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# Step Response: Modeling a Dynamic System with Rubber Isolators

## Step Response: Modeling a Dynamic System with Rubber Isolators

(OP)
Hello everyone. I am familiar with simple mechanical system modeling using springs and dashpots, like below photos, in a transfer function:

...but can anyone point me in the correct direction for modeling this system with a rubber isolator?
I cannot simply model isolators as springs/dashpots because polymer materials like rubber are nonlinear in compression/tension and have varying properties based on different frequencies.
What is a common technique to predict response of an isolator based on geometry and composition?

I'm basically looking for some book recommendations or input on where to start researching.

Thanks!

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

for non linear systems numerical simulation is common.

convert the system to standard form x'=f(x) where x is a vector of state variables. solve using your favorite method like rkc45.

=====================================
(2B)+(2B)' ?

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

(OP)
Can you elaborate on that? I'm not sure I follow.

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

I don't know how complex your structure is......but SAP2000, can do a non-linear, time-history analysis.

There are a variety of methods out there. Mario Paz's book on structural dynamics is a good resource for that.

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

So you need a book on modelling rubber-like materials in FEA? That's a fairly gnarly subject, you'll find that the geometry of the rubber affects its dynamic response, not just the composition of the material.

Not being a polymer FEA-er I don't have any books. The first paper to come to light is https://iopscience.iop.org/article/10.1088/1757-89...

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

(OP)

#### Quote (GregLocock)

So you need a book on modelling rubber-like materials in FEA? That's a fairly gnarly subject, you'll find that the geometry of the rubber affects its dynamic response, not just the composition of the material.

Not being a polymer FEA-er I don't have any books. The first paper to come to light is https://iopscience.iop.org/article/10.1088/1757-89...

Not necessarily FEA, but manual methods. I think my question should be "how to I correctly model a non-linear spring in a mechanical model" such as in my first post.

Where do I begin? Do I pick a known load and work around that point and take an average between the loading and unloading curves? Taylor series expansion? etc.
basic goal: matlab plot of response of a mass on the end of a polymer isolator if given a sinusoidal forcing input.

thanks

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

#### Quote:

basic goal: matlab plot of response of a mass on the end of a polymer isolator if given a sinusoidal forcing input.

I’m not sure nonlinear (plastic) deformation is compatible/appropriate with a continuous, sinusoidal force. If it is undergoing plastic deformations, than such a force would (I think) destroy it after X number of cycles. Almost all the Structural Dynamics texts treat such a condition with a short-term loading history.

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

Don't know about "plastic deformations" per se, but rubber isolators are routinely used for nearly continuous vibration isolation, such as on car motor mounts, and platform vibration isolation.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

#### Quote:

Don't know about "plastic deformations" per se, but rubber isolators are routinely used for nearly continuous vibration isolation, such as on car motor mounts, and platform vibration isolation

Yep. And almost all the manufacturers of them give you linear, elastic spring constants for them. (And a max. load capacity to observe.)

The OP needs to make clear if we are talking a base that can be represented by a linear spring constant.....or plastic (nonlinear) one. If it's the latter......a sinusoidal force (for large number of cycles) is not appropriate.

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

(OP)
Sorry. *or a step/impulse input
I want to know how a modeled mechanical system reacts to input. That is the goal.

I agree, a continuous sinusoidal force is not appropriate in this case.

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

OP- ah ok. Well the great news is I have worked on that very problem. What frequency response does a non linear spring give in an SDOF?

The bad news is that I use numerical methods, and having done it I didn't try and derive any rules of thumb.

In this case the mass is bouncing off the spring, rather than fixed to it.

script attached, it's written for Octave, if you have riches beyond the dreams of avarice then to convert it to Matlab change endif to end.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Step Response: Modeling a Dynamic System with Rubber Isolators

Folks,

I have been designing elastomer mountinga, and vibration control for some time, and there is a purpose designed calculation tool, free to use, which will help you out.

ISOMAG 2 is designed to carry out rigid body analysis of rubber mounted systems, and was originally developed through a research programme funded by the German government. It is an updated version of the original isomag code, which was released around 2004.
I have used this to design everything from simple passive isolation systems through to automotive engine mounting systems.
It is seems to have a good damping model, and I have always found the results to be accurate. It allows you to construct a system , apply various forms of excitation and measure system respone in both time and frequency domains

It can be found here, together with the user guide.

It is free for both private and commercial use.

BTW, it is used by most AVM manufacturers for system design.

I hope this helps

Tom

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