Numerical analysis of fractional nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass

This paper focuses on the numerical investigation of the fractional nonlinear oscillator for a restrained cantilever beam with an intermediate lumped mass. A numerical approach based upon the fractional complex transformation and the global residue harmonic balance method (FCT-GRHBM) is suggested for approximately solving this fractional oscillation system of fifth-order nonlinearity. The approximated fractional periodic solutions and frequencies are provided by FCT-GRHBM, which are not touched in the existing literature. Numerical results and sensitive analysis with respect to different parameters are shown to confirm its efficiency.