Modeling And Dynamic Analysis For The High-aspect-ratio Wings

Currently, large civil aircraft, large transport plane, big bomber andsurveillance plane have used high-aspect-ratio wings, because of its high energyefficiency. However, the high-aspect-ratio wings are slender structures, thus ifgravity and aeroloads applied on it, its deformation will be very large. Analyzingthe deformation of wings need to consider the geometry nonlinearity effect. Sowe will constitute the motion equation of wing which include the geometrynonlinearity effect and analyze the aeroelastical character of wing based on thoseequations. Our research work will focus on the three points below.The first one we regard the high-aspect-ratio wings as a clamped-free beamwhich cross-section have three degrees-of-freedom, that is flexure in twodirections and torsion around the normal direction of the cross-section. We willobtain the strain-displacement relation and the motion energy representation ofbeam infinitesimal part based on the Euler-Bernoulli beam assumption andrigid-body finite rotation theory. Then we will use the Hamilton theory to get thedynamical equations of the beam, those dynamical equations are nonlinear andcoupled the flexure motion and torsion motion of the beam, we will considersome simple formulations of them.In the second step, we will consider the position of wing cross-sectionrelative to the flow after the deformation, and get the effective angle through theangle between the cross-section axis and flow direction and the relative velocitythe flow to section. We will use quasi-steady aerodynamics model to obtain theaeroloads, and then constitute the aeroelastic equations of wing. Those equationsare partial differential equations, we employ Galerkin methods to discretize themand get the ordinary differential equations of the wing motion. Then we willmake the equation dimensionless for preparing to the next step discussion.In the third step, we consider the vibration of wing as an vibration whichhave small amplitude around a large static equilibrium. Based on this assumption,we can linearize the equation in mode space about the equilibrium of the wingand do dynamical analysis to research the change of dynamic character of thewing that caused by the deformation geometry nonlinearity. We will also researchthe aeroelastic stability of linearized aeroelastic equations of wings andinvestigate the effect of deformation nonlinear factors to the flutter criticalvelocity. After getting the flutter critical velocity we will simulate the responseof wing in time domain. The simulate results show that the response of the wingmay not converge in time domain, and it will become an stable periodical motion if flow velocity less than the flutter critical velocity. The nonlinear factorchanges the flutter velocity of the wing and also affects the response character ofthe wing when the air velocity near the flutter critical velocity.