Effect of Static Deflection on the Natural Frequency of a System with a Hardening Non-Linear Spring

Abstract

The effect of the static deflection on the natural frequency response is investigated for a single-degree-of-freedom system with a positive cubic non-linearity in the restoring force. The Ritz averaging method is used for the theoretical analysis, and by comparison with analogue computer solutions the first approximation, consisting of two terms, is shown to be satisfactory for most applications. Results indicate that in systems with a non-linear restoring force the existence of a static deflection produces significant effects and cannot be neglected in a theorectical analysis.