Flapwise Bending Vibration Analysis of a Double Tapered Rotating Nonlocal Euler–BernoullI Beam by the Differential Transform Method
I. Kurt1, M. O. Kaya2
1Yildiz Technical University, Istanbul, Yildiz , 34349, Turkey
2Istanbul Technical University, Istanbul, Maslak, 34469, Turkey
Keywords: нелокальная теория упругости, конусообразная балка, балка Эйлера - Бернулли, метод дифференциального преобразования, свободные колебания, nonlocal elasticity theory, tapered beam, Euler-Bernoulli beam theory, differential transform method, free vibration analysis
Abstract
Transverse (out-of-plane) vibrations of a rotating nanobeam tapered both in width and thickness are studied on the basis on the Euler-Bernoulli beam theory. The nonuniform nanobeam is modeled with allowance for a small-scale effect contained in the nonlocal Eringen elasticity theory. The axial force due to rotating movement (centrifugal stiffening) of the beam is included into the model. The governing partial differential equation of the structure is solved by implementing the differential transform method (DTM). The variations of the taper ratio, rotational velocity, hub radius, and nonlocal small-scale parameter are taken into consideration. Comparisons of the present results with available data are performed.
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