Analytical analysis of the vibration protection system of a human operator

The task of mathematical description and study of vibration isolation systems for seats of mobile machine operators is relevant, since operators of many construction, road and other mobile machines are exposed to significant vibration effects. An original analytical solution was proposed for the differential equation of forced oscillations of a linear oscillator with kinematic excitation, which describes the vertical oscillations of the seat with the operator, for given sinusoidal oscillations of the seat base. Analytical differentiation in time of the expression for the absolute displacement of the vibration-protected mass of the seat with the operator made it possible to obtain an analytical expression for the absolute velocity of the mass, the simplification of which made it possible to obtain a compact expression for the first and then the zero derivative of the absolute coordinate in the steady state oscillation mode. From the expression for the absolute displacement of the vibration-protected mass using a trigonometric transformation, an analytical expression for its amplitude was obtained, from which, in turn, an analytical expression for the transmission coefficient of the vibration protection system was obtained. The equation based on the analytical expression of the derivative of the transfer coefficient with respect to the circular frequency was solved analytically, which made it possible to obtain analytical expressions for the resonant amplitude of absolute displacements and the transfer coefficient. Examples of functional dependencies obtained using the derived analytical expressions are given. The obtained analytical expressions make it possible to conduct studies of vibration protection systems of seats with maximum accuracy.