Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams.

This paper employs a surface stress-driven nonlocal theory to investigate the synergistic impact of long-range interaction and surface energy on higher vibration modes of Bernoulli-Euler nanobeams made of functionally graded material. It takes into account surface effects such as the surface modulus of elasticity, residual surface stresses, surface density, and rotary inertia. The governing equation is derived through the application of Hamilton's principle.

Application of the Higher-Order Hamilton Approach to the Nonlinear Free Vibrations Analysis of Porous FG Nano-Beams in a Hygrothermal Environment Based on a Local/Nonlocal Stress Gradient Model of Elasticity.

Nonlinear transverse free vibrations of porous functionally-graded (FG) Bernoulli-Euler nanobeams in hygrothermal environments through the local/nonlocal stress gradient theory of elasticity were studied. By using the Galerkin method, the governing equations were reduced to a nonlinear ordinary differential equation. The closed form analytical solution of the nonlinear natural flexural frequency was then established using the higher-order Hamiltonian approach to nonlinear oscillators.

Dynamic Response of Multilayered Polymer Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) Nano-Beams in Hygro-Thermal Environment.

This work studies the dynamic response of Bernoulli-Euler multilayered polymer functionally graded carbon nanotubes-reinforced composite nano-beams subjected to hygro-thermal environments. The governing equations were derived by employing Hamilton's principle on the basis of the local/nonlocal stress gradient theory of elasticity (L/NStressG). A Wolfram language code in Mathematica was written to carry out a parametric investigation on the influence of different parameters on their dynamic response, such as the nonlocal parameter, the gradient length parameter, the mixture parameter and the hygro-thermal loadings and the total volume fraction of CNTs for different functionally graded distribution schemes.

Hygro-Thermal Vibrations of Porous FG Nano-Beams Based on Local/Nonlocal Stress Gradient Theory of Elasticity.

In this manuscript the dynamic response of porous functionally-graded (FG) Bernoulli-Euler nano-beams subjected to hygro-thermal environments is investigated by the local/nonlocal stress gradient theory of elasticity. In particular, the influence of several parameters on both the thermo-elastic material properties and the structural response of the FG nano-beams, such as material gradient index, porosity volume fraction, nonlocal parameter, gradient length parameter, and mixture parameter is examined. It is shown how the proposed approach is able to capture the dynamic behavior of porous functionally graded Bernoulli-Euler nano-beams under hygro-thermal loads and leads to well-posed structural problems of nano-mechanics.