Enhanced Stability of Two-Material Panels in Supersonic Flow: Optimization Strategy and Physical Explanation

Abstract

The dynamics of a two-material panel in supersonic flow is studied, with the aim of exploring the possibility of enhancing the stability of supersonic panels. The hybrid panel is longitudinally nonuniform and consists of a host segment (HS) and a hard ancillary segment (AS). By taking into account the aerodynamic load, aerodynamic heating, and structural nonlinearity, the general nonlinear governing equations of the hybrid panel for different boundary conditions are derived based on Hamilton’s principle. With the use of linearized governing equation, the stability of the panel subjected to supersonic airflow is investigated via finite element method (FEM). By comparing the present results with previous ones regarding a uniform panel in supersonic flow, the reliability of the FEM model is confirmed. The effects of length, position, and material properties of the AS on the flutter and buckling stability boundaries are discussed. Results show that the stability of the current supersonic panel can be enhanced by choosing a proper AS position. This paper also proposes a consistency hypothesis relating the extreme solutions to the inherent function, which could enable us to efficiently achieve the optimized solutions of the mathematical formulations and physically explain the optimal AS position. Furthermore, it is shown that the inherent function for force balance equations corresponds to the potential energy of a mechanical system, and thus the consistency hypothesis could degenerate into the principle of minimum potential energy.