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

Abstract

This manuscript employs a surface stress-driven nonlocal model to explore the combined effects of long-range interaction and surface energy on higher vibration modes of functionally graded nanobeams. The nanobeam theory, based on Bernoulli-Euler kinematics, incorporates surface effects such as surface elasticity, surface residual stresses, surface density, and rotary inertia. Hamilton's principle is applied to derive the governing equation with size-dependent considerations. The main outcomes of a parametric investigation, considering four different kinematic boundary conditions (Cantilever, Simply-Supported, Clamped-Pinned, and Doubly-Clamped) while varying the nonlocal parameter and material gradient index, are presented and discussed. Additionally, the normalized natural frequencies for the second, third, fourth and fifth modes of vibrations are provided and analyzed for each case under study. The results underscore the model's effectiveness in capturing surface energy effects on the overall dynamic behavior of functionally graded Bernoulli-Euler nanobeams, offering a cost-effective approach for designing and optimizing nano-scaled structures.