The Single-Degree-of-Freedom System

The easiest example to describe a vibrating system is a single-degree-of-freedom system (SDOF System). An inert mass is on a rigid base, separated by an elastic element.

The machine (= mass) is decoupled from its ambient area by way of a spring and a damper. Only one degree of freedom is applied and usually only the vertical movement is considered.

The special elastomers Regupol® and Regufoam® simultaneously serve as spring and damper.

The model is quite useful in explaining basic issues of vibration isolation and is helpful in selecting suitable elastomers.

The model can be applied to active as well as passive isolation jobs. A distinction is made between the time-dependent force and the kinematic excitation (auxiliary excitation) of the vibrator.

Equation of motion of the auxiliary-excited vibrator

The Single-Degree-of-Freedom System BSW Berleburger Schaumstoffwerk GmbH

Equation of motion of the force-excited vibrator

The Single-Degree-of-Freedom System BSW Berleburger Schaumstoffwerk GmbH
Graphic Active Isolation
Force excitation for the vibration isolation of machines – active isolation.
Graphic Passive Isolation
Kinematic or auxiliary excitation for the vibration isolation of equipment – passive isolation.

F(t) is the time-dependent force excitation and s(t) the timedependent kinematic excitation / auxiliary excitation. The coordinate x describes the movement of the vibrator, whose parameters mass, damping and rigidity are designated as m, b and c.