Oscillations in a nonlinear spring mechanism with one degree of freedom

Abstract

A new method for studying dynamics in a nonlinear spring- loaded mechanism is described, which consists in describing a spring as an elastic solid rod with conditional density and elastic modulus. When studying vibrations in such a rod, instead of the well-known second-order differential equation, two derived first-order equations are used that relate the acceleration and gradient of speed to the velocity and gradient of the change in the voltage of the particles of a given body. The frequency characteristic of the linear mechanism is given. The behavior of the mechanism in the presence of significant nonlinearity is considered. The self-oscillation parameters are determined that make it possible to estimate the design life.