Nonlocal dynamic stability analysis of a Timoshenko nanobeam subjected to a sequence of moving nanoparticles considering surface effects

Abstract

In this study, the dynamic stability of a Timoshenko nanobeam under the intermittent movement of nanoparticles is investigated considering surface effects. Simply-supported boundary conditions are assumed for a rectangular cross-section beam. The elastic foundation is modeled as a Pasternak elastic foundation. Also, the role of the nanoparticle inertia is considered. The nanoparticles move over the beam continuously with a constant velocity, and the friction between particles, and the beam is ignored. Governing equations are derived by Hamilton's principle in conjunction with nonlocal and Gurtin-Murdoch theories. Dynamic stability analysis of the nanobeam under induced excitation of moving nanoparticles is carried out, and the stability and instability regions are derived by incremental harmonic balance method (IHBM). The stability of the system is described in the plane (mass-velocity). A detailed study is conducted to examine the effects of various parameters such as the small scale parameter, surface constants, Pasternak foundation coefficients, and nanoparticles inertia on the dynamic instability region (DIR) of the nanobeam. The results show that considering surface theory has a negligible effect on the DIR of the nanobeam under the intermittent passage of nanoparticles. Pasternak and Winkler spring constants increase the stiffness and stability of the nanobeam. Also, considering moving mass inertia and small scale parameter shifts the DIR to the lower frequency zone.