Aeroelasticity lecture PDF

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INTRODUCTION Early aeroelastic design problems Up until world war I, the aircraft speeds were slow and the structural stiffness were large enough that the loads due to aeroelastic deformation were inconsequential for almost all airplanes. Back in 1909, six years after the Wright’s first flight, Bleriot flew from France across the English Channel at the speed of 40 mph. The aeroplane flown over the channel was an externally braced monoplane with wing wrapping control which became massively popular soon after. (Weisshaar, 1995)

(Weisshaar, 1995-p6)

The concept of the wing wrapping design was so that the wing torsional stiffness was relatively low so that the wing would be twisted by the pilot. However, this design started experiencing failure due to its low stiffness once the aircraft is mounted by a new engine with a higher power and airspeed. These failures began to occur for no apparent reason, therefore, at first it was thought that the structural failure occurs due to insufficient wire bracing strength within the aircraft wing. To overcome the failure, Bleriot started increasing the stiffness of the wings by strengthening the guy wires and also increasing the size of the main wing spar but none of these changes addressed the structural failure. Due to difficulties on addressing the wing failure, Britain has banned the monoplanes flights in 1912 but years later by the approaching of World War I required rescinding this ban and investigation started to address the wing failure of the aircraft. The recent finding was indicating that the thin wing monoplane designed was failing due to the twisting caused by the loads during the manoeuvring. Due to torsionally flexible wings design, they would allow the load to twist the wing tips easier at a higher speed overload the load the wing so quickly before the pilot could recover the aircraft stability. Most of the designers around the Europe influenced by the new Bleriot’s design which discovered new aeroelastic effect that later to be associated with the wing divergence effect. However, since the

analysis technology hasn’t been advanced yet, but the basics of the mechanism could be understood and analysed by designers. (Weisshaar, 1995) The early aeroelastic wing failures were documented on a fighter aircraft during the World War I occurred on the German Fokker monoplane. This high-performance aircraft started facing failures during high-speed pull-out manoeuvres. As it has been obtained from the static strength and deflection measurements results, it has been obtained that failure were occurred due to wing torsional deformation caused in increased airloads on the wing same as the Bleriot airplane. To overcome the failure, it was required to increase the torsional stiffness of the wing by repositioning a wing structure to eliminate the failure. During the World War I, British Handley bi-plane bomber started showing vibratory aeroelastic instability on the horizontal tail of the aircraft which was also known as flutter. Investigation in 1916 revealed that this flutter occurs due to interaction between the fuselage twisting motion and the anti-symmetrical pitch rotation of the independently actuated right and left elevators. To address the issue, the designers found out that by connecting the elevators to a common torque tube, they can eliminate the anti-symmetrical motion. Later on, this design is used for the tail flutter difficulties by attaching the both elevators to a same torque tube and this became a standard design practice since. As time passes by, the engines become lighter and more powerful. As the speed increasing, the monoplane again start showing failures, but this time, a new type of aeroelasticity instability occurred called wing-aileron flutter. In this type flutter, the wing warping effected the control and led to wing divergence and the aileron control led to the dynamic aeroelastic failure. Wing-aileron flutter occurs when the lift generated by the oscillation of an aileron or tab drives the wing bending or torsion deformation of the wing. The oscillation frequency is proportional to the air speed due their characteristic where the aileron acts as a weathervane that its rotational stiffness increases as the air speed increasing. As the aileron accelerated through the air, as well as air-loads transmission to the wing will introduce the oscillations of the wing and creates a mutual coupled vibration throughout the flight. (Weisshaar, 1995) The aircraft to be analysed for this lecture is the Lockheed Martin X-56A. It is designed to fly HighAltitude Long Endurance (HALE) and perform high-risk operations. This aircraft’s integrated flight and aeroelastic controls can manage multiple flutter mode to include; first symmetric body-freedom flutter (SBFF), first symmetric wing bending-torsion (SWBT) flutter and first anti-symmetric wing bending-torsion (AWBT) flutter, using a closed loop control system. Design Specifications of X-56A;       

It has a length of 7.5 ft wing span of 28 ft Powered by two 90-pound thrust turbojet engines Wing aspect ratio of 14 Speed of 222km/hr Weight of 480 lbs A set of stiff wings, three sets of flexible wings which forms blended swept back wing configuration.

Figure 1: Three-view drawing of X-56A aircraft

Generally, designing an aircraft against undesirable aeroelastic phenomena (flutter, divergence, gust, buckling) comes with a compromise in the performance. Improvement of an aircraft could translate to introduction of these unwanted phenomena which will make them unrealistic. This paper presents aeroelastic design for the X-56 in line with its operations. Different optimization and improvement methods using structural reconfigurations will be reviewed.

METHODOLOGY Wing flutter Flutter basically comes down to the number of modes coupling together of motion which facing oscillations created by aerodynamics forces that enables the energy to be transferred from the airstream to the structure of the body so that the amplitude of the motion will grows in time. Flutter has also been discussed on the early aircrafts as a mode of failure and illustrate vibration modes. Figure below illustrate the importance of acknowledge of the vibration modes on the aircraft structure during the flutter mode. (Weisshaar, 1995)

(Weisshaar, 1995-p.8)

Figure below indicated the time histories of the three different types of dynamic displacement behaviour acting against the wing and wing response to the disturbance while the aircraft flying. Looking at point A, the disturbance at point A caused by the airspeed is decays as the time increasing, however as the airspeed increase at point B, the harmonic oscillatory motion amplitude stays fixed regardless of the time length. Operating at point C however can come to disaster since the amplitude of the oscillation increases as time increase. These three motions are classified as stable, neutrally stable and unstable. (Weisshaar, 1995)

(Weisshaar, 1995-p.9)

To explain the forces acting on the wing, there are two characteristics of movements within the wing. If a sinusoidal force applied to the wing at a dynamic pressure A with a fixed maximum and minimum values and a specified frequency level, the resonant frequencies will be observed as it is shown on graph A. the resonant motion however can deform the wing shape either with respect to the wing cantilever support or it can be appearing as a torsional or twisting form. The wing motion however is not purely bending nor torsional in nature regardless of the airstream speed, it is purely a linear combination of both bending and torsional types. (Weisshaar, 1995) The wing resonant frequencies will get effected as the airspeed and dynamic pressure increase. According to (Cordier, 2018), once the wing has attaches to the fuselage of the aircraft, it has a natural structural frequency, however, this frequency can be affected by the external forces such as relative wind and aerodynamic forces and can create periodic frequency. Once the periodic frequency of the external force becomes the same as the natural structure frequency on the wing, the wing will experience a resonance vibration and the amplitude of the vibration can become critical and results in wing failure if it goes for a certain time.

Burnett (2016), designed and tested for active flutter suppression in the X-56A. He stated that geometry and mass distribution are very important parameters while considering aeroelastic behaviour of this aircraft. Modelling for mass distribution were done for both the stiff wings and flexible wings configurations. By using rigid/flex coupling variables, Rigid Flex Coupling behaviours were produced from which state-space models were generated. These models were in form of 400*400 state matrices and serve as the mathematical model.

Roots of this matrix were plotted in form of velocity-frequency and velocity-damping plots giving information about the SBFF, SWBT, AWBT, SW1B, AW1T and SW1T.

Figure 2 : Velocity-frquency and velocity-damping plots of the aircraft (Burnett, 2016)

In a similar development by Wesley (2015) and for purpose of this analysis, design variables were used iteratively to make geometric and structural changes. The type of design variables is dependent on shape configuration of the aircraft. Aeroelastic response or feedback serves as a constraint (inequality, equality and side) for further problem solving.

f ( X )=total structural weight∨flutter speeds Where; Inequality constraints,

hk ( X ) =0, k=1 , L

Equality constraints, Side constraints,

L

U

x i ∧x i

g j ( X ) ≤ 0, j=1 , M

L

x i ≤ xi ≤

U x i , i=1, N

are the lower and upper bounds on each design variables

Using data made available by Armstrong flight research centre, aeroelastic design of the aircraft against flutter was reviewed. Aeroelastic optimization and structural analysis was done by a MSC Nastran code and a CFD solver in an MDAO tool. A matrix describing pressure changes due to

unsteady aerodynamics were generated using the double lattice method in the MSC Nastran. The flutter analyses using MSC Nastran PK solution method merges structural and aerodynamics grids by spline interpolation and derives a general aeroelastic matrix using structural modal matrix.

Figure 3: Flowchart of flutter analysis for Aeroelastic mass balancing and tailoring in MDAO tool

AEROELASTICITY ANALYSIS OF LOCKHEED MARTIN X56A Aeroelastic Tailoring Aeroelastic tailoring can be defined as “the embodiment of directional stiffness into an aircraft structural design to control aeroelastic deformation, static or dynamic, in such a fashion as to affect the aerodynamic and structural performance of that aircraft in a beneficial way,” [1]. Conventionally, tailoring has been carried out with composite shell structures using bendtwist coupling inflicting either wash-in affect (causing tip leading edge up) or similarly washout affect (causing tip leading edge down). Conventional aeroelastic tailoring of X-56A targets on stiffness-primarily based techniques by designing a basic wing structure to avoid flutter action exceeding the given flight envelope with minimum structural weight and still meet the design parameters. Certain limitation factors were placed such composite failure index(CFI), flutter speed, buckling load factors (BLF) and flutter frequency.

After the flutter constraints was set to values between 0.002- 0.003 with an additional tolerance parameter, with the initial wing structure designed to be operated with safety factor 1.5 manoeuvre loads condition and able with stand G-force acting between a range of 2.5g and -1.0g, to guarantee flutter free within the given flight envelope the lowest flutter speed value ought to be greater than the normalized speed of 1.62. Once different design variables were set to optimize with minimization of weight of aircraft wing by tailoring, two cases were investigated, case 1 being 12 design variables that consists of ply thickness only and case 2 being 24 design variables which considers both ply thickness and ply orientation. Initially hybrid optimisation approach was executed by means of 2 steps, first using genetic algorithm (GA) and discrete design variable (DDV) which produces several thousands of feasible solutions which a tedious and time-consuming process, hence to resolve the accurate optimum design a continuous design variable (CDV) with design optimization tools (DOT) was implemented.

Table 1 – Aeroelastic Tailoring Cases

As for structural and normalized flutter responses cases 1 and 2 both have similar flutter mechanisms, but due to the application of different initial ply angles there is small difference in the flutter frequency and flutter speed. Once the results of both case 1 and case 2 were compared, was able to determine that case 2 which included both ply thickness and ply orientation had produced a much better design which additionally provides 10% of weight reduction on the overall wing design than the case 1. The only drawback in this that it is not very practical to manufacture these composite ply, as the airframe manufacture industry is able to produce only predefined composite ply thickness, therefore it must be round up or down to try and meet the design variables, although by this approach the critical flutter speed and frequency were satisfied with a minute weight reduction of the aircraft. In conclusion the concept of aeroelastic tailoring allows us to investigate the strength of composite materials and how vastly the orientation of these ply affects it, also using aeroelastic tailoring with hybrid optimization has improved the final design with flutter speed constraints under the flight envelope, while simultaneously maintain the least possible structural weight. For future development there are interchanges between curvilinear and straight structurers to design wings using curvilinear ribs, spars and panel stiffeners, also it might be beneficial

to allow tow steering or material grading to vary within the small sections of wing to have high impact and excellent buckling operation when compared to non-steered panels.

Flutter Mass Balancing for X-56A A Wing design adjustment technique was adopted to ensure flutter speeds were within the flight envelope. Using an object-oriented, MDAO (multidisciplinary design, analysis, and optimization) tool as an alternative to trial and error, various wing configuration analysis were carried out simultaneously. Flutter speeds of the aircraft non-validated design with EFEW (Empty Fuel Empty Water) configuration were within design requirement. A subsequent validated design after necessary ground vibration test (GVT) leaves the second and third predicted flutter outside the flight envelope. The validated design was taken as a baseline design for the flutter mass balancing simulation. At the speed of 222km/hr, normalized SWBT and AWBT flutter speeds are 1.48 and 1.68 respectively which are relatively high. The mass balancing technique was employed to checkmate these flutter speeds and put them back into flight envelope while total ballast weight meets with the requirement. This method is carried out without the need to alter wing ply thickness and orientation angles (aeroelastic tailoring). To enable change of total weight of the aircraft while flying, multi-points design was adopted. Two weight configurations, EFEW (Empty Fuel Empty Water) and FFFW (Full Fuel Empty Water) were accounted for. Design requirements for flutter speed and frequency constraints serve as the standard for the optimization. First flutter, SBFF (symmetric body freedom flutter) is 0.79 to 0.98, second flutter, SWBT (Symmetric wing bending torsion) is 0.98 to 1.18, the third flutter AWBT (Antisymmetric wing bending torsion) is 0.98 to 1.30. Initial predictions were made for baseline configuration. The velocity-damping and velocity-frequency graphs show EFEW baseline configuration. The graphs show that the symmetric wing first bending (SW1B) and the symmetric wing first torsion (SW1T) mode coupling created a SWBT normalized flutter speeds of 1.48 and AWBT of 1.68.

Figure 4: The speed-damping and speed-frequency graphs for empty fuel and empty water ballast configuration: (a) initial design; (b) final design with 20-lb nose and 4-lb trailing wing tip

These speeds need to be moved into the flight envelope. Mass balancing optimization using design optimization tool with continuous design variable helped to investigate ballast location of three wing configurations. For proper mass distribution and structural integrity, ballast masses were distributed from left to right sides of the wing. For configuration 1, six mass ballasts of around 5 lb were positioned at the leading edge. For configuration 2, thirteen mass ballasts were used. Ten of those of around 5 lb were shared between wing leading and trailing edges, one mass ballasts of 20 lb at the nose of the centre body. For configuration 3, mass distribution was improved by increasing the trailing wing tip up to 25-in in length having five mass ballast. Segments were formed at a 5-in length by each mass ballast. Configuration 3 is an improvement on configuration 1 and 2. A total of eleven mass ballasts were used to include a centre body nose ballast, and the five corresponding ballasts at the trailing edges.

Figure 5: Flutter mass balancing optimization design configurations

Flutter Mode

Normalized Speed Normalized Frequency EFE FFF Upper Lower EFE FFF Upper bound Lower W W bound bound W W requirement bound requirement requirement requirement SBFF 0.79 1.13 1.16 0.98 0.53 0.68 0.53 1.76 SWBT 0.98 1.48 1.48 1.18 1.17 2.34 2.25 2.35 AWBT 0.98 1.68 1.68 1.30 1.50 1.52 2.43 3.52 Table 2: Mass balancing baseline flutter predictions and requirements at Mach 0.16

Configuration

1

Number of ballast mass 6

Objective

Min. total ballast mass and target flutter speed

Design requirements Nose ballast (lb) Wing ballast (lb) Lower limit Upper limit Lower limit Upper limit N/A N/A 0.0 5.0

2

13

Min. total ballast 0.0 20.0 mass and target flutter speed 3 11 Min. the first 0.0 20.0 flutter speed Table 3: Flutter mass balancing design configurations descriptions

Configuration 1 Final value Lower limit Wing leading edge ballast (lb) 1 0.0 0.0 0.0 2 0.0 0.0 0.0 3 0.0 0.0 0.0 4 0.0 0.0 0.0 5 0.0 0.0 0.0 Wing trailing edge ballast (lb) 6 0.0 5.0 0.0 Table 4: Flutter mass balancing configuration 1 design variables

Variable Ballast

Initial value

0.0

5.0

0.0

5.0

Upper limit 5.0 5.0 5.0 5.0 5.0 5.0

Configuration 2 Final Value Lower limit Nose ballast (lb) 1 0.0 20.0 0.0 Wing leading edge ballast (lb) 2 0.0 0.0 0.0 3 0.0 0.0 0.0 4 0.0 0.0 0.0 5 0.0 0.0 0.0 6 0.0 0.0 0.0 7 0.0 0.0 0.0 Wing trailing edge ballast (lb) 8 0.0 0.0 0.0 9 0.0 0.0 0.0 10 0.0 0.0 0.0 11 0.0 0.0 0.0 12 0.0 0.0 0.0 13 0.0 5.0 0.0 Table 5: Flutter mass balancing configuration 2 design variables

Variable Ballast

Variable Ballast

Case I Initial value

Initial value

Final value

Case II Initial value

Configuration 3 Case III Final Initial value value

Upper limit 20.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0

Final value

Design requirement Lower Upper limit limit

Nose ballast (lb) 20.0 20.0 20.0 Wing tip boom ballast (lb) 2 0.0 0.0 0.0 0.0 1.0 3 0.0 0.0 4.8 0.0 1.0 4 0.0 0.0 0.0 0.0 1.0 5 0.0 0.0 0.0 0.3 1.0 6 0.0 5.0 0.0 4.7 1.0 Wing tip ballast x location (inch) 7 216 216 216 216 216 8 221 221 221 221 221 9 226 226 226 226 226 10 231 231 231 231 231 11 236 236 236 236 236 Table 6: Flutter mass balancing configuration 3 design va...