INVESTIGATION OF THE INFLUENCE OF WING SWEEP ON THE CRITICAL DIVERGENCE SPEED USING THE FINITE-ELEMENT LINEAR APPROXIMATION METHOD

Oleh Havaza, Dmytro Konotop

Abstract


The subject matter of the article is this influence of wing sweep on the critical divergence speed as one of the principal indicators of the static aeroelastic stability of an aircraft lifting surface. The goal of the article is to determine the qualitative and quantitative effects of backward and forward sweep on the critical divergence speed using the finite-element linear approximation method. To achieve this, the following tasks were addressed: to construct a simplified two-element wing model in which the planform geometry is represented by the parameter of relative displacement of the elastic axes; to express the stiffness matrices, aerodynamic influence matrices and coordinate transformation matrices in a single global coordinate system; to obtain the characteristic divergence equation after applying the nodal condensation method; to analyze three representative cases corresponding to swept, unswept and forward-swept wings; and to compare the resulting critical speeds in a relative form. The methods used are based on finite-element linear approximation, matrix representation of elastic and aerodynamic operators, transformation of local elastic and aerodynamic operators into a common global coordinate system and an analytical solution of the characteristic equation. The following results were obtained. It was shown that a positive relative displacement of the elastic axes, which corresponds to a swept wing, increases the critical divergence speed in comparison with a straight wing. For the unswept wing, the relative divergence speed is approximately 0.618 of the maximum value, whereas for the forward-swept wing this value decreases to 0.560, 0.518 and 0.484 depending on the magnitude of the negative displacement. Conclusions. The proposed two-element model enables clear tracing of the relationship between the sweep parameter and the condition for static aeroelastic instability. The scientific novelty consists in using a compact finite-element linear model for a preliminary analytical assessment of the influence of wing planform geometry on the critical divergence speed, which serves as a valuable tool at the early stages of aircraft design.


Keywords


swept wing; forward-swept wing; aeroelasticity; wing divergence; critical divergence speed; finite-element linear ap-proximation; nodal condensation

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DOI: https://doi.org/10.32620/aktt.2026.4.01