How will this vibration system generally behave?

[Mohammad Halawa]

TL;DR

The system is a 4 springs and 1 mass on a vibrating base, the system has a low natural frequencies (the mode shapes are: 4, 4.2, 5, 5.5, 8, 11, 11.2 Hz). When excited with a random vibration like in the attached PSD curve below.

 

[berkeman]

Welcome to the PF, Mohammad.

Can you give more details about this system? Can you upload a diagram or pictures? (use the "Attach files" button in the lower left of the Edit window)

Also, is this for schoolwork?

 

[Dr.D]

Looks like you gave mode frequencies, not mode shapes, We really need a picture and some coordinates to talk about hat this will do. Is this a seismic excitation?

 

[Mohammad Halawa]

Welcome to the PF, Mohammad.

Can you give more details about this system? Can you upload a diagram or pictures? (use the "Attach files" button in the lower left of the Edit window)

Also, is this for schoolwork?

Hello berkeman,

Thanks for the welcome.

Please find the following model and other information for the problem above:

Mode shapes (pics02-07 are the modes 1-6 respectively):


Mass : 19 KG , identical springs with coefficient: 12 kN/m tension/compression (48 kN/m for the 4 springs) and 3.9 kN/m in shear (15.6 kN/m for the 4 springs), damping ratio: 0.2 , box size: 300x250x300 mm (the height is 300 mm, but it is incorrectly simulated as less, but that won't affect the frequencies of the whole box).

When the PSD curve is integrated it result in the root mean square of the input accelerations (Grms), and the Grms here is 25G.

These are some points from the PSD curve above:

Freq (Hz)	5	25	30	40	50	55	75	80	100	105	150	190	255	300	500
PSD (G^2/Hz)	0.00359	0.00359	0.0108	0.0108	0.00467	0.0072	0.0072	0.14412	0.14412	0.03242	0.03242	0.1153	0.1153	0.04323	0.009

This is not a schoolwork but a project I am working on, the product is supposed to be military tested (810F standard) and this is one of the random vibrations it will be subjected to.

I am interested in the acceleration levels that will be transferred to the product (force amplification), and since the resonant frequencies are very close together, how will that affect the resulted force amplification ? In other words how can I consider the coupling of all the frequencies to the force amplification ?

Any references will greatly help, right now I am mostly looking in:
-Mechanical Vibration by S.S. Rao
-Vibration Analysis for Electronic Equipment by Dave S.

Please let me know if you need anything else, and thank you very much for your time !

M.Halawa

 

[Mohammad Halawa]

Looks like you gave mode frequencies, not mode shapes, We really need a picture and some coordinates to talk about hat this will do. Is this a seismic excitation?

Hello Dr. D,

Thank you for considering my problem while being inaccurate (mode shapes) and missing much information.

No, this is not a seismic excitation, it's a lab testing vibration for military standard products (810F). But due to the randomness of the excitation force I think it can be considered as seismic.

Please find the following model and other information for the problem above:

Mode shapes (pics02-07 are the modes 1-6 respectively):


Mass : 19 KG , identical springs with coefficient: 12 kN/m tension/compression (48 kN/m for the 4 springs) and 3.9 kN/m in shear (15.6 kN/m for the 4 springs), damping ratio: 0.2 , box size: 300x250x300 mm (the height is 300 mm, but it is incorrectly simulated as less, but that won't affect the frequencies of the whole box).

When the PSD curve is integrated it results in the root mean square of the input accelerations (Grms), and the Grms here is 25G.

These are some points from the PSD curve above:

Freq (Hz)	5	25	30	40	50	55	75	80	100	105	150	190	255	300	500
PSD (G^2/Hz)	0.00359	0.00359	0.0108	0.0108	0.00467	0.0072	0.0072	0.14412	0.14412	0.03242	0.03242	0.1153	0.1153	0.04323	0.009

The product is supposed to be military tested (810F standard) and this is one of the random vibrations it will be subjected to.

I am interested in the acceleration levels that will be transferred to the product (force amplification), and since the resonant frequencies are very close together, how will that affect the resulted force amplification ? In other words how can I consider the coupling of all the frequencies to the force amplification ?

Any references will greatly help, right now I am mostly looking in:
-Mechanical Vibration by S.S. Rao
-Vibration Analysis for Electronic Equipment by Dave S.

Please let me know if you need anything else, and thank you very much for your time !

M.Halawa

 

[FEAnalyst]

Since you already have finite element model in SolidWorks Simulation (I recognize it from the pictures) you can also perform random vibration analysis in this software. Just apply acceleration from curve and solve to get desired results.

 

[Mohammad Halawa]

Since you already have finite element model in SolidWorks Simulation (I recognize it from the pictures) you can also perform random vibration analysis in this software. Just apply acceleration from curve and solve to get desired results.

Thank you for your input and you're absolutely right!

I will do that, but also I always try to have a theoretical verification for my simulation to make sure that my simulation inputs are sound and enough (not a simulation expert). And I am also interested in knowing how to do it that way ;)

 

[Dr.D]

(the height is 300 mm, but it is incorrectly simulated as less, but that won't affect the frequencies of the whole box).

I think you are mistaken about this not mattering. By using the incorrect height, the pitch and roll moments of inertia will be incorrect. This will affect the eigenvectors and the eigenvalues.

 

[Mohammad Halawa]

Welcome to the PF, Mohammad.

Can you give more details about this system? Can you upload a diagram or pictures? (use the "Attach files" button in the lower left of the Edit window)

Also, is this for schoolwork?

I think you are mistaken about this not mattering. By using the incorrect height, the pitch and roll moments of inertia will be incorrect. This will affect the eigenvectors and the eigenvalues.

Again you're absolutely correct, that was very foolish of me to assume otherwise, thank you for pointing it out !

I am doing a more realistic simulation now and will upload the results soon.