA (~30 Hz) and I want to make sure that adding a relief valve is not going to cause a mode somewhere that is significantly lower.

 

[electricpete]

I suspect there may be some insight to be gained by studying a 2DOF system (transfer function analysis attached):

> # Original system: Ground===K1===M1.
> # Modified system: Ground===K1==M1===K2===M2
> # where M2<<M1
> # where both K1 and K2 have damping elements C1, C2 in parallel

> # Can we assume that the new mode introduced by addition of K2 M2 involves very little movement of M1?

> # Values to be studied:[M1=1000,M2=100,K1=1000,K2=10,C1=10,C2=0.1];

> # Original M1/K1 system has resonant frequency w=sqrt(1/1)=1
> # Added system creates a zero freq of M1 at w=sqrt(1/10)~0.3 (dynamic absorber effect)
>
> # Composite system has a root just above 1 (1.005) and a root below the zero at 0.3
> # Question: Does the root at 0.3 affect M1?
> # Answer:
> # Figure 1 shows comparatively small peak in M1 response at 0.3 when exciting force applied at M1
> # Figure 2 shows comparatively large peak in M1 response at 0.3 when exciting force applied at M2
> # Figure 3 shows comparatively small peak in M1 response at 0.3 when base is moved
> # Figure 4 is a zoom-in of Figure 3.
> # Results of course depend on values selected including damping

The bottom line, addition of K2, M2 did introduce a new mode at a frequency (0.3) much lower than the original resonant frequency (1.0). The motion of mass M1 in that new mode tends to be relatively small.

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(2B)+(2B)' ?

 

[electricpete]

So the valve would be fine by itself because its mode is an order of magnitude higher.

Whoops, I kind of missed that. I assume you mean the valve mounted to rigid base has resonant frequency an order of magnitude higher than the lowest mode of the original system?



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[electricpete]

Fwiw, attached is a spreadsheet to calculate resonant frequencies of 2dof systems.

If you use the parameters:
k1_ 1000
m1_ 1000
k2_ 1000
m2_ 100
... then you get resonant frequencies of 0.95 and 3.33. So while the original lowest frequency was w=sqrt(k1/m1)=1.0, the new lowest frequency after adding m2 and k2 is 0.95.

That is pretty close to the same value you'd get if you had simply added the 100 pounds to M1 on the SDOF (K2=infinity). Sqrt(1000/1100)~(1-0.1)^(-0.5)~1-0.5*0.1 = 1-0.05 =0.95

One thing to mention is of course generalized mass should be considered. If relief valve extends far away from pivot point of mode of interest than it's rotational inertia might become important.

Sorry for the rambling...

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[electricpete]

Correction in bold:

That is pretty close to the same value you'd get if you had simply added the 100 pounds to M1

should've been

That is pretty close to the same value you'd get if you had simply added the 100 mass units to M1

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