Approximation of distributed aerodynamic forces using a few concentrated forces to emulate panel flutter

Abstract

In this paper, flutter characteristic of the panel-like structure is studied using concentrated forces. The feasibility of replacing distributed aerodynamic forces with a few concentrated forces to emulating panel flutter in supersonic Mach number is considered. Panel flutter, as one of the unstable self-excited vibrations due to mutual interactions among elastic, inertial, and aerodynamic forces have been studied both analytically and experimentally. To this point, both analytical and experimental studies has been recorded using distributed aerodynamic loading. Regarding experimental studies, so far, flutter wind tunnel testing has been carried out to investigate the aeroelastic instabilities of an aircraft. However, in general, the flutter wind tunnel testing is expensive and complex. Likewise, the process requires a scaled down structure model which could lead to errors in the measured flutter boundary value. Therefore, as an alternative to flutter wind tunnel testing, the concept of “Dry Wind Tunnel” was recently proposed. It is an experimental technique to determine flutter speed and frequency of a full scaled structure by using shakers and sensors. The technique has been validated only for a wing like structure in subsonic Mach number

flutter characteristics in supersonic Mach number such as panel flutter has not been studied using dry wind tunnel concept. And, it is apparent that the experimental procedure for running supersonic flutter testing is even more complicated. Therefore, in the present study, the feasibility of dry wind tunnel concept in panel flutter is investigated. The study includes the linear panel flutter analysis and the emulated panel flutter analysis of a thin, uniform, and isotropic plate. The formulation of the aeroelastic equation consists of coupling between structural and aerodynamic model, derived using the classical method as well as finite element method. In the classical method, the theoretical formulation of the panel flutter is made by modal expansion technique using Galerkin’s approach in conjunction with numerical integration and orthogonality condition. The structural modeling of the plate is based on the classical small-deflection theory and aerodynamic force is evaluated using the piston theory, a widely used aerodynamic tool in panel flutter analysis. Similarly, in finite element method, commercially established finite element software is used to develop a structural-dynamic and to formulate aerodynamic forces. The approach to emulate supersonic panel flutter involves determining concentrated forces, equivalent to distributed aerodynamic forces, their numbers, and optimal location. Hence, the transformation between these force systems is achieved using surface spline interpolation. While, to determine the optimal location of concentrated forces, an optimization process that best represent emulated panel flutter solution against linear panel flutter solution is carried out. Numerical works on a rectangular plate of various aspect ratios and Mach numbers with different boundary conditions are conducted for linear panel flutter. Similarly, the emulated panel flutter analysis is performed using six concentrated forces with their optimized locations. The emulated panel flutter results for different boundary conditions are presented with their counterparts from linear panel flutter shows a good agreement.