The best way to answer this question is to study the most simple hysteretic dynamic system proposed by Bouc and Wen (see, e.g., Bouc, R., ‘Forced vibrations of mechanical systems with hysteresis’, in Proceedings of the Fourth Conference on Non-Linear Oscillations, 1967, p. 315; Wen, Y. K., ‘Method of random vibration of hysteretic systems’, ASCE Journal of Engineering Mechanics 102(2), 1976, 249–263). It can be shown that the forced vibration of Boyc-Wen system is asymptotically periodic (Ikhouane, F., & Rodellar, J. (2005). On the hysteretic Bouc–Wen model. Nonlinear dynamics, 42(1), 63-78).

My experience with elastomeric vibration isolators is limited by vibration control of precision instruments, that is, small vibrations (micron and sub-micron range). Hysteresis leads to dissipation of mechanical energy (damping) that can be described in terms of complex stiffness incorporating a (rather large) loss factor. In frame of this model, the dynamic reaction includes a phase shift but stays linear, described by complex transfer functions. See more in Vibration Control for Optomechanical Systems, by V.M. Ryaboy, World Scientific, 2021, ISBN 9789811237331, pages 132-137. https://www.amazon.com/Vibration-Control-Optomechanical-Systems-Vyacheslav/dp/9811237336/ ; Book Vibration Control for Optomechanical Systems

I haven't extensive knowledge on this matter either, but I have made some rubber isolator measurements using sine sweep in an isolator test stand, while at Ingemansson (and while young and promising - currently, I am only &)

For what it is worth. The tests I refer to were made in the late 90s, so memory is vague. Therefore, read what I write with a grain of salt.

No - I cannot recall seeing any harmonics due to nonlinear effects.

However, I vividly recall not getting the same data when doing a sine sweep with/without preconditioning (warm up) of the isolator or, for that matter., with preconditioning, not getting the same result doing a sine sweep from low-to-high/high-to-low frequency.

The warm up part was expected due to the Mullins effect.

https://en.wikipedia.org/wiki/Mullins_effect

Dealing with rubber, the best model I have come across is the Bergström-Boyce model.

I have not used it myself, but the data it produces is the best I've come across.

On second order harmonics - it is a common approach when dealing with detection of damage and some non-linear effects. For such phenomena to be clear, it may require stronger stiffness variation than is the case inside of rubber where molecule chains slide and reorient. If you look at the Code Aster link, you see what I am driving at.

To venture a guess, rubber, as it is viscoelastic, may be more dependent on temperature from internal warm up than internal stiffness variation. Some rubber manufacturers told me that they even may get internal melting when fatigue testing isolators at high amplitude with sustained excitation.

As https://www.researchgate.net/profile/Vyacheslav-Ryaboy writes, the isolator properties, while in reasonably steady state operation and at low amplitude, do remain linear. Only, knowing in advance, as in designing with accuracy, said state is somewhat of an art.

Just my 2 cents.

Hope this helps

Claes

Article Bergström-Boyce model for nonlinear finite rubber viscoelast...

https://codeaster.net/spip.php?article750

As hysteresis stress strain curves are non-linear, it will lead to harmonics and other non-linear effects. It is for example one of the listed causes of non-linearity in loudspeakers (check out some work by Wolfgang Klippel). However, for vibro-acoustic applications this effect is often small, and in a loudspeaker other non-linear effects typically dominates - also in the springs, where geometrical non-linearity is more important. I would guess the situation is similar for vibration isolation.

Hi

It seems it all boils down to initial conditions and amplitude and temperature - also ambient.

Vehicle bushings in rough terrain being worse off than, say, a gen set at steady state operation without background earthquake.

For isolators, the mullins effect, ie the difference in static and dynamic stiffness is sufficienyly well known to make it onto most datasheets.

The isolator itself being a significant noise source is something I've never heard about, ie the effect likely is there but - my money is on it being a rather weak effect.

Some isolators, eg woven metal ('svinto' 'brillo' pads) are designed to provide a progressively increasing stiffness with load - to provide constant fundamental resonance frequency - like airsprings.

It is in the function principle for loudspeakers to operate at as high stroke as possible to generate sound. Its primary load is dynamic.

This is not the case for most rubber isolators as they would risk melting from heat released by internal losses. Their primary load is static. I think this matters.

/Claes