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.
KlotterK.‘Non-linear vibration problems treated by the averaging method of W. Ritz: Part I, Fundamentals of the method’, Technical Report No. 17/1, 1951 (Stanford University).
3.
KlotterK.‘Non-linear vibration problems treated by the averaging method of W. Ritz: Part II, Single degree of freedom systems: Single term approximations’, Technical Report No. 17/II, 1951 (Stanford University).
4.
KlotterK.PloughJ. A.‘Non-linear vibration problems treated by the averaging method of W. Ritz: Part III, Single degree of freedom systems: Non-odd restoring forces—Two term approximations’, Technical Report No. 17/III, 1952 (Stanford University).
5.
BurgessJ. C.‘Harmonic, superharmonic and subharmonic response for single degree of freedom systems of the duffing type’, Technical Report No. 27, 1954 (Stanford University).
