Frequency–time domain method for an unrestrained aeroservoelastic system with actuator nonlinearities

The frequency–time domain method is an intriguing tool for analyzing nonlinear aeroelastic systems. However, the applications for closed-loop systems with actuator nonlinearities are challenging to implement; existing procedures require variable augmentation associated with control systems, which complicates the dynamic equations. To address these issues, this paper describes modifications to reconstruct nonlinear closed-loop systems. Nonlinear elements are disconnected at specific locations, whereas the remaining components are reorganized as frequency-domain blocks to obtain linear and impulse responses. Subsequently, a convolution integral is applied in the time domain to introduce the effects of nonlinearities into the outputs of nonlinear actuators. This hybrid frequency–time domain framework exhibits responses with various nonlinearities, leveraging both the frequency- and time-domain characteristics. Based on an unrestrained airfoil section, a closed-loop system with freeplay and actuator saturation is provided as a numerical example. Linear and nonlinear time responses induced by external excitation and initial conditions are calculated, validating the feasibility and accuracy of the proposed method. Furthermore, nonlinear frequency responses are directly obtained without additional operations. Notably, the proposed method enables efficient computations, reducing the computational time by an order of magnitude. This advantage scales effectively for advanced applications, for instance, uncertainty analysis. The introduction of unsteady aerodynamics is explored in the frequency domain to circumvent conventional approximation techniques, extending the applications of the frequency–time domain method.