Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory

Abstract

In the present manuscript, based on the nonlocal strain gradient theory, a nonclassical dynamic finite element model is developed to study and analyze the dynamic behavior of perforated nanobeam structures under moving mass/load. In the context of nonclassical continuum mechanics and Timoshenko beam theory, dynamic equations of motion of perforated nanobeams are derived including both size scale (nonlocal) and microstructure (strain gradient) effects. The modification of the geometrical parameters due to the perforation process is included in the equations of motion for squared holes arranged in the arrayed form. The effect of the moving mass (the inertia, Coriolis and centripetal forces, and the gravity force) or moving load are included in the proposed model. To remove shear locking problem in slender nanobeams, finite element model on nonclassical shape function basis is developed. Elements stiffness and mass matrices and force vector including the nonlocal and strain gradient effects are derived. The proposed model is verified and checked with previous works. Impacts of perforation, mass/load velocities, inertia of mass, microstructure parameter and nonlocal size scale effects on the dynamic and vibration responses of perforated nanobeam structures have been investigated in a wide context. The following model is beneficial for the design of MEMS/NEMS structures such as frequency filters, resonators, relay switches, accelerometers, and mass flow sensors, with perforation.