On a superposition method for the approximate determination of the eigenfrequencies of nonlinear conservative oscillators

Abstract Recently, Hu [A note on the frequency of nonlinear conservative oscillators, Journal of Sound and Vibration 286 (2005) 653–662] presented a superposition method for the approximate determination of frequencies of conservative oscillators when the nonlinear restoring force consists of a superposition of several individual characteristics. In this contribution, it is shown that the conjecture of Hu is not true in general, particularly for underlinear systems. Only for overlinear systems are there plausible reasons for the validity of the conjecture, but even for this case one has to use caution.