Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in model, their behaviors analyzed considering symmetry The model considered longitudinal–transverse simple supported Euler–Bernoulli beam, which accounted for von Kármán geometric nonlinearity, including first-order strain–displacement relationship. FG was made mixture metals ceramics, while volume fraction varied terms thickness when power law function used. nonlocal Eringen theory elasticity used nanobeam. governing equations associated boundary conditions gained using Hamilton’s principle. To truncate system with an infinite degree freedom, coupled discretized Galerkin–Bubnov approach. resulting nonlinear, ordinary differential equations, took into account curvature nanobeam, studied via Optimal Auxiliary Functions Method (OAFM). For this complex problem, explicit, analytical, approximate solution proposed near primary resonance. simultaneous effects following elements paper: presence curved nanobeam; transversal inertia, is not neglected paper; impact; proposes highly accurate analytical abovementioned conditions. Moreover, these conditions, local stability developed two variable expansion methods, Jacobian matrix Routh–Hurwitz criteria, global Lyapunov function.