Comparative Study on Post-Buckling Nonlinear Dynamics of Thin-Walled Structures with Different Geometries Under Thermo-Acoustic Loads

The nonlinear dynamic response of aerospace thin-walled structures in a post-buckling state under thermo-acoustic loads is critical for their design. This study investigates this phenomenon through integrated experimental and numerical approaches. Acoustic tests on thermally stressed flat plates yielded results in close agreement with finite element and reduced-order modal (FEM/ROM) simulations, with first-order frequency deviations within ±2 Hz and strain values of the same order of magnitude (10.7 µε vs. 9.5 µε at 50 °C). A key observation is the non-monotonic variation in the thermal modal frequency, which initially decreases then increases with the buckling coefficient, while dynamic strain data further validate the computational model. Comparative analysis of three Haynes 188 alloy geometries—flat plates, cylindrical shells, and spherical shells—reveals distinct behaviors rooted in their critical buckling temperatures (68.46 °C, 151.20 °C, and 698.28 °C, respectively): flat plates exhibit softening–hardening transitions with a frequency range of 491–624 Hz; cylindrical shells show irregular responses with a dramatic frequency drop from 1120 Hz to 360 Hz; and spherical shells maintain the highest stability and frequency range (1913–2109 Hz), governed by the buckling coefficient’s linear effect. Time-domain and probability density function (PDF) analyses elucidate the snap-through phenomena and the modulating roles of the buckling coefficient and sound pressure level (SPL). These findings underscore that geometric configuration and inherent stiffness are critical to post-buckling performance, providing a theoretical basis for designing aerospace components in extreme environments.