Nonlinear natural frequencies of an elastically restrained tapered beam

This paper presents the results of an analysis of an elastically restrained tapered cantilever beam using the harmonic balance and the time transformation methods. The results of the analysis show that the frequencies obtained from a two-term harmonic balance analysis are the most accurate and that the frequencies of the first and second modes of vibration change from a hardening mode (i.e. the frequency increases as the vibration amplitude increases) to a softening mode (i.e. the frequency decreases as the vibration amplitude increases) as the taper ratio of the beam is increased. The third mode is always softening regardless of the taper ratio.