Fredholm transformation approach to nonlocal flapwise-bending vibration of rotating tapered Rayleigh nanobeams

In this paper, a new Fredholm transformation approach is presented for flapwise-bending vibration analysis of nano-beams. The size-dependent effects are investigated using Eringen non-local elasticity theory. Also, using Rayleigh theory, the rotatory inertia effect on the flapwise vibration of beam is investigated. The novelty of presented approach is a new introduced change of variable that makes the process of solution simpler and shorter. In this paper, the bending moment acting on the cross section of beam, instead of mode shape function, is approximated using a power series. This idea converts the governing equation of motion into a simpler and shorter solvable one. The accuracy of presented approach is verified using comparison of obtained numerical results with those are available in the other published references.