structure design for a vibration test

[Txoleski]

Hello to all,

Recently we have acquired a shaker test bench and we need to design a support structure to make a vibration test of a part. We had an internal discussion about this matter but i wonder if you could let me know if we are working in the right direction.

Firstly we think that we should calculate the maximum mass of the whole part taking into account the test specifications and the vibration shaker limits.

As the acceleration in the test is constant i was able to calculate the mechanic power necessary to move a given mass in a frequency:

Pm=(M*a^2)/(2*(2*Pi)^2*f) Is this formula correct or am i missing something else?

Many thanks in advance.

 

[GregLocock]

I suggest you post the derivation of that equation, it seems to me to give a very low power estimate.

Cheers

Greg Locock


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[Txoleski]

Hi Greg,

Thanks for your reply. You're right, that formula gives low power consumption at high frequencies, that is the reason why i am not sure about that.

I will try to explain the way i got it:

Assuming that the displacement is sinusoidal

x=X*Sin(w*t)

(where w=2*Pi*f)

then velocity and acceleration

v=dx/dt= X*w*Cos(w*t)
a=dv/dt= -X*w^2*Sin(w*t)

In our test we must apply constant acceleration, so then the amplitude of the displacement=

a=X*w^2 => X=a/w^2

Hence, the higher the frequency the less the displacement we need to achieve a constant acceleration and less the power necessary.

The force necessary to move the structure should be F=m*a, and the mechanical work W=F*deltaX.

So then, taking root mean square values of the force and the displacement, I obtain that the Energy= 1/2* F * X and Power(Pm)= 1/2*F*X*f (F=force, f=frequency)

And expanding the equation:

Pm=1/2*m*a*X*f=1/2*m*a*(a/(w^2))*f=1/2*m*a^2/((2*Pi)^2*f)



( In case of a constant displacement is required i get other equation:

Pm=1/2*m*(X*Pi)^2*f^3 )


Am I missing something?

Many thanks in advance

 

[BrianE22]

Power = F x Vel (not 1/2 F x Vel). I get Power = ma^2/(2*pi*f).

 

[GregLocock]

The trouble is your assumptions are wrong and the actual answer could be higher or lower, by an order of magnitude.

Consider the case where you are testinga shock absorber with a mass of 2 kg and a c of say 1000 N/m/s

or a spring mass system with no damping and a steel spring.



Cheers

Greg Locock


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[Txoleski]

Thanks for your help,

That is why i consider important to do a modal analysis of the assembly. Theoretically, if the natural frequencies are far from our study range, could we avoid those effects of mass / damping?

 

[GregLocock]

That depends on the system. In my experience shaker systems for undamped structures are force limited, not power limited, and may sometimes be displacement limited, for instance at resonance.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[Txoleski]

Does it make sense to me. In fact, in the specifications of the shaker it appears the maximum force we can apply.

Thank you very much for your help.