# Modeling a mass hanging by a spring: motion in 3D time/freq domain

• Gunjan
In summary, Gunjan is trying to model an object hanging from a shell using a spring system. He wants to account for the movement of the shell and the platform. He has yet to post a figure, so we cannot answer his questions.

#### Gunjan

Hello everyone,

I am new here, and wondering if anyone would have some knowledge on a current problem I have been working on. I am trying to create time- and frequency domain 3D models of an object hanging using a spring from a fixed point within a shell. I am trying to figure out how the vibration of the shell would affect the object inside after the energy transfer through the spring. I would assume multibody-dynamics is the way to go but any input would be highly appreciated.

Thanks!

Here at PF, we really like concrete questions with complete problem statements. Good for you too, because your model will need to be complete before it does anything useful.

In this case it's nice to know more about the shell: it it spherical? Rigid? Floating in water, free to move on a flat surface without friction ? etc. etc.

I think you can get pretty far considering this as a two body problem with Newton equations.

Hello there,

Thanks for your reply. I will try to be a bit more specific here.

My target model will be an elliptical shell attached with a trapezoidal prism platform by a number of spring/dampers. The idea will be to model the movement of the platform in all three directions (x, y, z) as a function of time for different spring length, constant, damping coeff and locations where the spring is connecting the platform to the shell, for an external force that will be acting on the shell.

By doing this I should also be able to calculate the amplitude and frequency transfer from the shell to the platform via the spring system.

Gunjan said:
I am trying to create time- and frequency domain 3D models of an object hanging using a spring from a fixed point within a shell.
Welcome to the PF.

What experience do you have with modeling like this? Have you worked on numerical modeling problems in the past? If so, what tools did you use? If you coded them up yourself, what language(s) did you program in?

You mention in your Profile that you have a PhD. What area is it in, and what was your dissertation? Just curious -- knowing your background should help us to get you going in the right direction.

Have you worked on modeling simpler systems in the past? If so, what kind of systems? Have you looked at modeling slightly more constrained 3-D systems like vehicle suspensions?

https://arrow.dit.ie/cgi/viewcontent.cgi?article=1018&context=engscheleart

http://www.scielo.br/img/revistas/jbsmse/v30n1/fig01.jpg

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Gunjan
Thank you for your input. My background is in modeling but mostly in the fluid dynamics domain. I have used Fortran programming during the earlier years but switched to Comsol software afterwards.

I have indeed looked at the suspension model, which I believe is also an example model in Comsol. This one and also the other for washing machine were a couple of good examples I think for the problem I am looking at.

Thanks again.

berkeman
Do you want to model the shell as a flexible body or as a rigid body? This makes quite a bit of difference.

Also, will your input motion be constant in direction, or will it vary?

Sorry I should have added. Both the shell and the platform will act as rigid body. Input motion will be constant but to model different input motions I can always run multiple simulations for this particular case.

We still need further clarification. How many degrees of freedom do you want to model for the platform? If the shell is not elastically supported, is this any different from the classic problem of a pendulum on a moving support? Seems like that is what you have here, unless I've missed something.

At the moment I would go for 6 DOF. Roll, pitch, heave and yaw for platform and two spring/damper that will make the platform hang from the outer shell. My degrees of freedom could go up if connect more attachments between the platform and the shell in future. This could very well be analogous to a classic pendulum problem as you mention.

Sorry I would add 2 more DOF to the platform for its sway motion along x and y-directions.

Gunjan said:
My degrees of freedom could go up if connect more attachments between the platform and the shell in future.

This suggests confusion about DOF. Attachments (springs, dampers) do not add DOF. The number of DOF depends on the number of coordinates required to describe the state of the mass.

Since you have yet to post a figure, I suspect we are wasting our time trying to answer.

I have thought about it a bit further and in this system there will only b total 6 DOF (3 translational and 3 rotational). In this preliminary diagram I just have the initial 2 spring/dampers attached to the platform that is free to swing in any direction. The points where the springs connect the shell to platform are fixed. Both shell and platform are rigid bodies.

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So, you have several steps to work through:
1) Decide how you will describe the angular degrees of freedom (what kind of coordinates you will use);
2) Work through the system kinematics with that choice;
3) Write the kinetic & potential energy functions and the generalized nonconservative virtual work;
4) Apply Hamilton's Principle.
Bingo! the result.

Thanks for the steps Dr. D. This sounds like a good solution analytically for sure. I was wondering if I could get an advice on doing this numerically with the commercial software Comsol. I would think the current physics would be similar to that of a spherical pendulum motion or vehicle suspension (as stated above). If that is the case, I might be able to create a numerical model for my system in a similar manner.

I know nothing of that particular software, so I cannot speak that. I have to ask, however, why you would want to develop a model tied to a particular software in preference to an analytical model that can be implemented in any computer language?

This is just a side project, and that is why I was trying to do it with the software. Also faster I can get the result, better it is. Where again that software would come handy. On the other hand I am not a pro computer programmer either.

Gunjan said:
I have thought about it a bit further and in this system there will only b total 6 DOF (3 translational and 3 rotational). In this preliminary diagram I just have the initial 2 spring/dampers attached to the platform that is free to swing in any direction. The points where the springs connect the shell to platform are fixed. Both shell and platform are rigid bodies.
are we still talking about the
Gunjan said:
object hanging using a spring from a fixed point within a shell

I have been trying to find out ways to model it with that software. It almost seems like something that would be similar to a spherical spring pendulum problem but having trouble defining the length of the spring. I would think the length could be an important parameter when comes to displacement in 3-dimensions.