Article Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory Farzad Ebrahimi, Mohammad Reza Barati and Parisa Haghi Abstract The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nano- beam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal par- ameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc. Keywords Wave propagation, rotating nanobeam, FGM, nonlocal elasticity, Euler–Bernoulli theory 1. Introduction In recent years, nanostructures are of great interest to researchers not only because of their fundamental sci- entific richness, but also for the reason that they have the potential to handle the future critical revolutions of technologies. There has been considerable attention and interest in miniaturization of mechanical and elec- tromechanical devices. Currently, electromechanical systems reach the submillimeter or micrometer size scale. Therefore, there is intense interest in the creation and development of electromechanical and mechanical systems in the nanometer scale which are of great importance in future goals of nanotechnology. Nanomachines are systems with moving parts of nanometer scale size. Rotating nanostructures include nanoscale molecular bearings, nanogears and nanotur- bines and multiple gear systems (Robertson et al., 1994; Srivastava, 1997; Zhang et al., 2004). Appropriate information about the mechanical behavior of nanostructures, such as bending, vibration and buckling, is required for efficient design of these devices. The development of simplified models for the dynamics of complex nano-technological systems is thus necessary. This is because, for many cases, fully atomistic simulations would be computationally expen- sive and prohibitive. Because of these above-mentioned difficulties, higher order continuum theories are suggested for modeling of nanostructures. The size- dependent Eringen’s nonlocal elasticity theory, that was first introduced by Eringen in 1983, is useful in dealing with phenomena whose origins lie in organiza- tions smaller than the classical continuum models. Such nonlocal continuum mechanics have been widely accepted and have been applied to many problems con- taining wave propagation and vibration of rotating Department of Mechanical Engineering, Imam Khomeini International University, Iran Corresponding author: Farzad Ebrahimi, Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran. Email: febrahimy@eng.ikiu.ac.ir Received: 11 September 2016; accepted: 20 April 2017 Journal of Vibration and Control 1–10 ! The Author(s) 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1077546317711537 journals.sagepub.com/home/jvc