Dynamic stability analysis of functionally graded Euler-Bernoulli nanobeams under a sequence of moving nanoparticle based on nonlocal elasticity theory

Document Type : English


1 Mechanical Engineering group, Pardis College, Isfahan University of Technology, Isfahan 84156-83111, Iran

2 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, 84175-119, Iran


This study investigates the dynamic stability of the Euler-Bernoulli functionally graded (FGM) nanobeam based on the nonlocal elasticity theory while considering surface effects. Nanoparticles pass over nanobeam sequentially with a constant velocity, and the nanoparticle inertia is also considered. A thermal gradient with constant temperature changes is applied to this nanobeam. The functionally graded nanobeam properties, including Young’s modulus, density, surface residual stress, and surface modulus are taken by the power law. The classical equations of motion are obtained by applying the Hamilton’s principle according to the energy method. The governing equations are extracted using nonlocal elasticity theory, and the surface effects are taken by Gurtin-Murdoch theory. The dynamic stability graphs will be presented on nanoparticle mass-velocity coordinates. This article investigated the small scale effect parameter, temperature changes, Pasternak environment shearing and elastic constants, and the volume fraction parameter in power law. The results show that increasing Pasternak foundation constants increase the functionally graded nanobeam stability, and increasing small scale parameter reduces its stability. Increasing nanobeam temperature shifts the functionally graded stability region of nanobeam towards faster nanoparticle velocity, which indicates a higher dynamic stability for the nanobeam.