The two-dimensional unsteady supersonic flow around a convex corner

The flow around a convex corner is one of the most important elementary flows. In this paper, we are concerned with the two-dimensional (2D) unsteady supersonic flow turning a convex corner. We firstly give the properties of general centered simple for the two-dimensional isentropic irrotational pesudo-steady Euler equations. Then, by using the properties of general centered simple waves, we construct the self-similar solution for the two-dimensional isentropic irrotational supersonic flow around a convex corner and prove that the supersonic flow turns the convex corner by a centered expansion wave or a centered compression wave under appropriate conditions on the downstream state.

Structural health monitoring based on sensitivity vector fields and attractor morphing

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Structural Health Monitoring of a Nonlinear Aeroelastic System Based on Attractor Analysis

The dynamic response of a thermo-shielding panel forced by unsteady aerodynamic loads and a archetypal Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third order piston theory to model the unsteady supersonic flow which interacts with the panel. To identify damage, we analyze the shape of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Measurements are obtained by simulation at only one location along the panel. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Most of the current studies of such problems are based on linear theories. In contrast, the results presented are obtained using nonlinear dynamics, and have the advantage of an increased accuracy and sensitivity.