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Dynamic analysis of rotating double‐tapered cantilever Timoshenko nano‐beam using the nonlocal strain gradient theory
Author(s) -
Li Yongqiang,
Li Meng
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6616
Subject(s) - cantilever , timoshenko beam theory , vibration , nyström method , angular velocity , discretization , nonlinear system , beam (structure) , mathematics , equations of motion , hamilton's principle , physics , classical mechanics , mechanics , mathematical analysis , materials science , optics , integral equation , acoustics , composite material , quantum mechanics
Based on the nonlocal strain gradient theory, the coupling nonlinear dynamic equations of a rotating double‐tapered cantilever Timoshenko nano‐beam are derived using the Hamilton principle. The equation of motion is discretized via the differential quadrature method. The effects of the angular velocity, nonlocal parameter, slenderness ratio, cross‐section parameter, and taper ratios are examined and discussed. It is shown that taper ratios and cross‐section parameter play a significant role in the vibration response of a rotating cantilever nano‐beam. Further as rotational angular velocity increases, the taper ratios and cross‐section parameter effect on the frequency response are increased for first modes of vibration.