Nonlinear aeroelastic analysis of a two-dimensional wing with control surface in supersonic flow

Abstract

Based on the piston theory of supersonic flow and the energy method, a two dimensional wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the chaotic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condition of stable limit cycle flutter of the aeroelastic system, the vibrations in the plunging and pitching of the wing can approximately be considered to be simple harmonic excitation to the control surface. The motion of the control surface can approximately be modeled by a nonlinear oscillation of one-degree-of-freedom. The range of the chaotic response of the aeroelastic system is approximately determined by means of the chaotic response of the nonlinear oscillator. The rich dynamic behaviors of the control surface are represented as bifurcation diagrams, phase-plane portraits and PS diagrams. The theoretical analysis is verified by the numerical results.

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“…Guo and Chen 194 studied the supersonic nonlinear flutter of a binary airfoil with gap nonlinearity and cubic nonlinearity, and found that it has bifurcation and amplitude jumping phenomena. Zheng 195 analyzed the flutter of cubic nonlinear control surfaces in supersonic airflow. Librescu et al 196 investigated the flutter stability of a cubic nonlinear wing under supersonic airflow.…”

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“…Marzocca et al (2002) studied the aeroelastic response of a 2D airfoil in a compressible flow field and exposed to blast loading. Using the piston theory of supersonic flow and the energy method, Zheng (2010) derived the governing equations of a 2D wing with three degrees of freedom. He considered the cubic stiffness in control surface direction.…”