Reducing the vibration effects on a human operator of a construction, road or handling machine is an urgent task, since the vibration loads produced by the internal combustion engine, vehicle engine interacting with the support surface microrelief, as well as the machine working attachment, adversely affect the machine operator and increase the machine parts and assemblies wear. The operator may develop occupational diseases caused by vibrations. In this regard, the research objective is to develop the mathematical apparatus simulating the dynamic processes of the passive vibration protection systems oscillations at the design stage. Therefore, the problem developing a mathematical model that makes it possible to study the oscillations of a single degree of freedom passive vibration protection systems with any given static characteristic, was solved. On the basis of the dynamic equations of a single translational degree of freedom vibration system describing the vibration protection suspended operator’s seat, the mathematical model solving the differential equation of the system oscillations taking into account the spring loaded mass displacements damping and three-segment static characteristics of the vibration isolation mechanism with limiters was simulated using the package Simulink of MATLAB system. An example of using the developed mathematical model for modelling vibrations of a spring-loaded mass under the sinusoidal external influences is given. The preset vertical displacements of the machine base, i.e. its base chassis act as the external influences. The examples of the obtained simulation results, namely the vertical displacements and accelerations of the spring-loaded mass are presented. The maximum accelerations of the spring-loaded mass were found out to significantly increase, when the machine base forced displacements amplitude exceeds by half of the horizontal section of the quasi-zero static characteristic of the vibration protection suspension.
