New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter

Abstract

A simply supported plate fluttering in hypersonic flow is investigated considering both the airflow and structural nonlinearities. Third-order piston theory is used for nonlinear aerodynamic loading, and von Karman plate theory is used for modeling the nonlinear strain-displacement relation. The Galerkin method is applied to project the partial differential governing equations (PDEs) into a set of ordinary differential equations (ODEs) in time, which is then solved by numerical integration method. In observation of limit cycle oscillations (LCO) and evolution of dynamic behaviors, nonlinear aerodynamic loading produces a smaller positive deflection peak and more complex bifurcation diagrams compared with linear aerodynamics. Moreover, a LCO obtained with the linear aerodynamics is mostly a nonsimple harmonic motion but when the aerodynamic nonlinearity is considered more complex motions are obtained, which is important in the evaluation of fatigue life. The parameters of Mach number, dynamic pressure, and in-plane thermal stresses all affect the aerodynamic nonlinearity. For a specific Mach number, there is a critical dynamic pressure beyond which the aerodynamic nonlinearity has to be considered. For a higher temperature, a lower critical dynamic pressure is required. Each nonlinear aerodynamic term in the full third-order piston theory is evaluated, based on which the nonlinear aerodynamic formulation has been simplified.

Aeroelastic analysis and flutter control of wings and panels: A review

“…The effect of viscoelastic damping material on the flutter bounds was studied, and the influence of the mode selection order on the convergence of the result was also analyzed. Xie et al 118 used the Galerkin method to analyze the nonlinear flutter response of simply supported panels. The structural nonlinearity and nonlinear aerodynamic load were considered, and the influences of Mach number, aerodynamic pressure and in‐plane thermal load on the nonlinear flutter response of the panel were studied.…”

Analysis of Nonlinear Vibrations and Dynamic Responses in a Trapezoidal Cantilever Plate Using the Rayleigh‐Ritz Approach Combined with the Affine Transformation

“…Later on, Xie et al [16] extended the work of Ye and Dowell and used the same model to examine the chaotic motions and the routes to chaos with the increasing of dynamic pressure. The bifurcation behaviors of a simply supported square plate with the airflow and structural nonlinearities were also studied, and they evaluated the effect of the aerodynamic nonlinearity [17]. Bakhtiari-Nejad and Nazari [18] analyzed the nonlinear vibration of a cantilever plate with viscoelastic laminate by Rayleigh-Ritz method.…”

Novel Nonstationarity Assessment Method for Hypersonic Flutter Flight Tests

“…Numerical simulation is an economic (and popular) research method, but the environmental conditions of physical flight experiments are rarely simulated. The causes of nonlinearity and complexity in hypersonic flows, such as real gas effects, boundary layershock wave interactions, changes in material properties due to aerodynamic heating, and nonlinear aeroelastic interactions between the flow field and structures [4,5], as well as the monolithic coupling of aerodynamic thermal characteristics, aerodynamic force, elastic force, and inertia, are highly complex. The partitioned simulation method is currently the most often applied approach to hypersonic aircraft research, but it unfortunately requires that weak coupling characteristics be ignored per the limited capability of existing software programs.…”