Fractional nonlocal couple stress waves in magnetoelastic nanobeam using homotopy perturbation technique

Abstract

This research investigates the mechanical behavior of nanomaterials under various physical conditions by integrating fractional-order viscoelasticity, nonlocal elasticity theory, and Maxwell’s electromagnetic relations. The study aims to accurately model the viscoelastic characteristics of nanomaterials using fractional calculus, specifically the Riemann–Liouville fractional derivative, to capture internal damping effects. The nonlocal elasticity theory is employed to account for nanoscale size effects by incorporating a nonlocal parameter that describes the influence of strain at different locations on the stress experienced at a given point. The governing equations for nanobeams subjected to magnetic fields are derived using Hamilton’s principle and further simplified through nonlocal couple stress theory. To solve the resulting complex differential equations, the homotopy perturbation technique (HPT) is applied, providing approximate analytical solutions. The study considers various boundary conditions, including simply supported (S–S), clamped-simply supported (C-S), and clamped–clamped (C–C), to ensure a comprehensive understanding of structural responses. The developed model is validated, by comparing the obtained results with benchmark results, and the outcomes are tabulated to confirm the effectiveness of the approach. These findings contribute to the development of advanced nanostructures, offering valuable insights for applications in nanotechnology and material science.