Reduced-Order Nonlinear Dynamic Analysis and Lyapunov-Based Chaos Characterization of SMA Hybrid Composite Actuator Beams Under Thermo-Aeroelastic Excitation

This study investigates the nonlinear dynamic response and chaos evolution of a shape memory alloy hybrid composite (SMAHC) actuator beam under coupled thermal, harmonic, and aerodynamic excitations. A reduced-order nonlinear dynamic model was developed by combining Euler–Bernoulli beam theory, von Karman geometric nonlinearity, the Brinson SMA constitutive relation, and first-order piston-theory aerodynamics. The governing equations were derived from Hamilton’s principle, discretized by the weighted residual method, and solved using the Newmark-beta algorithm. Chaotic evolution was quantified using a largest Lyapunov exponent-based chaos intensity indicator rather than the exact Kolmogorov–Sinai entropy. The reduced-order model was compared with ABAQUS finite element simulations under representative coupled aerodynamic and harmonic loading. The MATLAB prediction and ABAQUS response gave a dominant frequency of approximately 9.50 Hz, close to the prescribed excitation frequency of 9.55 Hz, with peak displacement amplitudes of approximately 0.0285 mm and 0.0324 mm, respectively. A supplementary ABAQUS modal-frequency separation check supported the use of the two-mode reduced-order model for the dominant low-frequency response, while also clarifying its limitation for high-dimensional chaotic modal interactions. The parametric results showed that an increasing excitation amplitude and aerodynamic load promoted frequency broadening and chaotic transitions. The Lyapunov-based indicator rose near γ = 65 under λ* = 100 and near λ* = 328 under γ = 30. Temperature-dependent SMA recovery stress further shifted the transition threshold by modifying the effective stiffness and internal restoring action of the beam. These results provide a reduced-order framework for interpreting nonlinear response transitions in SMAHC actuator beams in thermo-aeroelastic environments.