FUNCTION OF ISOLATORS
Vibration phenomena which occur mostly in the industrial field are caused by unbalanced rotating bodies of machines or by intrinsic imbalances in industrial equipment (e.g. single cylinder reciprocating machines); such phenomena can not be ignored. In order to allow the correct operation of the industrial machinery and satisfactory protection of structures and plants connected to the machinery, vibration must be reduced by operating directly on the body which causes the vibration (e.g. balancing of rotating shaft) and by isolating structures (e.g. machine housing) from the machine itself: this means that an intermediate member, positioned between the vibrating body and the structure must absorb part of the energy caused by the vibration and transmitting only a small part of this vibration: this task is performed by isolators. Isolation is extremely important in order to reduce noise in work environments, both to respond to ergonomic requirements in those environments, and to respect the ever more restrictive regulations regarding sound pollution.

VIBRATION THEORY
The study of vibration, as in many technical fields, involves the use of mathematical models which are capable of simulating physical phenomena and from these models it is possible to extract results that are applicable when resolving real problems. Questions linked to vibration phenomena where isolators are used, refer to the model in which a suspended mass M (machine) subject to a periodic exciter force (sinusoidal for simplicity) and connected to the housing (or frame) by a spring damper system which simulates the behaviour of the isolator (see figure 1)

The model is regulated by the differential equation m + c + kx = F0 sin µ t which describes the dynamic behaviour.

The goal is to understand the required dimensions of the isolator which connects the oscillating body to the support structure (which can be considered of unlimited mass) so that the amplitude of the force transmitted by the isolator is tolerable.
If the machine is directly connected to the housing , the same exciter force F0 sin twill be transmitted to the casing. If the isolator is positioned between the mass and the support, the force 
T=kx + c is transmitted to the structure where kx represents the part of the force transmitted by the spring (which represents the elastic properties of the isolator) and c that of the damper which simulates the viscous (damping) properties of the rubber.
The effectiveness of the isolator is calculated using the ratio   with T0 force as amplitude transmitted by isolator and F0 as amplitude of exciter force.
This size is the function of the damping properties of the rubber (directly linked to hardness [° Shore]- [° Shore]- is the dependence index) and the ratio between the system's exciter frequency and natural frequency [see note on natural frequency].

The trend of ,directly linked to the mathematical model that describes the system, shows that if we work in a field in which the ratio <1 we must use higher damping i.e. 60 ° Shore isolator with loads close to the acceptable maximum for dynamic loads. 
If  >2 we must use an isolator with lower damping (45-50° Shore) or a 60° Shore isolator but gradually reduce loads weighing on each element of the suspension with the increase of the exciter frequency f. The following shows how to apply these observations for autodimensioning.

NATURAL FREQUENCY
he natural frequency which is indicated by fn is a property of any system formed by a suspended mass on a spring damper system. Such a system is formed by a machine above an isolator with stiffness coefficient K. In reality, it must be considered that generally several isolators are necessary per machine, therefore the system is considered as that given by a mass equivalent to the machine's mass divided by the number of isolators used.Notwithstanding that fn is a property dependent on geometric, physical and material characteristics of the system, it is easily calculated if the weight of the machine which offloads on each isolator is known and the stiffness coefficient of the isolator is supplied by the company Ferri Renzo.Mathematical definition:

fn= Hz but as P=Kh [Kg] with h isolator arrow under the weight P then P=Mg with M mass on isolator and g gravity acceleration, then it can be written:

fn= Hz