Free vibration analysis of functionally graded nanobeams based on surface stress-driven nonlocal model

A surface stress-driven nonlocal model is employed in this manuscript to study the coupled effects of the long-range interaction and surface energy on the free vibrations of nano-beams made of metal-ceramic functionally graded material. The nanobeam theory is formulated based on the Bernoulli-Euler kinematics and surface effects include surface elasticity, surface residual stresses, surface density and rotary inertia. Hamilton's principle is applied to derive the size-dependent governing equation. The main results of a parametric investigation, carried out considering four different kinematic boundary conditions, i.e. Cantilever, Simply-Supported, Clamped-Pinned and Doubly-Clamped, are also presented and discussed, varying the nonlocal parameter and the material gradient index. The results show how the proposed model is able to capture surface energy effects on the overall dynamic behavior of functionally graded Bernoulli-Euler nanobeams and provides a cost-effective method for the design and the optimization of nano-scaled structures.