Study of the antivibration suspended seat oscillations with quasi-zero stiffness effect under sinusoidal excitation

The relevant task of reducing the vibrations transmitted to a human operator of a construction or road vehicle during operating process is accomplished, among other things, by conducting the research on mathematical models. Oscillations simulation of the human operator's seat antivibration suspension by means of the numerical solution of the ordinary differential equations system remains one of the main methods of the study, used in particular for the discrete mathematical models verification. Therefore, the problem of determining the rational value of the maximum integration step by using the numerical method in solving the systems of the ordinary differential equations describing the operator's anti-vibration suspended seat oscillations is relevant. A discrete mathematical model of a human operator's seat performing the forced vertical oscillations during kinematic excitation of base movements was developed through the use of the differential equation of the translational oscillations of mass on a movable base. The prescribed displacements of the seat base are described by the harmonic oscillation equation. The numerical solution of the ordinary differential equations system is carried out via the built-in ode45 function of the MATLAB mathematical modeling system. Moreover, the parameters of the developed mathematical model are described, the calculation scheme and an example of a static force characteristic including the quasi-zero stiffness region in the middle section of the characteristic are given. The determination accuracy of the maximum acceleration of the seat in the steady-state oscillation mode is shown to decrease when the value of the maximum allowable integration step increases. It is recommended to limit the value of the maximum allowable integration step to one hundredth of a second. Besides, the effect of the values duality of the maximum acceleration and maximum internal movement of the seat relative to its own base with small changes in the base displacement amplitude, which must be taken into account in modeling, is also revealed. (paper)