Analytical Solution of the Differential Equation of Forced Oscillations of a Vibration Protection System With a Piecewise Linear Static Force Characteristic Under Harmonic Kinematic Excitation of Base Displacements

Abstract

The need to protect operators of mobile machines from vibrations determines the relevance of the development of mathematical models for studying the dynamic processes of forced vibrations of the vibration-protected mass of the seat with the operator. Analytical solutions have the advantage of being the most accurate. For the design scheme of a vibration protection system with one degree of freedom in the form of a linear oscillator with kinematic excitation, an analytical solution to the problem of forced harmonic oscillations was obtained for the given values of the parameters: the initial absolute displacements and speed of the vibration-protected mass, the initial phase of the given harmonic oscillations of the seat base. At the same time, the expression of the static power characteristic of the vibration protection system was a straight line with a vertical displacement, which made it possible to break the transient process into separate time intervals, within which the local coordinate, showing the deformation of the vibration protection mechanism, is within a separate rectilinear segment of the piecewise linear static characteristic. The results of the comparative analysis showed a significant discrepancy between the piecewise analytical solution and the solution obtained by the numerical integration method.