Small scale and spin effects on free transverse vibration of size-dependent nano-scale beams

  • M. R. Ilkhani
  • R. NazemnezhadEmail author
  • Sh. Hosseini-Hashemi
Technical Paper


This study aims to investigate the transverse vibration of size-dependent nano-beam which spins about its longitudinal axis. To this end, nano-beams are modeled based on the Euler–Bernoulli and Timoshenko theories. To consider the size dependency of the nano-beams, the nonlocal elasticity theory is used. By using an exact analytical solution, the governing equations of motions are solved. Comprehensive results are presented to show the effects of various boundary conditions, nonlocal scale parameter, rotational speed, and geometrical parameters on natural frequencies and critical speeds of spinning nano-beam. As spinning nano-beams are the main part of any rotary nano-machines, conclusions of present analysis promote researcher’s information about the vibrational behavior of spinning nano-beams.


Free vibration Rotating nano-beam Spinning nano-beam Nonlocal elasticity Critical speed 



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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Composite group, Engineering DepartmentThe University of Nottingham, University ParkNottinghamUK
  2. 2.School of EngineeringDamghan UniversityDamghanIran
  3. 3.Impact Research Laboratory, Department of Mechanical EngineeringIran University of Science and TechnologyTehranIran
  4. 4.Center of Excellence in Railway TransportationIran University of Science and TechnologyTehranIran

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