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Structural Dynamics and Aeroelasticity

Having completed the simple static structural analysis of the preliminary airframe design, finally attention can be given to the topics of structural dynamics and aeroelasticity. It is, of course, well known that aircraft can suffer from the phenomena of divergence, control reversal, and flutter, where a build-up of static deflection or vibration is caused by the interactions of fluid forces and structural elasticity. These behaviors are controlled by the rigidity and inertia of the airframe. Provided the structure is reasonably stiff and the centers of mass in the aerodynamic surfaces are not too far aft, it is usually quite simple to avoid aeroelastic problems in small UAVs: issues mostly arise in larger high-speed aircraft, particularly those with swept wings. Nonetheless, such behavior can ultimately be catastrophic and has led to the failure of many engineering systems over the years, including perhaps most famously the loss of the first Tacoma Narrows suspension bridge.[1] We find that the claddings we apply to our foam aerodynamic surfaces increase their torsional stiffness so much that, combined with the use of CFRP spars and stiff control linkages, we do not experience aeroelastic problems in aircraft of the size we build. Even so, all aircraft designs should be checked for possible divergence, control reversal, and flutter problems during the preliminary design phase.

Static aeroelasticity problems, that is, those that are characterized by a steady increase in deflection rather than vibration, are broadly grouped into two main effects; divergence and - for surfaces containing control flaps - control reversal. Divergence arises when the action of the airflow over the wing gives rise to torsional loads that cause the wing to twist and so, by changing the angle of attack, increase the twisting moment until ultimately the wing fails. Control reversal arises when the hinge reactions induced by control flap deflection twist the wing sufficiently that its changed angle of attack more than counteracts the desired action of the flap deflection.[2] In both cases, the effects increase with the square of the air speed and are heavily dependent on the torsional rigidity of the structure. The designer needs to establish that the onset of these problems occurs at significantly higher speeds than the aircraft will experience in flight. A typical margin is that the divergence or control reversal speed should be more than 25% higher than the maximum dive speed in the Vn diagram. If this is not achieved, the torsional rigidity of the wing must be improved, either by the addition of material or by changes to the thickness-to-chord ratio of the outer surface.

Flutter is a vibration caused by the action of the aerodynamic forces, and depends both on the stiffness of the aerodynamic surface and also on its inertial properties. For surfaces containing control flaps, three types of flutter can be distinguished: torsional-flexural flutter, torsional control flap flutter, and flexural control flap flutter. Note that here we deal with what may be called classical flutter, where the flow remains attached and relatively smooth. Other forms exist that are not relevant to the kind of small UAVs being considered here, such as

  • • stall flutter, due to dynamic flow separation;
  • • transonic flutter, due to the interaction of moving shocks and resultant boundary layer separation;
  • • buffeting, caused by highly turbulent unsteady flow.

Torsional-flexural flutter is closely related to divergence but now the mass of the wing comes into play. If the center of mass of the wing lies behind the torsional axis, as a gust gives the wing an upwards impulse, it also tends to pitch the nose up, thus increasing the lift being generated. The rigidity of the wing counteracts this change, slowing the upwards motion before accelerating it back down again, now causing the nose to pitch downwards and thus causing an oscillatory behavior. If the frequency of this forcing motion nears the natural frequency of the structure, flutter will occur, which will tend to give rise to fatigue problems and ultimately structural failure. Again, an onset speed should be estimated for the airframe to establish that this lies sufficiently far above the maximum dive speed. To do this, one must estimate the natural frequency of the wing structure in both the primary flapping and twisting modes. This additionally requires any heavy masses in the aerodynamic surfaces to be considered in the analysis model; normally just the control surface servos need to be considered unless fuel or payload elements are carried by the wing spars.

Torsional control flap flutter arises when the wing twists around its torsional axis causing the control flap to be accelerated up and down. If the flap itself has a center of mass lying behind its hinge line, it will tend to deflect in the opposite direction to the main body of the wing. This inertial effect is similar to control reversal but is now oscillatory in nature. It is generally prevented by ensuring that either the control linkage on the flap is sufficiently stiff that it drives the flutter frequency higher than any likely aerodynamic excitation or the control surface center of mass lies forward of the hinge line, if necessary by the addition of added weights in the control surface leading edge. Flexural control flap flutter is also caused by the flap center of mass lying behind the hinge line, but now excited by flexural motions of the main wing rather than torsional ones. Again, this can be dealt with by a sufficiently stiff control linkage or by bringing the center of mass of the flap forward of the hinge line with added weights. Control flap flutter is sufficiently rare in small fixed-wing UAVs, and it consequences are sufficiently limited in terms of structural redesign, that in our view it need not be considered at the preliminary design stage of such UAVs.

  • [1] Where wind blowing along Puget Sound excited the deck of the bridge in much the same way as flight speed canexcite vibrations of wings, ultimately causing the bridge to collapse completely in November 1940.
  • [2] So, for example, if the starboard aileron is deflected upwards to decrease the lift of the starboard wing, yet theresulting torsional load causes the wing angle of attack to increase; the overall effect may be an increase in lift, thatis, the reverse of what is required.
 
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