Panels of hypersonic vehicles, operating in a force-thermal-acoustic load environment subjected to external stochastic perturbations, exhibit complex nonlinear aeroelastic vibrations reducing the dynamic reliability. The equations of motion under the interaction of aerodynamic pressure and thermoacoustic loads are established based on von-Karman theory. Particularly, the model considers both the temperature variation and its rate of change, assuming a linear temperature evolution over time with two forms. For the rate-dependent thermoacoustic loads, the magnitude and the rate both have a large impact on the dynamic behavior. Rate-dependent regime switching of the transient response is analyzed using recurrence plots, and rate-dependent stochastic switching is detected by contour plots. Finally, the responses-based time-dependent reliability is defined and analyzed. Results from the dynamic reliability region show that the reliability decreases earlier and recovers later under the influence of the rate. This work clarifies the mechanism of rate-dependent thermoacoustic loads and provides guidance for the structural design of hypersonic vehicles.
GUO et al. (2026) studied this question.