Surface effects on resonance frequencies of axially functionally graded Timoshenko nanocantilevers with attached nanoparticle

Free vibration analysis of functionally graded nanocantilevers carrying a nanoparticle is made. Due to nanoscale beams, the Timoshenko beam theory incorporating surface effects is used. An emphasis is placed on the effect of the mass and rotational inertia of the nanoparticle and the gradient index on the resonance frequencies for nanowires made of functionally graded materials. The initial value method of a system of ordinary differential equations is developed to determine the resonance frequencies. The resonance frequencies of functionally graded nanocantilevers with attached mass are calculated for various indices. The method's effectiveness is verified by comparing our results with previous ones for special cases. Numerical results shed light on the influences of the surface effects, attached mass and its rotational inertia, and gradient index on the resonance frequencies.