Hi

I am afraid that I do not  understand your question. Can you please try stating it differently?

The below are some guesses on my part. I hope some of them is what you are asking about.

If your interest is general vibration isolation, I have a small introduction covering some things you usually do not find in textbooks written here http://qringtech.com/2014/01/28/need-to-know-about-vibration-isolation/

If your question is why some manufacturers use isolator springs with non-linear  properties and/or multi-state configurations, it can be because e.g. a weak spring is what you need at idling (vehicle standing still with no load) and a stiff spring is required at full throttle (maximum acceleration) or e.g. the engine may hit the car body.

Some isolator elements are semi-active, i.e. have electronic ports that open/close to modify its properties. The element properties can be linear or non-linear per 'state', depending on what your want.

Non-linear properties like progressive stiffness can be used also to modify the Noise Vibration Harshness (NVH) character of a vehicle, i.e. you may want a smooth ride at constant speed cruise (=weaker spring) and a more aggressive sound at active driving (=stiffer spring at higher load).

On top of this, you find active elements that can be powered to generate its own force to cancel unwanted sound/vibration.

Please note that people more skilled than me on the automotive application can make the list of why:s much, much longer than I am able to.

In short, you tweak your system to do what you want and a non-linear isolator elements brings more design options in a single component. Space is difficult to get in modern vehicles, which is also an important reason to have more functions per component.

Hope this helps

Claes

Increase the damping

Hello, Salah,

There are two points that I'd like to state in my answer. The first one is that, no matter how hard you try, you will always end up with a weakly or strongly nonlinear system. Linearization is a simplification that, when well applied, leads to a model that represents well the motion of the system under investigation, given that all the displacements are small enough. The great advantage of performing such simplification is that it leads to equations that we already know how to solve.

The second point is that, for different operating regimes, sometimes it is desirable to have different values for the same component. In many applications, it is usual to find springs that have low stiffness for lower deflections and higher stiffness for higher deflections. It happens because when these springs are not deflected, this kind of system is actually "idling", and lower stiffness helps to reduce the transmission of vibration in this situation. When such system is "working", then the spring is deflected, and higher stiffness increases the transmission of efforts without the need for a large deformation.

Therefore, sometimes the nonlinearities are accidental, while in other cases it is there for a very specific reason.

Best wishes,

Vinícius

Yes, the question is unclear. I think Dr. Claes Richard Fredö has kindly rephrased the question in several possible permutations and provided good answers.   

Hi

I advice you see these documents. You will find what you need.

Best regards

https://engineering.purdue.edu/FEND2/student_resources/MSME_Thesis_TF.pdf

http://www.eng.ox.ac.uk/civil/publications/theses/neild.pdf