Nonlinear Aero-Thermo-Elastic Analysis of Laminated Composite Beams with Surface-Bonded FGMs Layers Subjected to a Concentrated Harmonic Load

In this study, the nonlinear forced vibration response of fiber-reinforced laminated composite beams coated with functionally graded materials (FGMs) is investigated under the combined action of aero-thermoelastic loads and a concentrated harmonic excitation. The mathematical formulation is established using the Euler–Bernoulli beam theory, where von Kármán geometric nonlinearities are taken into account, along with the modified third-order piston theory to represent aerodynamic effects. By neglecting axial inertia, the resulting set of nonlinear governing equations is simplified into a single equation. This equation is discretized through the Galerkin procedure, yielding a nonlinear ordinary differential equation. An analytical solution is, then, obtained by applying the method of multiple time scales (MTS). Furthermore, a comprehensive parametric analysis is carried out to evaluate how factors such as the power-law index, stacking sequence, temperature field, load amplitude and position, free-stream velocity, and Mach number influence both the lateral dynamic deflection and the frequency response characteristics (FRCs) of the beams, offering useful guidelines for structural design optimization.