Analytical nonlinear flutter and sensitivity analysis of aircraft wings subjected to a transverse follower force

Abstract

In the present study, the nonlinear aeroelastic and sensitivity analysis of high aspect ratio wings subjected to a transverse follower force are discussed. A nonlinear structural model of wings is extracted and coupled with an incompressible unsteady aerodynamic model. The governing equations of motions are obtained via Hamilton’s principle and Galerkin method. Utilizing the method of multiple-scales, analytical approximate flutter response of the system is obtained. For validation, the analytical solution is compared with numerical solution and good agreement is observed. The time history of the tip displacement and tip twist solution are plotted for different airspeeds. Effects of follower force and its spanwise location and also the wing geometric characteristics on the flutter margin are discussed. Moreover, flutter margin sensitivity to different design parameters is analyzed. Results indicate that increasing the wing chord makes the system unstable. Furthermore, according to the analytical solution, effects of the wing chord and mass per unit length on the flutter margins are more important than the other system parameters.

Nonlinear forced vibration analysis of aircraft wings with rotating unbalanced mass of the propeller system

“…To solve the nonlinear ordinary differential equations of motion (21) for wing vibration, the multiple-scales approach is used to obtain the system responses in time and frequency domains. In this method, an expansion representing the response to be a function of multiple independent scales is used, where is a small parameter representing the time scale [17]. In order to implement the method of multiple scales to solve Eq.…”

“…They derived the frequency response functions under the subharmonic resonance for the first-order mode and primary resonance for the second-order mode by the method of multiple scales. Using the method of multiple scales (MMS), Zafari et al [17] presented an analytical approach to analyze the nonlinear flutter responses of a wing under a transverse follower force. MMS has also been used in the other nonlinear multi-degree of freedom systems such as nonlinear chatter vibration [18][19][20], nonlinear vibration of micro structures [21] and nonlinear vibroacoustic problems [22].…”