Investigation of Thermally Induced Stiffness Variation and Its Aeroelastic Implications in Supersonic Flight

In this study, the influence of thermal loading in a supersonic flight environment on the mechanical stiffness of elastic structures and the corresponding aeroelastic stability limits is investigated analytically. Recognizing that elevated temperatures inherently alter constituent elastic properties, a temperature-dependent continuous elasticity framework is incorporated directly into the governing differential operators of the structural domain. The macro-mechanical behavior of representative panel- and wing-type elements is modeled utilizing the Euler–Bernoulli beam formulation, while high-speed supersonic aerodynamic effects are represented through linearized first-order piston theory. The continuous spatial displacement fields are discretized by means of a modal expansion, and the coupled aeroelastic system is subsequently transformed into a finite set of dynamic state-space equations using the Ritz–Galerkin truncation method. The numerical and analytical outputs demonstrate that aerothermal softening not only induces continuous erosion in the material stiffness but also directly modulates the aeroelastic pole trajectories, thereby prematurely contracting the safe supersonic flight envelope. The primary novelty of the proposed framework lies in the derivation of explicit analytical expressions that directly map temperature-dependent stiffness variations onto supersonic aeroelastic instability boundaries. Because this approach is formulated in a generalized analytical form, it can be applied across diverse material systems, geometric profiles, and thermal conditions with reduced computational overhead compared to full fluid–structure interaction solvers, thereby providing a theoretical basis for preliminary stability assessment of supersonic aerospace configurations operating under high-temperature conditions.