Dynamic behavior of nanobeams under axial loads: Integral elasticity modeling and size‐dependent eigenfrequencies assessment

Abstract

In this article, eigenfrequencies of nano-beams under axial loads are assessed by making recourse to the well-posed stress-driven nonlocal model (SDM) and strain-driven two-phase local/nonlocal formulation (NstrainG) of elasticity and Bernoulli-Euler kinematics. The developed nonlocal methodology is applicable to a wide variety of nano-engineered materials, such as carbon nanotubes, and modern small-scale beam-like devices of nanotechnological interest. Eigenfrequencies calculated using SDM, are compared with NstrainG and other pertinent results in literature obtained by other nonlocal strategies. Influence of nonlocal thermoelastic effects and initial axial force (tension and compression) on dynamic responses are analyzed and discussed. Model hardening size effects from stress-driven approach is compared to model softening size effects from strain-driven two-phase local/nonlocal approach for increasing nonlocal parameters.

Deep learning framework for carbon nanotubes: Mechanical properties and modeling strategies

“…Simple mechanical models and quite complex [50,51] nonlocal formulations can be found in the literature nowadays, making various claims concerning the nonlocality of nanoscopic structures, carbon nanotubes in particular. Static [52] and dynamic [53] problems in homogeneous and composite structures [54][55][56] are addressed for both isothermal and nonisothermal environments. The nonlocal mechanics in the above works is based on the stress and strain fields in the neighborhood of a point under consideration and is also related to the size-effects in nanoscopic structures.…”

Free Vibrations of Bernoulli-Euler Nanobeams with Point Mass Interacting with Heavy Fluid Using Nonlocal Elasticity

“…The PurelySDM strategy is a special form of Nonlocal Stress Gradient (NStressG) elasticity where gradient length and mixture parameters are zero [ 14 , 15 ] and the theory involves the use of appropriate constitutive boundary conditions. The theory is an example of nonlocal approach that leads to well-posed structural problems in Nano-Mechanics.…”