Non-linear aeroelastic investigations of store(s)-induced limit cycle oscillations

Abstract

In the current work, the study of the aeroelastic behaviour of a wing with external store(s), such as a missile or drop fuel tank, is presented. The aeroelastic governing equations derived for a cantilever wing with coupled bending and torsion modes account for structural and aerodynamic non-linearities. Coupling terms retained in the aeroelastic governing equations are due to: (a) the non-linear beam theory, (b) the aerodynamic non-linearities of a quasi-steady model with stall, and (c) the non-linear kinematics terms of the store(s). As presented in the paper, this aircraft configuration can induce pathologies, such as store(s)-induced limit cycle oscillations (or si-LCOs), very different from the one of a clean wing configuration, and from the one obtained from the linearized form of the aeroelastic governing equations. Time domain simulation, phase portrait, and bifurcation analyses are performed for various velocities, initial conditions, and store(s)-sensitive parameters — such as store mass, number, location along the wing — to examine the dynamic aeroelastic instabilities of the system (e.g. the onset of flutter and LCO). Numerical studies indicate the presence of regions of subcritical Hopf-bifurcation, corresponding to an unstable LCO, for velocities below the linear flutter velocity.

An efficient method for nonlinear aeroelasticy of slender wings

“…Substituting the integral parts of (16) by mentioned DOF (22) and adding the related differential equations (23), (16) converts to an ODE system with eight boundary conditions as:…”

“…The nonlinear structural equations of motion of an inextensional slender Euler-Bernoulli beam are investigated in some of the recent works such as Arafat [23], Malatkar [24], Kim [16], and Abbas et al [22] based on the Crespo da Silva research [25] which is used in the present paper to derive the structural equations of motion. Considering large deformations and small strains, neglecting warping, shear deformation, and small Poisson effects of the beam, Fig.…”

“…Sadr et al [21] studied the nonlinear behavior of a high flexibility long span 2-D wing of a human powered aircraft with considering large deflection. Abbas et al [22] studied the aeroelastic behavior of a wing with external store(s). They implemented the nonlinear beam theory included both kinematic and geometric nonlinearities, the aerodynamic nonlinearities of a quasi-steady model with a subsonic stall model, and the nonlinear kinematics terms of the store(s).…”

Energy harvesting from aeroelastic vibrations induced by discrete gust loads

“…The loads are modeled in the time domain using Wagner's and Kussner's indicial functions (Abbas et al, 2008;Bisplinghoff et al, 2013;Sedaghat et al, 2000;Wright and Cooper, 2008). The two-dimensional (2D) representation of the loads can be extended to three dimensions by using strip theory for relatively high-aspect-ratio wings.…”

Normal form representation of the aeroelastic response of the Goland wing

“…The study provided a complete nonlinear analysis of a fully-nonlinear aeroelastic system and identified various bifurcation characteristics. Abbas et al [4] conducted computational investigations to predict LCO of the Goland wing/store configuration and performed a sensitivity analysis to examine the effect of external stores on the aeroelastic behavior of the wing and the type of instability at the flutter onset. The aerodynamic model was based on a nonlinear quasi-steady representation with a stall model.…”