The Effect of Static Deflection on the Harmonic Resonance of a System with a Hardening Non-Linear Spring

Abstract

In a vibrating system with a non-linear restoring force the effect of gravity, if it influences the equilibrium of motion, is not completely balanced by the static deflection force. This produces in most cases an increase of the magnitude of non-linearity because of the displacement of the static equilibrium point on the restoring force characteristic. The static deflection parameter thus offers a more complete definition of this effect and is consequently used in the vibration equation in preference to the force of gravity. Previous investigation of the free vibration indicates that the existence of a static deflection must result in considerable changes of the forced vibration response.