Computational modeling of surface energy effects on linear and nonlinear frequencies in different crystalline orientations of anodic aluminum micro-beams.

In this paper, the influence of surface energy (SE) on the linear and nonlinear frequencies of anodic aluminum micro beams with [100] and [111] crystalline orientations resting on an elastic substrate are analyzed based on the Timoshenko beam (TB) and Euler-Bernoulli (EB) models, spanning Nano- to micro-scale dimensions. Given the high ratio of surface-to-volume the studied micro beams, the proposed model incorporates SE effects. To extract the micro beam frequencies, the governing the Galerkin method with trigonometric and polynomial shape functions corresponding to clamped-clamped, clamped-simply supported, and simply supported boundary conditions are used. By assuming a harmonic temporal response, the natural frequencies are derived. The study examines the influence of crystalline orientation ([100] and [111]), beam length, elastic substrate coefficient, moment of inertia, and shear deformation (via the TB) under various boundary conditions on the nonlinear and linear frequencies of the micro Timoshenko beam models and Euler-Bernoulli. A comparative analysis reveals that the EB yields higher estimates for both linear and nonlinear frequencies compared to the TB, which accounts for rotational inertia and shear deformation effects. Furthermore, the results demonstrate that crystalline orientation significantly impacts the linear and nonlinear frequencies. Specifically, the anodic aluminum microbe am with [111] crystalline orientation exhibits higher linear and nonlinear frequencies due to its greater stiffness compared to the [100] orientation.