Forcing Frequency Limit 1

[Bobfromoh]

It has been awhile since I last did dynamic
analysis. I have a vertical pipe that will be subjected to an external load that will cause the pipe to vibrate. I need to place the supports but keep them to a minimum.

I seem to remember about a rule of thumb concering the forcing frequency versus the natural frequency. This ratio will help determine how much, if any the dynamic load will affect the pipe.

Sorry for not being more specific? Does this make sense and/or is anyone familiar with the above statement?

 

[spongebob007]

Do an internet search on "transmissibility" or "transmissibility plots"

 

[IRstuff]

The basic rule of thumb is that the forcing frequency needs to be a minimum of one octave away from the resonance frequency to no excite resonance.

TTFN

FAQ731-376

 

[SylvestreW]

You are asking about a few differen things.

First, you need to know the natural frequency of the system. Then, to avoid a problem, the forcing frequency should be at least 3 times less than the natural frequency.

If the forcing frequency is too close to the natural frequency, you can get a resonance problem.

If there's a resonance problem, you can calculate the mode shape and then you can then put supports at the anti-nodes in order to prevent motion of the pipes, while minimizing the number of clamps.

 

[Transient1]

This falls under the realm of harmonic analyses.

(1) Having the pipe resonance greater than or equal to one octave away from the input forcing frequency is sufficient to not excite a resonance. Not sure where sylvestreW is coming up with 3 times. Take a look at any transmissibility curve for any SDOF system.

(2) Remember, not exciting a resonance is not the same as canceling the input force. You are simply not amplifying the input force by following the 1st bullet.

(3)Lastly, if your pipe resonance is less than (1/SQRT(2)) times the forcing frequency you will be in the sweet spot of attenuating the input force. However, in this case the joints of the pipes will possibily be subjected to higher forces than if the pipes are adequately supported (without attenuating the input force).

 

[izax1]

Bobfromoh
First ou need to find the frequency of the ecternal force. The you calculate the natural frequency of the pipe using a cantilever model. This natural frequency will change depending on No off and position of supports. No off supports and/or position is correct if your natural frequency is at least 2x the frequency of the ecternal laod.

 

[ORTIZCORNEJO]

Depending on the amount of damping inherent in the pipe then this determines how far away does the resonant frequency must be from the excitation frequency. An empty pipe has very low material (as opposed to viscous or friction) damping force available. Thus the first two or three natural mode frequencies should be at least 30% away from the excitation frequency. If the viscosity and pressure of the fluid the pipe is carrying is high then this "thick" high pressure fluid will yield some friction damping. However, if the viscosity and pressure is low then there will be little if any damping.

Having discussed the boundary conditions of the design it is now time to do some calculations to anticipate "ball park" expected natural frequencies. Depending upon the pipe and fluid I would approximate the system modulus of elasticity as a weighted mixture of pipe metal and flexible like modulus and by trial and error derive the stiffness of the system to calculate the first three modes: single sinusoid, double sinusoid and triple sinusoid. Tubular section stiffness calcs can be found in Blevin's "Formulas for Natural Frequencies and Modes" Once the stiffness is known then go back to Blevins to calculate natural frequencies. Going the whole route of an FEA simulation the same question will be encountered, what is the right Young modulus of elasticity for a pipe carrying a fluid under pressure? There are FEA modeling techniques that overcome the issue however, it may be an overkill if the first three physical modes are what is needed. Bracing should be placed at the antinodes of the modal responses. So far we discussed the simple approach.

Another factor here is that the above calculations do not anticipate pipe response to the excitation coming from "water hammer" that is reverse flow events nor the effects of acoustic wave excitation due to the fluid pulsations if any. "Water hammer effect" includes a wide spectrum of frequencies that will call for not only structural modal frequencies but also some type of elastomeric damper in the bracing. Fluid pulsation induced resonances call for the application of some type of inline type of preferably tuned fluidic damper.

Location of the pipe braces must also take into account that the pipe will grow/shrink due to either sun/cold-weather exposure or to exposure the fluid temperature. The pipe must be allowed to expand at one end freely otherwise if constrained at both ends, this will create a major thermal growth problem possible setting up the pipe in shape of one of its natural resonant modes. At refineries, they install loops in the pipes to dissipate thermal expansion and also this loop disarms some higher frequency acoustic pulsations. Tubas with their curved divergent piping amplify low frequencies . . . . however most fluid pulsation love straight runs to survive.

Therefore, depending upon how critical is the pipe application one must take into account all of the variables or some and then apply the proper analytical tool.

 

[Bobfromoh]

Thanks for the responses. Now the hard part comes putting
the theory into practice.